diff --git a/analysis/Minkowski.cpp b/analysis/Minkowski.cpp
index 2e1e0f85..e64b2c70 100644
--- a/analysis/Minkowski.cpp
+++ b/analysis/Minkowski.cpp
@@ -73,9 +73,9 @@ void Minkowski::ComputeScalar(const DoubleArray& Field, const double isovalue)
 	//int Nx = Field.size(0);
 	//int Ny = Field.size(1);
 	//int Nz = Field.size(2);
-	for (int k=0; k<Nz-1; k++){
-		for (int j=0; j<Ny-1; j++){
-			for (int i=0; i<Nx-1; i++){
+	for (int k=1; k<Nz-1; k++){
+		for (int j=1; j<Ny-1; j++){
+			for (int i=1; i<Nx-1; i++){
 				object.LocalIsosurface(Field,isovalue,i,j,k);
 				for (int idx=0; idx<object.TriangleCount; idx++){
 					e1 = object.Face(idx); 
@@ -106,7 +106,21 @@ void Minkowski::ComputeScalar(const DoubleArray& Field, const double isovalue)
 					Xi -= 0.5;
 				}
 				// Euler characteristic -- each vertex shared by four cubes
-				Xi += 0.25*double(object.VertexCount);
+				//Xi += 0.25*double(object.VertexCount);
+				// check if vertices are at corners
+				for (int idx=0; idx<object.VertexCount; idx++){
+				  /*auto P1 = object.vertex.coords(idx);
+					if ( remainder(P1.x,1.0)==0.0 && remainder(P1.y,1.0)==0.0  && remainder(P1.z,1.0)==0.0 ){
+					  Xi += 0.125;
+					}
+					else
+				  */
+					Xi += 0.25;
+				}
+				/*double nside_extern = double(npts);
+				double nside_intern = double(npts)-3.0;
+				EulerChar=0.0;
+				if (npts > 0)	EulerChar = (0.25*nvert - nside_intern - 0.5*nside_extern + nface); */
 			}
 		}
 	}
@@ -143,7 +157,7 @@ void Minkowski::MeasureObject(){
 	 *    0 - labels the object
 	 *    1 - labels the rest of the 
 	 */
-
+        //DoubleArray smooth_distance(Nx,Ny,Nz);
 	for (int k=0; k<Nz; k++){
 		for (int j=0; j<Ny; j++){
 			for (int i=0; i<Nx; i++){
@@ -152,6 +166,44 @@ void Minkowski::MeasureObject(){
 		}
 	}	
 	CalcDist(distance,id,*Dm);
+	//Mean3D(distance,smooth_distance);
+	//Eikonal(distance, id, *Dm, 20, {true, true, true});
+	ComputeScalar(distance,0.0);
+}
+
+
+void Minkowski::MeasureObject(double factor, const DoubleArray &Phi){
+	/*
+	 *  compute the distance to an object 
+	 * 
+	 * THIS ALGORITHM ASSUMES THAT id() is populated with phase id to distinguish objects
+	 *    0 - labels the object
+	 *    1 - labels the rest of the 
+	 */
+	for (int k=0; k<Nz; k++){
+		for (int j=0; j<Ny; j++){
+			for (int i=0; i<Nx; i++){
+				distance(i,j,k) =2.0*double(id(i,j,k))-1.0;
+			}
+		}
+	}	
+	CalcDist(distance,id,*Dm);
+	
+	for (int k=0; k<Nz; k++){
+		for (int j=0; j<Ny; j++){
+			for (int i=0; i<Nx; i++){
+				double value = Phi(i,j,k);
+				double dist_value = distance(i,j,k);
+				if (dist_value < 2.5 &&  dist_value > -2.5) {
+					double new_distance = factor*log((1.0+value)/(1.0-value));
+					if (dist_value*new_distance < 0.0 )
+						new_distance = (-1.0)*new_distance;
+					distance(i,j,k) = new_distance;					
+				}
+			}
+		}
+	}
+	
 	ComputeScalar(distance,0.0);
 
 }
@@ -201,6 +253,50 @@ int Minkowski::MeasureConnectedPathway(){
 	return n_connected_components; 
 }
 
+int Minkowski::MeasureConnectedPathway(double factor, const DoubleArray &Phi){
+	/*
+	 * compute the connected pathway for object with LABEL in id field
+	 * compute the labels for connected components
+	 * compute the distance to the connected pathway
+	 * 
+	 * THIS ALGORITHM ASSUMES THAT id() is populated with phase id to distinguish objects
+	 */
+	
+	char LABEL = 0;
+	for (int k=0; k<Nz; k++){
+		for (int j=0; j<Ny; j++){
+			for (int i=0; i<Nx; i++){
+				if (id(i,j,k) == LABEL){
+					distance(i,j,k) = 1.0;
+				}
+				else
+					distance(i,j,k) = -1.0;
+			}
+		}
+	}
+	
+	// Extract only the connected part of NWP
+	double vF=0.0; 
+	n_connected_components = ComputeGlobalBlobIDs(Nx-2,Ny-2,Nz-2,Dm->rank_info,distance,distance,vF,vF,label,Dm->Comm);
+//	int n_connected_components = ComputeGlobalPhaseComponent(Nx-2,Ny-2,Nz-2,Dm->rank_info,const IntArray &PhaseID, int &VALUE, BlobIDArray &GlobalBlobID, Dm->Comm )
+	MPI_Barrier(Dm->Comm);
+	
+	for (int k=0; k<Nz; k++){
+		for (int j=0; j<Ny; j++){
+			for (int i=0; i<Nx; i++){
+				if ( label(i,j,k) == 0){
+					id(i,j,k) = 0;
+				}
+				else{
+					id(i,j,k) = 1;
+				}
+			}
+		}
+	}
+	MeasureObject(factor,Phi);
+	return n_connected_components; 
+}
+
 
 void Minkowski::PrintAll()
 {
diff --git a/analysis/Minkowski.h b/analysis/Minkowski.h
index 3449d3fa..b1e3b2a0 100644
--- a/analysis/Minkowski.h
+++ b/analysis/Minkowski.h
@@ -25,6 +25,7 @@
 #include "common/Communication.h"
 #include "analysis/analysis.h"
 #include "analysis/distance.h"
+#include "analysis/filters.h"
 
 #include "common/Utilities.h"
 #include "common/MPI_Helpers.h"
@@ -77,7 +78,9 @@ public:
 	Minkowski(std::shared_ptr <Domain> Dm);
 	~Minkowski();
 	void MeasureObject();
+	void MeasureObject(double factor, const DoubleArray &Phi);
 	int MeasureConnectedPathway();
+	int MeasureConnectedPathway(double factor, const DoubleArray &Phi);
 	void ComputeScalar(const DoubleArray& Field, const double isovalue);
 
 	void PrintAll();
diff --git a/analysis/SubPhase.cpp b/analysis/SubPhase.cpp
index 2a5e3350..8e937f7e 100644
--- a/analysis/SubPhase.cpp
+++ b/analysis/SubPhase.cpp
@@ -427,13 +427,13 @@ void SubPhase::Full(){
 		}
 	}
 	// measure the whole object
-	morph_n->MeasureObject();
+	morph_n->MeasureObject();//0.5/beta,Phi);
 	nd.V = morph_n->V(); 
 	nd.A = morph_n->A(); 
 	nd.H = morph_n->H(); 
 	nd.X = morph_n->X(); 
 	// measure only the connected part
-	nd.Nc = morph_n->MeasureConnectedPathway();
+	nd.Nc = morph_n->MeasureConnectedPathway();//0.5/beta,Phi);
 	nc.V = morph_n->V(); 
 	nc.A = morph_n->A(); 
 	nc.H = morph_n->H(); 
@@ -475,13 +475,13 @@ void SubPhase::Full(){
 			}
 		}
 	}	
-	morph_w->MeasureObject();
+	morph_w->MeasureObject();//-0.5/beta,Phi);
 	wd.V = morph_w->V(); 
 	wd.A = morph_w->A(); 
 	wd.H = morph_w->H(); 
 	wd.X = morph_w->X(); 
 	// measure only the connected part
-	wd.Nc = morph_w->MeasureConnectedPathway();
+	wd.Nc = morph_w->MeasureConnectedPathway();//-0.5/beta,Phi);
 	wc.V = morph_w->V(); 
 	wc.A = morph_w->A(); 
 	wc.H = morph_w->H(); 
diff --git a/analysis/dcel.cpp b/analysis/dcel.cpp
index ca21c0e6..91102acf 100644
--- a/analysis/dcel.cpp
+++ b/analysis/dcel.cpp
@@ -1,7 +1,5 @@
 #include "analysis/dcel.h"
 
-
-
 DECL::DECL(){
 }
 
@@ -15,6 +13,25 @@ int DECL::Face(int index){
 	return FaceData[index];
 }
 
+void DECL::Write(){
+	int e1,e2,e3;
+	FILE *TRIANGLES;
+	TRIANGLES = fopen("triangles.stl","w");
+	fprintf(TRIANGLES,"solid \n");
+	for (int idx=0; idx<TriangleCount; idx++){
+		e1 = Face(idx); 
+		e2 = halfedge.next(e1);
+		e3 = halfedge.next(e2);
+		auto P1 = vertex.coords(halfedge.v1(e1));
+		auto P2 = vertex.coords(halfedge.v1(e2));
+		auto P3 = vertex.coords(halfedge.v1(e3));
+		fprintf(TRIANGLES,"vertex %f %f %f\n",P1.x,P1.y,P1.z);
+		fprintf(TRIANGLES,"vertex %f %f %f\n",P2.x,P2.y,P2.z);
+		fprintf(TRIANGLES,"vertex %f %f %f\n",P3.x,P3.y,P3.z);
+	}
+	fclose(TRIANGLES);
+}
+
 void DECL::LocalIsosurface(const DoubleArray& A, double value, const int i, const int j, const int k){
 	Point P,Q;
 	Point PlaceHolder;
@@ -350,243 +367,43 @@ double DECL::EdgeAngle(int edge)
 	return angle;
 }
 
-void Isosurface(DoubleArray &A, const double &v)
+void iso_surface(const Array<double>&Field, const double isovalue)
 {
-    NULL_USE( v );
-
-	Point P,Q;
-	Point PlaceHolder;
-	Point C0,C1,C2,C3,C4,C5,C6,C7;
-
-	int TriangleCount;
-	int VertexCount;
-	int CubeIndex;
-
-	Point VertexList[12];
-	Point NewVertexList[12];
-	int LocalRemap[12];
-
-	Point cellvertices[20];
-    std::array<std::array<int,3>,20> Triangles;
-    Triangles.fill( { 0 } );
-
-	// Values from array 'A' at the cube corners
-	double CubeValues[8];
-
-	int Nx = A.size(0);
-	int Ny = A.size(1);
-	int Nz = A.size(2);
-
-	// Points corresponding to cube corners
-	C0.x = 0.0; C0.y = 0.0; C0.z = 0.0;
-	C1.x = 1.0; C1.y = 0.0; C1.z = 0.0;
-	C2.x = 1.0; C2.y = 1.0; C2.z = 0.0;
-	C3.x = 0.0; C3.y = 1.0; C3.z = 0.0;
-	C4.x = 0.0; C4.y = 0.0; C4.z = 1.0;
-	C5.x = 1.0; C5.y = 0.0; C5.z = 1.0;
-	C6.x = 1.0; C6.y = 1.0; C6.z = 1.0;
-	C7.x = 0.0; C7.y = 1.0; C7.z = 1.0;							
-
-	std::vector<std::array<int,6>> HalfEdge;
-	for (int k=1; k<Nz-1; k++){		
-		for (int j=1; j<Ny-1; j++){
-			for (int i=1; i<Nx-1; i++){
-				// Set the corner values for this cube
-				CubeValues[0] = A(i,j,k);
-				CubeValues[1] = A(i+1,j,k);
-				CubeValues[2] = A(i+1,j+1,k);
-				CubeValues[3] = A(i,j+1,k);
-				CubeValues[4] = A(i,j,k+1);
-				CubeValues[5] = A(i+1,j,k+1);
-				CubeValues[6] = A(i+1,j+1,k+1);
-				CubeValues[7] = A(i,j+1,k+1);
-
-				//Determine the index into the edge table which
-				//tells us which vertices are inside of the surface
-				CubeIndex = 0;
-				if (CubeValues[0] < 0.0f) CubeIndex |= 1;
-				if (CubeValues[1] < 0.0f) CubeIndex |= 2;
-				if (CubeValues[2] < 0.0f) CubeIndex |= 4;
-				if (CubeValues[3] < 0.0f) CubeIndex |= 8;
-				if (CubeValues[4] < 0.0f) CubeIndex |= 16;
-				if (CubeValues[5] < 0.0f) CubeIndex |= 32;
-				if (CubeValues[6] < 0.0f) CubeIndex |= 64;
-				if (CubeValues[7] < 0.0f) CubeIndex |= 128;
-
-				//Find the vertices where the surface intersects the cube
-				if (edgeTable[CubeIndex] & 1){
-					P = VertexInterp(C0,C1,CubeValues[0],CubeValues[1]);
-					VertexList[0] = P;
-					Q = C0;
-				}
-				if (edgeTable[CubeIndex] & 2){
-					P = VertexInterp(C1,C2,CubeValues[1],CubeValues[2]);
-					VertexList[1] = P;
-					Q = C1;
-				}
-				if (edgeTable[CubeIndex] & 4){
-					P = VertexInterp(C2,C3,CubeValues[2],CubeValues[3]);
-					VertexList[2] =	P;
-					Q = C2;
-				}
-				if (edgeTable[CubeIndex] & 8){
-					P = VertexInterp(C3,C0,CubeValues[3],CubeValues[0]);
-					VertexList[3] =	P;
-					Q = C3;
-				}
-				if (edgeTable[CubeIndex] & 16){
-					P = VertexInterp(C4,C5,CubeValues[4],CubeValues[5]);
-					VertexList[4] =	P;
-					Q = C4;
-				}
-				if (edgeTable[CubeIndex] & 32){
-					P = VertexInterp(C5,C6,CubeValues[5],CubeValues[6]);
-					VertexList[5] = P;
-					Q = C5;
-				}
-				if (edgeTable[CubeIndex] & 64){ 
-					P = VertexInterp(C6,C7,CubeValues[6],CubeValues[7]);
-					VertexList[6] = P;
-					Q = C6;
-				}
-				if (edgeTable[CubeIndex] & 128){
-					P = VertexInterp(C7,C4,CubeValues[7],CubeValues[4]);
-					VertexList[7] =	P;
-					Q = C7;
-				}
-				if (edgeTable[CubeIndex] & 256){
-					P = VertexInterp(C0,C4,CubeValues[0],CubeValues[4]);
-					VertexList[8] =	P;
-					Q = C0;
-				}
-				if (edgeTable[CubeIndex] & 512){
-					P = VertexInterp(C1,C5,CubeValues[1],CubeValues[5]);
-					VertexList[9] =	P;
-					Q = C1;
-				}
-				if (edgeTable[CubeIndex] & 1024){
-					P = VertexInterp(C2,C6,CubeValues[2],CubeValues[6]);
-					VertexList[10] = P;
-					Q = C2;
-				}
-				if (edgeTable[CubeIndex] & 2048){
-					P = VertexInterp(C3,C7,CubeValues[3],CubeValues[7]);
-					VertexList[11] = P;
-					Q = C3;
-				}
-
-				VertexCount=0;
-				for (int idx=0;idx<12;idx++)
-					LocalRemap[idx] = -1;
-
-				for (int idx=0;triTable[CubeIndex][idx]!=-1;idx++)
-				{
-					if(LocalRemap[triTable[CubeIndex][idx]] == -1)
-					{
-						NewVertexList[VertexCount] = VertexList[triTable[CubeIndex][idx]];
-						LocalRemap[triTable[CubeIndex][idx]] = VertexCount;
-						VertexCount++;
-					}
-				}
-
-				for (int idx=0;idx<VertexCount;idx++) {
-					P = NewVertexList[idx];
-					//P.x  += i;
-					//P.y  += j;
-					//P.z  += k;
-					cellvertices[idx] = P;
-				}
-
-				TriangleCount = 0;
-				for (int idx=0;triTable[CubeIndex][idx]!=-1;idx+=3) {
-					Triangles[TriangleCount][0] = LocalRemap[triTable[CubeIndex][idx+0]];
-					Triangles[TriangleCount][1] = LocalRemap[triTable[CubeIndex][idx+1]];
-					Triangles[TriangleCount][2] = LocalRemap[triTable[CubeIndex][idx+2]];
-					TriangleCount++;
-				}
-				int nTris = TriangleCount;
-
-				// Now add the local values to the DECL data structure
-				HalfEdge.resize(nTris*3);
-				int idx_edge=0;
-				for (int idx=0; idx<TriangleCount; idx++){
-					int V1 = Triangles[idx][0];
-					int V2 = Triangles[idx][1];
-					int V3 = Triangles[idx][2];
-					// first edge: V1->V2 
-					HalfEdge[idx_edge][0] = V1;  // first vertex
-					HalfEdge[idx_edge][1] = V2;  // second vertex
-					HalfEdge[idx_edge][2] = idx; // triangle
-					HalfEdge[idx_edge][3] = -1;  // twin
-					HalfEdge[idx_edge][4] = idx_edge+2;  // previous edge
-					HalfEdge[idx_edge][5] = idx_edge+1;  // next edge
-					idx_edge++;
-					// second edge: V2->V3
-					HalfEdge[idx_edge][0] = V2;  // first vertex
-					HalfEdge[idx_edge][1] = V3;  // second vertex
-					HalfEdge[idx_edge][2] = idx; // triangle
-					HalfEdge[idx_edge][3] = -1;  // twin
-					HalfEdge[idx_edge][4] = idx_edge-1;  // previous edge
-					HalfEdge[idx_edge][5] = idx_edge+1;  // next edge
-					idx_edge++;
-					// third edge: V3->V1
-					HalfEdge[idx_edge][0] = V3;  // first vertex
-					HalfEdge[idx_edge][1] = V1;  // second vertex
-					HalfEdge[idx_edge][2] = idx; // triangle
-					HalfEdge[idx_edge][3] = -1;  // twin
-					HalfEdge[idx_edge][4] = idx_edge-1;  // previous edge
-					HalfEdge[idx_edge][5] = idx_edge-2;  // next edge
-					idx_edge++;
-				}
-				int EdgeCount=idx_edge;
-				for (int idx=0; idx<EdgeCount; idx++){
-					int V1=HalfEdge[idx][0];
-					int V2=HalfEdge[idx][1];
-					// Find all the twins within the cube
-					for (int jdx=0; idx<EdgeCount; jdx++){
-						if (HalfEdge[jdx][1] == V1 && HalfEdge[jdx][0] == V2){
-							// this is the pair
-							HalfEdge[idx][3] = jdx;
-							HalfEdge[jdx][3] = idx;
-						}
-						if (HalfEdge[jdx][1] == V2 && HalfEdge[jdx][0] == V1 && !(idx==jdx)){
-							std::printf("WARNING: half edges with identical orientation! \n");
-						}
-					}	
-					// Use "ghost" twins if edge is on a cube face
-					P = cellvertices[V1];
-					Q = cellvertices[V2];
-					if (P.x == 0.0 && Q.x == 0.0) HalfEdge[idx_edge][3] = -1;  // ghost twin for x=0 face
-					if (P.x == 1.0 && Q.x == 1.0) HalfEdge[idx_edge][3] = -2;  // ghost twin for x=1 face
-					if (P.y == 0.0 && Q.y == 0.0) HalfEdge[idx_edge][3] = -3;  // ghost twin for y=0 face
-					if (P.y == 1.0 && Q.y == 1.0) HalfEdge[idx_edge][3] = -4;  // ghost twin for y=1 face
-					if (P.z == 0.0 && Q.z == 0.0) HalfEdge[idx_edge][3] = -5;  // ghost twin for z=0 face
-					if (P.z == 1.0 && Q.z == 1.0) HalfEdge[idx_edge][3] = -6;  // ghost twin for z=1 face
-				}
-				// Find all the angles
-				/*for (int idx=0; idx<EdgeCount; idx++){
-					int V1=HalfEdge[idx][0];
-					int V2=HalfEdge[idx][1];
-					int T1= HalfEdge[idx_edge][2];
-					int twin=HalfEdge[idx_edge][3];
-					if (twin == -1){
-						
-					}
-				}*/
-
-				// Map vertices to global coordinates
-				for (int idx=0;idx<VertexCount;idx++) {
-					P = cellvertices[idx];
-					P.x  += i;
-					P.y  += j;
-					P.z  += k;
-					cellvertices[idx] = P;
-				}
-			}
-		}
-	}
+  DECL object;
+  int e1,e2,e3;
+  FILE *TRIANGLES;
+  TRIANGLES = fopen("isosurface.stl","w");
+  fprintf(TRIANGLES,"solid isosurface\n");
+  int Nx = Field.size(0);
+  int Ny = Field.size(1);
+  int Nz = Field.size(2);
+  for (int k=1; k<Nz-1; k++){
+    for (int j=1; j<Ny-1; j++){
+      for (int i=1; i<Nx-1; i++){
+        object.LocalIsosurface(Field,isovalue,i,j,k);
+        for (int idx=0; idx<object.TriangleCount; idx++){
+          e1 = object.Face(idx);
+          e2 = object.halfedge.next(e1);
+          e3 = object.halfedge.next(e2);
+          auto P1 = object.vertex.coords(object.halfedge.v1(e1));
+          auto P2 = object.vertex.coords(object.halfedge.v1(e2));
+          auto P3 = object.vertex.coords(object.halfedge.v1(e3));
+	  auto Normal  = object.TriNormal(e1);
+	  // P1.x += 1.0*i; P1.y += 1.0*j; P1.z +=1.0*k;
+          //P2.x += 1.0*i; P2.y += 1.0*j; P2.z +=1.0*k;
+          //P3.x += 1.0*i; P3.y += 1.0*j; P3.z +=1.0*k;
+          fprintf(TRIANGLES,"facet normal %f %f %f\n",Normal.x,Normal.y,Normal.z);
+	  fprintf(TRIANGLES,"   outer loop\n");
+	  fprintf(TRIANGLES,"      vertex %f %f %f\n",P1.x,P1.y,P1.z);
+          fprintf(TRIANGLES,"      vertex %f %f %f\n",P2.x,P2.y,P2.z);
+          fprintf(TRIANGLES,"      vertex %f %f %f\n",P3.x,P3.y,P3.z);
+	  fprintf(TRIANGLES,"   endloop\n");
+	  fprintf(TRIANGLES,"endfacet\n");
 
+        }
+      }
+    }
+  }
+  fprintf(TRIANGLES,"endsolid isosurface\n");
+  fclose(TRIANGLES);
 }
-
-
-
diff --git a/analysis/dcel.h b/analysis/dcel.h
index d8cbb1f7..0e6b2b1d 100644
--- a/analysis/dcel.h
+++ b/analysis/dcel.h
@@ -1,3 +1,6 @@
+#ifndef DCEL_INC
+#define DCEL_INC
+
 #include <vector>
 #include "analysis/pmmc.h"
 
@@ -67,6 +70,7 @@ public:
 	Vertex vertex;
 	Halfedge halfedge;
 	void LocalIsosurface(const DoubleArray& A, double value, int i, int j, int k);
+	void Write();
 	int Face(int index);
 	
 	double origin(int edge);
@@ -78,3 +82,7 @@ public:
 private:
 	std::vector<int> FaceData;
 };
+
+void iso_surface(const Array<double>&Field, const double isovalue);
+
+#endif
diff --git a/analysis/distance.cpp b/analysis/distance.cpp
index d5ca291c..4cce3cb5 100644
--- a/analysis/distance.cpp
+++ b/analysis/distance.cpp
@@ -197,6 +197,148 @@ void CalcVecDist( Array<Vec> &d, const Array<int> &ID0, const Domain &Dm,
     }
 }
 
+double Eikonal(DoubleArray &Distance, const Array<char> &ID, Domain &Dm, int timesteps, const std::array<bool,3>& periodic){
+
+  /*
+   * This routine converts the data in the Distance array to a signed distance
+   * by solving the equation df/dt = sign(1-|grad f|), where Distance provides
+   * the values of f on the mesh associated with domain Dm
+   * It has been tested with segmented data initialized to values [-1,1]
+   * and will converge toward the signed distance to the surface bounding the associated phases
+   *
+   * Reference:
+   * Min C (2010) On reinitializing level set functions, Journal of Computational Physics229
+   */
+
+  int i,j,k;
+  double dt=0.1;
+  double Dx,Dy,Dz;
+  double Dxp,Dxm,Dyp,Dym,Dzp,Dzm;
+  double Dxxp,Dxxm,Dyyp,Dyym,Dzzp,Dzzm;
+  double sign,norm;
+  double LocalVar,GlobalVar,LocalMax,GlobalMax;
+
+  int xdim,ydim,zdim;
+  xdim=Dm.Nx-2;
+  ydim=Dm.Ny-2;
+  zdim=Dm.Nz-2;
+  //fillHalo<double> fillData(Dm.Comm, Dm.rank_info,xdim,ydim,zdim,1,1,1,0,1);
+  fillHalo<double> fillData(  Dm.Comm, Dm.rank_info, {xdim, ydim, zdim}, {1,1,1}, 50, 1, {true,true,true}, periodic );
+
+  // Arrays to store the second derivatives
+  DoubleArray Dxx(Dm.Nx,Dm.Ny,Dm.Nz);
+  DoubleArray Dyy(Dm.Nx,Dm.Ny,Dm.Nz);
+  DoubleArray Dzz(Dm.Nx,Dm.Ny,Dm.Nz);
+
+  int count = 0;
+  while (count < timesteps){
+
+    // Communicate the halo of values
+    fillData.fill(Distance);
+
+    // Compute second order derivatives
+    for (k=1;k<Dm.Nz-1;k++){
+      for (j=1;j<Dm.Ny-1;j++){
+	for (i=1;i<Dm.Nx-1;i++){
+	  Dxx(i,j,k) = Distance(i+1,j,k) + Distance(i-1,j,k) - 2*Distance(i,j,k);
+	  Dyy(i,j,k) = Distance(i,j+1,k) + Distance(i,j-1,k) - 2*Distance(i,j,k);
+	  Dzz(i,j,k) = Distance(i,j,k+1) + Distance(i,j,k-1) - 2*Distance(i,j,k);
+	}
+      }
+    }
+    fillData.fill(Dxx);
+    fillData.fill(Dyy);
+    fillData.fill(Dzz);
+
+    LocalMax=LocalVar=0.0;
+    // Execute the next timestep
+    for (k=1;k<Dm.Nz-1;k++){
+      for (j=1;j<Dm.Ny-1;j++){
+	for (i=1;i<Dm.Nx-1;i++){
+
+	  int n = k*Dm.Nx*Dm.Ny + j*Dm.Nx + i;
+
+	  sign = -1;
+	  if (ID(i,j,k) == 1) sign = 1;
+
+	  // local second derivative terms
+	  Dxxp = minmod(Dxx(i,j,k),Dxx(i+1,j,k));
+	  Dyyp = minmod(Dyy(i,j,k),Dyy(i,j+1,k));
+	  Dzzp = minmod(Dzz(i,j,k),Dzz(i,j,k+1));
+	  Dxxm = minmod(Dxx(i,j,k),Dxx(i-1,j,k));
+	  Dyym = minmod(Dyy(i,j,k),Dyy(i,j-1,k));
+	  Dzzm = minmod(Dzz(i,j,k),Dzz(i,j,k-1));
+
+	  /* //............Compute upwind derivatives ...................
+                    Dxp = Distance(i+1,j,k) - Distance(i,j,k) + 0.5*Dxxp;
+                    Dyp = Distance(i,j+1,k) - Distance(i,j,k) + 0.5*Dyyp;
+                    Dzp = Distance(i,j,k+1) - Distance(i,j,k) + 0.5*Dzzp;
+                    Dxm = Distance(i,j,k) - Distance(i-1,j,k) + 0.5*Dxxm;
+                    Dym = Distance(i,j,k) - Distance(i,j-1,k) + 0.5*Dyym;
+                    Dzm = Distance(i,j,k) - Distance(i,j,k-1) + 0.5*Dzzm;
+	  */
+	  Dxp = Distance(i+1,j,k)- Distance(i,j,k) - 0.5*Dxxp;
+	  Dyp = Distance(i,j+1,k)- Distance(i,j,k) - 0.5*Dyyp;
+	  Dzp = Distance(i,j,k+1)- Distance(i,j,k) - 0.5*Dzzp;
+
+	  Dxm = Distance(i,j,k) - Distance(i-1,j,k) + 0.5*Dxxm;
+	  Dym = Distance(i,j,k) - Distance(i,j-1,k) + 0.5*Dyym;
+	  Dzm = Distance(i,j,k) - Distance(i,j,k-1) + 0.5*Dzzm;
+
+	  // Compute upwind derivatives for Godunov Hamiltonian
+	  if (sign < 0.0){
+	    if (Dxp + Dxm > 0.f)  Dx = Dxp*Dxp;
+	    else Dx = Dxm*Dxm;
+
+	    if (Dyp + Dym > 0.f)  Dy = Dyp*Dyp;
+	    else Dy = Dym*Dym;
+
+	    if (Dzp + Dzm > 0.f)  Dz = Dzp*Dzp;
+	    else Dz = Dzm*Dzm;
+	  }
+	  else{
+
+	    if (Dxp + Dxm < 0.f)  Dx = Dxp*Dxp;
+	    else Dx = Dxm*Dxm;
+
+	    if (Dyp + Dym < 0.f)  Dy = Dyp*Dyp;
+	    else Dy = Dym*Dym;
+
+	    if (Dzp + Dzm < 0.f)  Dz = Dzp*Dzp;
+	    else Dz = Dzm*Dzm;
+	  }
+
+	  //Dx = max(Dxp*Dxp,Dxm*Dxm);
+	  //Dy = max(Dyp*Dyp,Dym*Dym);
+	  //Dz = max(Dzp*Dzp,Dzm*Dzm);
+
+	  norm=sqrt(Dx + Dy + Dz);
+	  if (norm > 1.0) norm=1.0;
+
+	  Distance(i,j,k) += dt*sign*(1.0 - norm);
+	  LocalVar +=  dt*sign*(1.0 - norm);
+
+	  if (fabs(dt*sign*(1.0 - norm)) > LocalMax)
+	    LocalMax = fabs(dt*sign*(1.0 - norm));
+	}
+      }
+    }
+
+    MPI_Allreduce(&LocalVar,&GlobalVar,1,MPI_DOUBLE,MPI_SUM,Dm.Comm);
+    MPI_Allreduce(&LocalMax,&GlobalMax,1,MPI_DOUBLE,MPI_MAX,Dm.Comm);
+    GlobalVar /= Dm.Volume;
+    count++;
+
+    if (count%50 == 0 && Dm.rank()==0 )
+      printf("Time=%i, Max variation=%f, Global variation=%f \n",count,GlobalMax,GlobalVar);
+
+    if (fabs(GlobalMax) < 1e-5){
+      if (Dm.rank()==0) printf("Exiting with max tolerance of 1e-5 \n");
+      count=timesteps;
+    }
+  }
+  return GlobalVar;
+}
 
 // Explicit instantiations
 template void CalcDist<float>( Array<float>&, const Array<char>&, const Domain&, const std::array<bool,3>&, const std::array<double,3>& );
diff --git a/analysis/distance.h b/analysis/distance.h
index 32cc8ecb..26d7dfe7 100644
--- a/analysis/distance.h
+++ b/analysis/distance.h
@@ -31,6 +31,16 @@ struct Vec {
 };
 inline bool operator<(const Vec& l, const Vec& r){ return l.x*l.x+l.y*l.y+l.z*l.z < r.x*r.x+r.y*r.y+r.z*r.z; }
 
+inline double minmod(double &a, double &b){
+
+  double value;
+
+  value = a;
+  if ( a*b < 0.0)    value=0.0;
+  else if (fabs(a) > fabs(b)) value = b;
+
+  return value;
+}
 
 /*!
  * @brief  Calculate the distance using a simple method
@@ -55,4 +65,16 @@ void CalcDist( Array<TYPE> &Distance, const Array<char> &ID, const Domain &Dm,
 void CalcVecDist( Array<Vec> &Distance, const Array<int> &ID, const Domain &Dm,
     const std::array<bool,3>& periodic = {true,true,true}, const std::array<double,3>& dx = {1,1,1} );
 
+
+/*!
+ * @brief  Calculate the distance based on solution of Eikonal equation
+ * @details  This routine calculates the signed distance to the nearest domain surface.
+ * @param[out] Distance     Distance function
+ * @param[in] ID            Domain id
+ * @param[in] Dm            Domain information
+ * @param[in] timesteps      number of timesteps to run for Eikonal solver
+ * @param[in] periodic      Directions that are periodic 
+ */
+double Eikonal(DoubleArray &Distance,  const Array<char> &ID, Domain &Dm, int timesteps, const std::array<bool,3>& periodic);
+
 #endif
diff --git a/analysis/filters.cpp b/analysis/filters.cpp
index 8f60d42f..5e06cdda 100644
--- a/analysis/filters.cpp
+++ b/analysis/filters.cpp
@@ -17,6 +17,33 @@
 #include "math.h"
 #include "ProfilerApp.h"
 
+void Mean3D( const Array<double> &Input, Array<double> &Output )
+{
+	PROFILE_START("Mean3D");
+	// Perform a 3D Mean filter on Input array
+	int i,j,k;
+
+	int Nx = int(Input.size(0));
+	int Ny = int(Input.size(1));
+	int Nz = int(Input.size(2));
+
+	for (k=1; k<Nz-1; k++){
+		for (j=1; j<Ny-1; j++){
+			for (i=1; i<Nx-1; i++){
+			  double MeanValue = Input(i,j,k);
+			  // next neighbors
+			  MeanValue += Input(i+1,j,k)+Input(i,j+1,k)+Input(i,j,k+1)+Input(i-1,j,k)+Input(i,j-1,k)+Input(i,j,k-1);
+			  MeanValue += Input(i+1,j+1,k)+Input(i-1,j+1,k)+Input(i+1,j-1,k)+Input(i-1,j-1,k);
+			  MeanValue += Input(i+1,j,k+1)+Input(i-1,j,k+1)+Input(i+1,j,k-1)+Input(i-1,j,k-1);
+			  MeanValue += Input(i,j+1,k+1)+Input(i,j-1,k+1)+Input(i,j+1,k-1)+Input(i,j-1,k-1);
+			  MeanValue += Input(i+1,j+1,k+1)+Input(i-1,j+1,k+1)+Input(i+1,j-1,k+1)+Input(i-1,j-1,k+1);
+			  MeanValue += Input(i+1,j+1,k-1)+Input(i-1,j+1,k-1)+Input(i+1,j-1,k-1)+Input(i-1,j-1,k-1);
+			  Output(i,j,k) = MeanValue/27.0;
+			}
+		}
+	}
+	PROFILE_STOP("Mean3D");
+}
 
 void Med3D( const Array<float> &Input, Array<float> &Output )
 {
diff --git a/analysis/filters.h b/analysis/filters.h
index a1fe7927..fb436c55 100644
--- a/analysis/filters.h
+++ b/analysis/filters.h
@@ -19,6 +19,13 @@
 
 #include "common/Array.h"
 
+/*!
+ * @brief  Filter image
+ * @details  This routine performs a mean filter
+ * @param[in] Input     Input image
+ * @param[out] Output   Output image
+ */
+void Mean3D( const Array<double> &Input, Array<double> &Output );
 
 /*!
  * @brief  Filter image
@@ -28,7 +35,6 @@
  */
 void Med3D( const Array<float> &Input, Array<float> &Output );
 
-
 /*!
  * @brief  Filter image
  * @details  This routine performs a non-linear local means filter
diff --git a/common/Domain.cpp b/common/Domain.cpp
index 0cdb3532..796ae447 100644
--- a/common/Domain.cpp
+++ b/common/Domain.cpp
@@ -710,7 +710,7 @@ void Domain::AggregateLabels( const std::string& filename ){
 	int full_ny = npy*(ny-2);
 	int full_nz = npz*(nz-2);
 	int local_size = (nx-2)*(ny-2)*(nz-2);
-	long int full_size = long(full_nx)*long(full_ny)*long(full_nz);
+	unsigned long int full_size = long(full_nx)*long(full_ny)*long(full_nz);
 	
 	signed char *LocalID;
 	LocalID = new signed char [local_size];
@@ -740,7 +740,7 @@ void Domain::AggregateLabels( const std::string& filename ){
 					int y = j-1;
 					int z = k-1;
 					int n_local = (k-1)*(nx-2)*(ny-2) + (j-1)*(nx-2) + i-1;
-					int n_full = z*full_nx*full_ny + y*full_nx + x;
+					unsigned long int n_full = z*long(full_nx)*long(full_ny) + y*long(full_nx) + x;
 					FullID[n_full] = LocalID[n_local];
 				}
 			}
@@ -760,7 +760,7 @@ void Domain::AggregateLabels( const std::string& filename ){
 						int y = j-1 + ipy*(ny-2);
 						int z = k-1 + ipz*(nz-2);
 						int n_local = (k-1)*(nx-2)*(ny-2) + (j-1)*(nx-2) + i-1;
-						int n_full = z*full_nx*full_ny + y*full_nx + x;
+						unsigned long int n_full = z*long(full_nx)*long(full_ny) + y*long(full_nx) + x;
 						FullID[n_full] = LocalID[n_local];
 					}
 				}
diff --git a/common/ScaLBL.cpp b/common/ScaLBL.cpp
index c896ad9c..816098a7 100644
--- a/common/ScaLBL.cpp
+++ b/common/ScaLBL.cpp
@@ -95,43 +95,43 @@ ScaLBL_Communicator::ScaLBL_Communicator(std::shared_ptr <Domain> Dm){
 	BoundaryCondition = Dm->BoundaryCondition;
 	//......................................................................................
 
-	ScaLBL_AllocateZeroCopy((void **) &sendbuf_x, 5*sendCount_x*sizeof(double));	// Allocate device memory
-	ScaLBL_AllocateZeroCopy((void **) &sendbuf_X, 5*sendCount_X*sizeof(double));	// Allocate device memory
-	ScaLBL_AllocateZeroCopy((void **) &sendbuf_y, 5*sendCount_y*sizeof(double));	// Allocate device memory
-	ScaLBL_AllocateZeroCopy((void **) &sendbuf_Y, 5*sendCount_Y*sizeof(double));	// Allocate device memory
-	ScaLBL_AllocateZeroCopy((void **) &sendbuf_z, 5*sendCount_z*sizeof(double));	// Allocate device memory
-	ScaLBL_AllocateZeroCopy((void **) &sendbuf_Z, 5*sendCount_Z*sizeof(double));	// Allocate device memory
-	ScaLBL_AllocateZeroCopy((void **) &sendbuf_xy, sendCount_xy*sizeof(double));	// Allocate device memory
-	ScaLBL_AllocateZeroCopy((void **) &sendbuf_xY, sendCount_xY*sizeof(double));	// Allocate device memory
-	ScaLBL_AllocateZeroCopy((void **) &sendbuf_Xy, sendCount_Xy*sizeof(double));	// Allocate device memory
-	ScaLBL_AllocateZeroCopy((void **) &sendbuf_XY, sendCount_XY*sizeof(double));	// Allocate device memory
-	ScaLBL_AllocateZeroCopy((void **) &sendbuf_xz, sendCount_xz*sizeof(double));	// Allocate device memory
-	ScaLBL_AllocateZeroCopy((void **) &sendbuf_xZ, sendCount_xZ*sizeof(double));	// Allocate device memory
-	ScaLBL_AllocateZeroCopy((void **) &sendbuf_Xz, sendCount_Xz*sizeof(double));	// Allocate device memory
-	ScaLBL_AllocateZeroCopy((void **) &sendbuf_XZ, sendCount_XZ*sizeof(double));	// Allocate device memory
-	ScaLBL_AllocateZeroCopy((void **) &sendbuf_yz, sendCount_yz*sizeof(double));	// Allocate device memory
-	ScaLBL_AllocateZeroCopy((void **) &sendbuf_yZ, sendCount_yZ*sizeof(double));	// Allocate device memory
-	ScaLBL_AllocateZeroCopy((void **) &sendbuf_Yz, sendCount_Yz*sizeof(double));	// Allocate device memory
-	ScaLBL_AllocateZeroCopy((void **) &sendbuf_YZ, sendCount_YZ*sizeof(double));	// Allocate device memory
+	ScaLBL_AllocateZeroCopy((void **) &sendbuf_x, 2*5*sendCount_x*sizeof(double));	// Allocate device memory
+	ScaLBL_AllocateZeroCopy((void **) &sendbuf_X, 2*5*sendCount_X*sizeof(double));	// Allocate device memory
+	ScaLBL_AllocateZeroCopy((void **) &sendbuf_y, 2*5*sendCount_y*sizeof(double));	// Allocate device memory
+	ScaLBL_AllocateZeroCopy((void **) &sendbuf_Y, 2*5*sendCount_Y*sizeof(double));	// Allocate device memory
+	ScaLBL_AllocateZeroCopy((void **) &sendbuf_z, 2*5*sendCount_z*sizeof(double));	// Allocate device memory
+	ScaLBL_AllocateZeroCopy((void **) &sendbuf_Z, 2*5*sendCount_Z*sizeof(double));	// Allocate device memory
+	ScaLBL_AllocateZeroCopy((void **) &sendbuf_xy, 2*sendCount_xy*sizeof(double));	// Allocate device memory
+	ScaLBL_AllocateZeroCopy((void **) &sendbuf_xY, 2*sendCount_xY*sizeof(double));	// Allocate device memory
+	ScaLBL_AllocateZeroCopy((void **) &sendbuf_Xy, 2*sendCount_Xy*sizeof(double));	// Allocate device memory
+	ScaLBL_AllocateZeroCopy((void **) &sendbuf_XY, 2*sendCount_XY*sizeof(double));	// Allocate device memory
+	ScaLBL_AllocateZeroCopy((void **) &sendbuf_xz, 2*sendCount_xz*sizeof(double));	// Allocate device memory
+	ScaLBL_AllocateZeroCopy((void **) &sendbuf_xZ, 2*sendCount_xZ*sizeof(double));	// Allocate device memory
+	ScaLBL_AllocateZeroCopy((void **) &sendbuf_Xz, 2*sendCount_Xz*sizeof(double));	// Allocate device memory
+	ScaLBL_AllocateZeroCopy((void **) &sendbuf_XZ, 2*sendCount_XZ*sizeof(double));	// Allocate device memory
+	ScaLBL_AllocateZeroCopy((void **) &sendbuf_yz, 2*sendCount_yz*sizeof(double));	// Allocate device memory
+	ScaLBL_AllocateZeroCopy((void **) &sendbuf_yZ, 2*sendCount_yZ*sizeof(double));	// Allocate device memory
+	ScaLBL_AllocateZeroCopy((void **) &sendbuf_Yz, 2*sendCount_Yz*sizeof(double));	// Allocate device memory
+	ScaLBL_AllocateZeroCopy((void **) &sendbuf_YZ, 2*sendCount_YZ*sizeof(double));	// Allocate device memory
 	//......................................................................................
-	ScaLBL_AllocateZeroCopy((void **) &recvbuf_x, 5*recvCount_x*sizeof(double));	// Allocate device memory
-	ScaLBL_AllocateZeroCopy((void **) &recvbuf_X, 5*recvCount_X*sizeof(double));	// Allocate device memory
-	ScaLBL_AllocateZeroCopy((void **) &recvbuf_y, 5*recvCount_y*sizeof(double));	// Allocate device memory
-	ScaLBL_AllocateZeroCopy((void **) &recvbuf_Y, 5*recvCount_Y*sizeof(double));	// Allocate device memory
-	ScaLBL_AllocateZeroCopy((void **) &recvbuf_z, 5*recvCount_z*sizeof(double));	// Allocate device memory
-	ScaLBL_AllocateZeroCopy((void **) &recvbuf_Z, 5*recvCount_Z*sizeof(double));	// Allocate device memory
-	ScaLBL_AllocateZeroCopy((void **) &recvbuf_xy, recvCount_xy*sizeof(double));	// Allocate device memory
-	ScaLBL_AllocateZeroCopy((void **) &recvbuf_xY, recvCount_xY*sizeof(double));	// Allocate device memory
-	ScaLBL_AllocateZeroCopy((void **) &recvbuf_Xy, recvCount_Xy*sizeof(double));	// Allocate device memory
-	ScaLBL_AllocateZeroCopy((void **) &recvbuf_XY, recvCount_XY*sizeof(double));	// Allocate device memory
-	ScaLBL_AllocateZeroCopy((void **) &recvbuf_xz, recvCount_xz*sizeof(double));	// Allocate device memory
-	ScaLBL_AllocateZeroCopy((void **) &recvbuf_xZ, recvCount_xZ*sizeof(double));	// Allocate device memory
-	ScaLBL_AllocateZeroCopy((void **) &recvbuf_Xz, recvCount_Xz*sizeof(double));	// Allocate device memory
-	ScaLBL_AllocateZeroCopy((void **) &recvbuf_XZ, recvCount_XZ*sizeof(double));	// Allocate device memory
-	ScaLBL_AllocateZeroCopy((void **) &recvbuf_yz, recvCount_yz*sizeof(double));	// Allocate device memory
-	ScaLBL_AllocateZeroCopy((void **) &recvbuf_yZ, recvCount_yZ*sizeof(double));	// Allocate device memory
-	ScaLBL_AllocateZeroCopy((void **) &recvbuf_Yz, recvCount_Yz*sizeof(double));	// Allocate device memory
-	ScaLBL_AllocateZeroCopy((void **) &recvbuf_YZ, recvCount_YZ*sizeof(double));	// Allocate device memory
+	ScaLBL_AllocateZeroCopy((void **) &recvbuf_x, 2*5*recvCount_x*sizeof(double));	// Allocate device memory
+	ScaLBL_AllocateZeroCopy((void **) &recvbuf_X, 2*5*recvCount_X*sizeof(double));	// Allocate device memory
+	ScaLBL_AllocateZeroCopy((void **) &recvbuf_y, 2*5*recvCount_y*sizeof(double));	// Allocate device memory
+	ScaLBL_AllocateZeroCopy((void **) &recvbuf_Y, 2*5*recvCount_Y*sizeof(double));	// Allocate device memory
+	ScaLBL_AllocateZeroCopy((void **) &recvbuf_z, 2*5*recvCount_z*sizeof(double));	// Allocate device memory
+	ScaLBL_AllocateZeroCopy((void **) &recvbuf_Z, 2*5*recvCount_Z*sizeof(double));	// Allocate device memory
+	ScaLBL_AllocateZeroCopy((void **) &recvbuf_xy, 2*recvCount_xy*sizeof(double));	// Allocate device memory
+	ScaLBL_AllocateZeroCopy((void **) &recvbuf_xY, 2*recvCount_xY*sizeof(double));	// Allocate device memory
+	ScaLBL_AllocateZeroCopy((void **) &recvbuf_Xy, 2*recvCount_Xy*sizeof(double));	// Allocate device memory
+	ScaLBL_AllocateZeroCopy((void **) &recvbuf_XY, 2*recvCount_XY*sizeof(double));	// Allocate device memory
+	ScaLBL_AllocateZeroCopy((void **) &recvbuf_xz, 2*recvCount_xz*sizeof(double));	// Allocate device memory
+	ScaLBL_AllocateZeroCopy((void **) &recvbuf_xZ, 2*recvCount_xZ*sizeof(double));	// Allocate device memory
+	ScaLBL_AllocateZeroCopy((void **) &recvbuf_Xz, 2*recvCount_Xz*sizeof(double));	// Allocate device memory
+	ScaLBL_AllocateZeroCopy((void **) &recvbuf_XZ, 2*recvCount_XZ*sizeof(double));	// Allocate device memory
+	ScaLBL_AllocateZeroCopy((void **) &recvbuf_yz, 2*recvCount_yz*sizeof(double));	// Allocate device memory
+	ScaLBL_AllocateZeroCopy((void **) &recvbuf_yZ, 2*recvCount_yZ*sizeof(double));	// Allocate device memory
+	ScaLBL_AllocateZeroCopy((void **) &recvbuf_Yz, 2*recvCount_Yz*sizeof(double));	// Allocate device memory
+	ScaLBL_AllocateZeroCopy((void **) &recvbuf_YZ, 2*recvCount_YZ*sizeof(double));	// Allocate device memory
 	//......................................................................................
 	ScaLBL_AllocateZeroCopy((void **) &dvcSendList_x, sendCount_x*sizeof(int));	// Allocate device memory
 	ScaLBL_AllocateZeroCopy((void **) &dvcSendList_X, sendCount_X*sizeof(int));	// Allocate device memory
@@ -1125,6 +1125,7 @@ void ScaLBL_Communicator::RecvGrad(double *phi, double *grad){
 	ScaLBL_Gradient_Unpack(1.0,-1,0,0,dvcRecvDist_x,0,recvCount_x,recvbuf_x,phi,grad,N);
 	ScaLBL_Gradient_Unpack(0.5,-1,-1,0,dvcRecvDist_x,recvCount_x,recvCount_x,recvbuf_x,phi,grad,N);
 	ScaLBL_Gradient_Unpack(0.5,-1,1,0,dvcRecvDist_x,2*recvCount_x,recvCount_x,recvbuf_x,phi,grad,N);
+	ScaLBL_Gradient_Unpack(0.5,-1,0,-1,dvcRecvDist_x,3*recvCount_x,recvCount_x,recvbuf_x,phi,grad,N);
 	ScaLBL_Gradient_Unpack(0.5,-1,0,1,dvcRecvDist_x,4*recvCount_x,recvCount_x,recvbuf_x,phi,grad,N);
 	//...................................................................................
 	//...Packing for X face(1,7,9,11,13)................................
diff --git a/common/ScaLBL.h b/common/ScaLBL.h
index b492efc3..e379bfad 100644
--- a/common/ScaLBL.h
+++ b/common/ScaLBL.h
@@ -71,7 +71,7 @@ extern "C" void ScaLBL_D3Q19_AAeven_BGK(double *dist, int start, int finish, int
 
 extern "C" void ScaLBL_D3Q19_AAodd_BGK(int *neighborList, double *dist, int start, int finish, int Np, double rlx, double Fx, double Fy, double Fz);
 
-// GREYSCALE MODEL
+// GREYSCALE MODEL (Single-component)
 
 extern "C" void ScaLBL_D3Q19_GreyIMRT_Init(double *Dist, int Np, double Den);
 
@@ -87,6 +87,119 @@ extern "C" void ScaLBL_D3Q19_AAeven_Greyscale_IMRT(double *dist, int start, int
 extern "C" void ScaLBL_D3Q19_AAodd_Greyscale_IMRT(int *neighborList, double *dist, int start, int finish, int Np, double rlx, double rlx_eff, double Fx, double Fy, double Fz, 
                                              double *Poros,double *Perm, double *Velocity,double Den,double *Pressure);
 
+extern "C" void ScaLBL_D3Q19_AAeven_Greyscale_MRT(double *dist, int start, int finish, int Np, double rlx, double rlx_eff, double Fx, double Fy, double Fz,
+                                              double *Poros,double *Perm, double *Velocity,double Den,double *Pressure);
+
+extern "C" void ScaLBL_D3Q19_AAodd_Greyscale_MRT(int *neighborList, double *dist, int start, int finish, int Np, double rlx, double rlx_eff, double Fx, double Fy, double Fz, 
+                                             double *Poros,double *Perm, double *Velocity,double Den,double *Pressure);
+// GREYSCALE FREE-ENERGY MODEL (Two-component)
+
+//extern "C" void ScaLBL_D3Q19_AAeven_GreyscaleFE(double *dist, double *Aq, double *Bq, double *Den,
+//                double *DenGradA, double *DenGradB, double *SolidForce, int start, int finish, int Np,
+//                double tauA,double tauB,double tauA_eff,double tauB_eff,double rhoA,double rhoB,double Gsc, double Gx, double Gy, double Gz,
+//                double *Poros,double *Perm, double *Velocity,double *Pressure);
+//
+//extern "C" void ScaLBL_D3Q19_AAodd_GreyscaleFE(int *neighborList, double *dist, double *Aq, double *Bq, double *Den,
+//                double *DenGradA, double *DenGradB, double *SolidForce, int start, int finish, int Np,
+//                double tauA,double tauB,double tauA_eff,double tauB_eff,double rhoA,double rhoB,double Gsc, double Gx, double Gy, double Gz,
+//                double *Poros,double *Perm, double *Velocity,double *Pressure);
+//
+//extern "C" void ScaLBL_D3Q19_AAeven_GreyscaleFEChem(double *dist, double *Cq, double *Phi, double *SolidForce, int start, int finish, int Np,
+//                double tauA,double tauB,double tauA_eff,double tauB_eff,double rhoA,double rhoB,double gamma,double kappaA,double kappaB,double lambdaA,double lambdaB,
+//                double Gx, double Gy, double Gz,
+//                double *Poros,double *Perm, double *Velocity,double *Pressure,double *PressureGrad,double *PressTensorGrad,double *PhiLap);
+//
+//extern "C" void ScaLBL_D3Q19_AAodd_GreyscaleFEChem(int *neighborList, double *dist, double *Cq, double *Phi, double *SolidForce, int start, int finish, int Np,
+//                double tauA,double tauB,double tauA_eff,double tauB_eff,double rhoA,double rhoB,double gamma,double kappaA,double kappaB,double lambdaA,double lambdaB,
+//                double Gx, double Gy, double Gz,
+//                double *Poros,double *Perm, double *Velocity,double *Pressure,double *PressureGrad,double *PressTensorGrad,double *PhiLap);
+//
+//extern "C" void ScaLBL_D3Q7_GreyscaleFE_Init(double *Den, double *Cq, double *PhiLap, double gamma, double kappaA, double kappaB, double lambdaA, double lambdaB, int start, int finish, int Np);
+//
+//extern "C" void ScaLBL_D3Q19_GreyscaleFE_IMRT_Init(double *dist, double *Den, double rhoA, double rhoB, int Np);
+//
+//extern "C" void ScaLBL_D3Q7_AAodd_GreyscaleFEDensity(int *NeighborList, double *Aq, double *Bq, double *Den, double *Phi, int start, int finish, int Np);
+//
+//extern "C" void ScaLBL_D3Q7_AAeven_GreyscaleFEDensity(double *Aq, double *Bq, double *Den, double *Phi, int start, int finish, int Np);
+//
+//extern "C" void ScaLBL_D3Q7_AAodd_GreyscaleFEPhi(int *NeighborList, double *Cq, double *Phi, int start, int finish, int Np);
+//
+//extern "C" void ScaLBL_D3Q7_AAeven_GreyscaleFEPhi(double *Cq, double *Phi, int start, int finish, int Np);
+//
+//extern "C" void ScaLBL_D3Q19_GreyscaleFE_Gradient(int *neighborList, double *Den, double *DenGrad, int start, int finish, int Np);
+//
+//extern "C" void ScaLBL_D3Q19_GreyscaleFE_Laplacian(int *neighborList, double *Den, double *DenLap, int start, int finish, int Np);
+//
+//extern "C" void ScaLBL_D3Q19_GreyscaleFE_Pressure(double *dist, double *Den, double *Porosity,double *Velocity,
+//                double *Pressure, double rhoA,double rhoB, int Np);
+//
+//extern "C" void ScaLBL_D3Q19_GreyscaleFE_PressureTensor(int *neighborList, double *Phi,double *Pressure, double *PressTensor, double *PhiLap,
+//      		     double kappaA,double kappaB,double lambdaA,double lambdaB, int start, int finish, int Np);
+
+// GREYSCALE SHAN-CHEN MODEL (Two-component)
+
+//extern "C" void ScaLBL_D3Q19_GreyscaleSC_Init(int *Map, double *distA, double *distB, double *DenA, double *DenB, int Np);
+//
+//extern "C" void ScaLBL_D3Q19_AAodd_GreyscaleSC_Density(int *NeighborList, int *Map, double *distA, double *distB, double *DenA, double *DenB, int start, int finish, int Np);
+//
+//extern "C" void ScaLBL_D3Q19_AAeven_GreyscaleSC_Density(int *Map, double *distA, double *distB, double *DenA, double *DenB, int start, int finish, int Np);
+//
+//extern "C" void ScaLBL_D3Q19_AAodd_GreyscaleSC_MRT(int *neighborList, int *Mpa, double *distA, double *distB, double *DenA,double *DenB, double *DenGradA, double *DenGradB, 
+//                double *SolidForceA, double *SolidForceB, double *Poros,double *Perm, double *Velocity,double *Pressure, 
+//                double tauA,double tauB,double tauA_eff,double tauB_eff, double Gsc, double Gx, double Gy, double Gz,                                                 
+//                int start, int finish, int Np);
+//
+//extern "C" void ScaLBL_D3Q19_AAeven_GreyscaleSC_MRT(int *Map,double *distA, double *distB, double *DenA,double *DenB, double *DenGradA, double *DenGradB, 
+//                double *SolidForceA, double *SolidForceB, double *Poros,double *Perm, double *Velocity,double *Pressure, 
+//                double tauA,double tauB,double tauA_eff,double tauB_eff, double Gsc, double Gx, double Gy, double Gz,                                                 
+//                int start, int finish, int Np);
+//
+//extern "C" void ScaLBL_D3Q19_AAodd_GreyscaleSC_BGK(int *neighborList, int *Map, double *distA, double *distB, double *DenA, double *DenB, double *DenGradA, double *DenGradB, 
+//                double *SolidForceA, double *SolidForceB, double *Poros,double *Perm, double *Velocity,double *Pressure, 
+//                double tauA,double tauB,double tauA_eff,double tauB_eff, double Gsc, double Gx, double Gy, double Gz,                                                 
+//                int start, int finish, int Np);
+//
+//extern "C" void ScaLBL_D3Q19_AAeven_GreyscaleSC_BGK(int *Map, double *distA, double *distB, double *DenA, double *DenB, double *DenGradA, double *DenGradB, 
+//                double *SolidForceA, double *SolidForceB, double *Poros,double *Perm, double *Velocity,double *Pressure, 
+//                double tauA,double tauB,double tauA_eff,double tauB_eff, double Gsc, double Gx, double Gy, double Gz,                                                 
+//                int start, int finish, int Np);
+//
+//extern "C" void ScaLBL_D3Q19_GreyscaleSC_Gradient(int *neighborList, int *Map, double *Den, double *DenGrad, int strideY, int strideZ,int start, int finish, int Np);
+//
+//extern "C" void ScaLBL_GreyscaleSC_BC_z(int *list, int *Map, double *DenA, double *DenB, double vA, double vB, int count);
+//
+//extern "C" void ScaLBL_GreyscaleSC_BC_Z(int *list, int *Map, double *DenA, double *DenB, double vA, double vB, int count);
+//
+//extern "C" void ScaLBL_GreyscaleSC_AAeven_Pressure_BC_z(int *list, double *distA, double *distB, double dinA, double dinB, int count, int N);
+//
+//extern "C" void ScaLBL_GreyscaleSC_AAeven_Pressure_BC_Z(int *list, double *distA, double *distB, double doutA, double doutB, int count, int N);
+//
+//extern "C" void ScaLBL_GreyscaleSC_AAodd_Pressure_BC_z(int *neighborList, int *list, double *distA, double *distB, double dinA, double dinB, int count, int N);
+//
+//extern "C" void ScaLBL_GreyscaleSC_AAodd_Pressure_BC_Z(int *neighborList, int *list, double *distA, double *distB, double doutA, double doutB, int count, int N);
+
+// GREYSCALE COLOR MODEL (Two-component)
+//extern "C" void ScaLBL_D3Q19_GreyscaleColor_Init(double *dist, double *Porosity, int Np);
+
+//extern "C" void ScaLBL_D3Q19_AAeven_GreyscaleColor(int *Map, double *dist, double *Aq, double *Bq, double *Den, 
+//        double *ColorGrad,double *Phi,double *GreySolidGrad, double *Poros,double *Perm,double *Vel, 
+//        double rhoA, double rhoB, double tauA, double tauB,double tauA_eff,double tauB_eff, double alpha, double beta,
+//		double Fx, double Fy, double Fz, int strideY, int strideZ, int start, int finish, int Np);
+//
+//extern "C" void ScaLBL_D3Q19_AAodd_GreyscaleColor(int *d_neighborList, int *Map, double *dist, double *Aq, double *Bq, double *Den, 
+//		double *ColorGrad,double *Phi, double *GreySolidGrad, double *Poros,double *Perm,double *Vel, 
+//        double rhoA, double rhoB, double tauA, double tauB, double tauA_eff,double tauB_eff, double alpha, double beta,
+//		double Fx, double Fy, double Fz, int strideY, int strideZ, int start, int finish, int Np);
+
+extern "C" void ScaLBL_D3Q19_AAeven_GreyscaleColor(int *Map, double *dist, double *Aq, double *Bq, double *Den, 
+        double *Phi,double *GreySolidGrad, double *Poros,double *Perm,double *Vel, 
+        double rhoA, double rhoB, double tauA, double tauB,double tauA_eff,double tauB_eff, double alpha, double beta,
+		double Fx, double Fy, double Fz, int strideY, int strideZ, int start, int finish, int Np);
+
+extern "C" void ScaLBL_D3Q19_AAodd_GreyscaleColor(int *d_neighborList, int *Map, double *dist, double *Aq, double *Bq, double *Den, 
+		double *Phi, double *GreySolidGrad, double *Poros,double *Perm,double *Vel, 
+        double rhoA, double rhoB, double tauA, double tauB, double tauA_eff,double tauB_eff, double alpha, double beta,
+		double Fx, double Fy, double Fz, int strideY, int strideZ, int start, int finish, int Np);
 
 // MRT MODEL
 extern "C" void ScaLBL_D3Q19_AAeven_MRT(double *dist, int start, int finish, int Np, double rlx_setA, double rlx_setB, double Fx,
@@ -200,6 +313,8 @@ public:
 	int MemoryOptimizedLayoutAA(IntArray &Map, int *neighborList, signed char *id, int Np);
 	void SendD3Q19AA(double *dist);
 	void RecvD3Q19AA(double *dist);
+//	void BiSendD3Q7(double *A_even, double *A_odd, double *B_even, double *B_odd);
+//	void BiRecvD3Q7(double *A_even, double *A_odd, double *B_even, double *B_odd);
 	void BiSendD3Q7AA(double *Aq, double *Bq);
 	void BiRecvD3Q7AA(double *Aq, double *Bq);
 	void TriSendD3Q7AA(double *Aq, double *Bq, double *Cq);
@@ -217,6 +332,12 @@ public:
 	void D3Q19_Reflection_BC_z(double *fq);
 	void D3Q19_Reflection_BC_Z(double *fq);
 	double D3Q19_Flux_BC_z(int *neighborList, double *fq, double flux, int time);
+	void GreyscaleSC_BC_z(int *Map, double *DenA, double *DenB, double vA, double vB);
+	void GreyscaleSC_BC_Z(int *Map, double *DenA, double *DenB, double vA, double vB);
+    void GreyscaleSC_Pressure_BC_z(int *neighborList, double *fqA, double *fqB, double dinA, double dinB, int time);
+    void GreyscaleSC_Pressure_BC_Z(int *neighborList, double *fqA, double *fqB, double doutA, double doutB, int time);
+//	void TestSendD3Q19(double *f_even, double *f_odd);
+//	void TestRecvD3Q19(double *f_even, double *f_odd);
 
 	// Debugging and unit testing functions
 	void PrintD3Q19();
diff --git a/cpu/D3Q19.cpp b/cpu/D3Q19.cpp
index 3b25e55d..8d897e84 100644
--- a/cpu/D3Q19.cpp
+++ b/cpu/D3Q19.cpp
@@ -99,33 +99,6 @@ extern "C" void ScaLBL_D3Q19_Init(double *dist, int Np)
 	}
 }
 
-
-extern "C" void ScaLBL_D3Q19_GreyIMRT_Init(double *dist, int Np, double Den)
-{
-	int n;
-	for (n=0; n<Np; n++){
-		dist[n] = Den - 0.6666666666666667;
-		dist[Np+n] = 0.055555555555555555;		//double(100*n)+1.f;
-		dist[2*Np+n] = 0.055555555555555555;	//double(100*n)+2.f;
-		dist[3*Np+n] = 0.055555555555555555;	//double(100*n)+3.f;
-		dist[4*Np+n] = 0.055555555555555555;	//double(100*n)+4.f;
-		dist[5*Np+n] = 0.055555555555555555;	//double(100*n)+5.f;
-		dist[6*Np+n] = 0.055555555555555555;	//double(100*n)+6.f;
-		dist[7*Np+n] = 0.0277777777777778;   //double(100*n)+7.f;
-		dist[8*Np+n] = 0.0277777777777778;   //double(100*n)+8.f;
-		dist[9*Np+n] = 0.0277777777777778;   //double(100*n)+9.f;
-		dist[10*Np+n] = 0.0277777777777778;  //double(100*n)+10.f;
-		dist[11*Np+n] = 0.0277777777777778;  //double(100*n)+11.f;
-		dist[12*Np+n] = 0.0277777777777778;  //double(100*n)+12.f;
-		dist[13*Np+n] = 0.0277777777777778;  //double(100*n)+13.f;
-		dist[14*Np+n] = 0.0277777777777778;  //double(100*n)+14.f;
-		dist[15*Np+n] = 0.0277777777777778;  //double(100*n)+15.f;
-		dist[16*Np+n] = 0.0277777777777778;  //double(100*n)+16.f;
-		dist[17*Np+n] = 0.0277777777777778;  //double(100*n)+17.f;
-		dist[18*Np+n] = 0.0277777777777778;  //double(100*n)+18.f;
-	}
-}
-
 //*************************************************************************
 extern "C" void ScaLBL_D3Q19_Swap(char *ID, double *disteven, double *distodd, int Nx, int Ny, int Nz)
 {
diff --git a/cpu/Greyscale.cpp b/cpu/Greyscale.cpp
index c0fa1ae0..eda7bbdb 100644
--- a/cpu/Greyscale.cpp
+++ b/cpu/Greyscale.cpp
@@ -909,9 +909,9 @@ extern "C" void ScaLBL_D3Q19_AAeven_Greyscale_IMRT(double *dist, int start, int
 
         //-------------------- IMRT collison where body force has higher-order terms -------------//
 //		//..............carry out relaxation process...............................................
-//		m1 = m1 + rlx_setA*((-30*Den+19*(ux*ux+uy*uy+uz*uz)/porosity + 57*pressure*porosity) - m1) 
+//		m1 = m1 + rlx_setA*((-30*Den+19*Den*(ux*ux+uy*uy+uz*uz)/porosity + 57*pressure*porosity) - m1) 
 //                + (1-0.5*rlx_setA)*38*(Fx*ux+Fy*uy+Fz*uz)/porosity;
-//		m2 = m2 + rlx_setA*((12*Den - 5.5*(ux*ux+uy*uy+uz*uz)/porosity-27*pressure*porosity) - m2)
+//		m2 = m2 + rlx_setA*((12*Den - 5.5*Den*(ux*ux+uy*uy+uz*uz)/porosity-27*pressure*porosity) - m2)
 //                + (1-0.5*rlx_setA)*11*(-Fx*ux-Fy*uy-Fz*uz)/porosity;
 //        jx = jx + Fx;
 //		m4 = m4 + rlx_setB*((-0.6666666666666666*ux*Den) - m4)
@@ -944,8 +944,8 @@ extern "C" void ScaLBL_D3Q19_AAeven_Greyscale_IMRT(double *dist, int start, int
 
         //-------------------- IMRT collison where body force has NO higher-order terms -------------//
 		//..............carry out relaxation process...............................................
-		m1 = m1 + rlx_setA*((-30*Den+19*(ux*ux+uy*uy+uz*uz)/porosity + 57*pressure*porosity) - m1);
-		m2 = m2 + rlx_setA*((12*Den - 5.5*(ux*ux+uy*uy+uz*uz)/porosity-27*pressure*porosity) - m2);
+		m1 = m1 + rlx_setA*((-30*Den+19*Den*(ux*ux+uy*uy+uz*uz)/porosity + 57*pressure*porosity) - m1);
+		m2 = m2 + rlx_setA*((12*Den - 5.5*Den*(ux*ux+uy*uy+uz*uz)/porosity-27*pressure*porosity) - m2);
         jx = jx + Fx;
 		m4 = m4 + rlx_setB*((-0.6666666666666666*ux*Den) - m4)
                 + (1-0.5*rlx_setB)*(-0.6666666666666666*Fx);
@@ -1416,9 +1416,9 @@ extern "C" void ScaLBL_D3Q19_AAodd_Greyscale_IMRT(int *neighborList, double *dis
 
         //-------------------- IMRT collison where body force has higher-order terms -------------//
 //		//..............carry out relaxation process...............................................
-//		m1 = m1 + rlx_setA*((-30*Den+19*(ux*ux+uy*uy+uz*uz)/porosity + 57*pressure*porosity) - m1) 
+//		m1 = m1 + rlx_setA*((-30*Den+19*Den*(ux*ux+uy*uy+uz*uz)/porosity + 57*pressure*porosity) - m1) 
 //                + (1-0.5*rlx_setA)*38*(Fx*ux+Fy*uy+Fz*uz)/porosity;
-//		m2 = m2 + rlx_setA*((12*Den - 5.5*(ux*ux+uy*uy+uz*uz)/porosity-27*pressure*porosity) - m2)
+//		m2 = m2 + rlx_setA*((12*Den - 5.5*Den*(ux*ux+uy*uy+uz*uz)/porosity-27*pressure*porosity) - m2)
 //                + (1-0.5*rlx_setA)*11*(-Fx*ux-Fy*uy-Fz*uz)/porosity;
 //        jx = jx + Fx;
 //		m4 = m4 + rlx_setB*((-0.6666666666666666*ux*Den) - m4)
@@ -1451,8 +1451,8 @@ extern "C" void ScaLBL_D3Q19_AAodd_Greyscale_IMRT(int *neighborList, double *dis
 
         //-------------------- IMRT collison where body force has NO higher-order terms -------------//
 		//..............carry out relaxation process...............................................
-		m1 = m1 + rlx_setA*((-30*Den+19*(ux*ux+uy*uy+uz*uz)/porosity + 57*pressure*porosity) - m1);
-		m2 = m2 + rlx_setA*((12*Den - 5.5*(ux*ux+uy*uy+uz*uz)/porosity-27*pressure*porosity) - m2);
+		m1 = m1 + rlx_setA*((-30*Den+19*Den*(ux*ux+uy*uy+uz*uz)/porosity + 57*pressure*porosity) - m1);
+		m2 = m2 + rlx_setA*((12*Den - 5.5*Den*(ux*ux+uy*uy+uz*uz)/porosity-27*pressure*porosity) - m2);
         jx = jx + Fx;
 		m4 = m4 + rlx_setB*((-0.6666666666666666*ux*Den) - m4)
                 + (1-0.5*rlx_setB)*(-0.6666666666666666*Fx);
@@ -1580,3 +1580,1063 @@ extern "C" void ScaLBL_D3Q19_AAodd_Greyscale_IMRT(int *neighborList, double *dis
 	}
 }
 
+
+extern "C" void ScaLBL_D3Q19_AAodd_Greyscale_MRT(int *neighborList, double *dist, int start, int finish, int Np, double rlx, double rlx_eff, double Gx, double Gy, double Gz,double *Poros,double *Perm, double *Velocity,double rho0,double *Pressure){
+
+	int n, nread;
+	int nr1,nr2,nr3,nr4,nr5,nr6;
+	int nr7,nr8,nr9,nr10;
+	int nr11,nr12,nr13,nr14;
+	double vx,vy,vz,v_mag;
+    double ux,uy,uz,u_mag;
+    double pressure;//defined for this incompressible model
+	// conserved momemnts
+	double rho,jx,jy,jz;
+	// non-conserved moments
+	double m1,m2,m4,m6,m8,m9,m10,m11,m12,m13,m14,m15,m16,m17,m18;
+    double fq;
+	//double f0,f1,f2,f3,f4,f5,f6,f7,f8,f9,f10,f11,f12,f13,f14,f15,f16,f17,f18;
+    double GeoFun;//geometric function from Guo's PRE 66, 036304 (2002)
+    double porosity;
+    double perm;//voxel permeability
+    double c0, c1; //Guo's model parameters
+    double mu_eff = (1.0/rlx_eff-0.5)/3.0;//kinematic viscosity
+    double Fx, Fy, Fz;//The total body force including Brinkman force and user-specified (Gx,Gy,Gz)
+    double rlx_setA = rlx;
+    double rlx_setB = 8.f*(2.f-rlx_setA)/(8.f-rlx_setA);
+
+	const double mrt_V1=0.05263157894736842;
+	const double mrt_V2=0.012531328320802;
+	const double mrt_V3=0.04761904761904762;
+	const double mrt_V4=0.004594820384294068;
+	const double mrt_V5=0.01587301587301587;
+	const double mrt_V6=0.0555555555555555555555555;
+	const double mrt_V7=0.02777777777777778;
+	const double mrt_V8=0.08333333333333333;
+	const double mrt_V9=0.003341687552213868;
+	const double mrt_V10=0.003968253968253968;
+	const double mrt_V11=0.01388888888888889;
+	const double mrt_V12=0.04166666666666666;
+
+	for (int n=start; n<finish; n++){
+        //........................................................................
+        //					READ THE DISTRIBUTIONS
+        //		(read from opposite array due to previous swap operation)
+        //........................................................................
+        // q=0
+		fq = dist[n];
+		rho = fq;
+		m1  = -30.0*fq;
+		m2  = 12.0*fq;
+
+		// q=1
+		//nread = neighborList[n]; // neighbor 2 
+		//fq = dist[nread]; // reading the f1 data into register fq		
+		nr1 = neighborList[n]; 
+		fq = dist[nr1]; // reading the f1 data into register fq
+		rho += fq;
+		m1 -= 11.0*fq;
+		m2 -= 4.0*fq;
+		jx = fq;
+		m4 = -4.0*fq;
+		m9 = 2.0*fq;
+		m10 = -4.0*fq;
+
+		// f2 = dist[10*Np+n];
+		//nread = neighborList[n+Np]; // neighbor 1 ( < 10Np => even part of dist)
+		//fq = dist[nread];  // reading the f2 data into register fq
+		nr2 = neighborList[n+Np]; // neighbor 1 ( < 10Np => even part of dist)
+		fq = dist[nr2];  // reading the f2 data into register fq
+		rho += fq;
+		m1 -= 11.0*(fq);
+		m2 -= 4.0*(fq);
+		jx -= fq;
+		m4 += 4.0*(fq);
+		m9 += 2.0*(fq);
+		m10 -= 4.0*(fq);
+
+		// q=3
+		//nread = neighborList[n+2*Np]; // neighbor 4
+		//fq = dist[nread];
+		nr3 = neighborList[n+2*Np]; // neighbor 4
+		fq = dist[nr3];
+		rho += fq;
+		m1 -= 11.0*fq;
+		m2 -= 4.0*fq;
+		jy = fq;
+		m6 = -4.0*fq;
+		m9 -= fq;
+		m10 += 2.0*fq;
+		m11 = fq;
+		m12 = -2.0*fq;
+
+		// q = 4
+		//nread = neighborList[n+3*Np]; // neighbor 3
+		//fq = dist[nread];
+		nr4 = neighborList[n+3*Np]; // neighbor 3
+		fq = dist[nr4];
+		rho+= fq;
+		m1 -= 11.0*fq;
+		m2 -= 4.0*fq;
+		jy -= fq;
+		m6 += 4.0*fq;
+		m9 -= fq;
+		m10 += 2.0*fq;
+		m11 += fq;
+		m12 -= 2.0*fq;
+
+		// q=5
+		//nread = neighborList[n+4*Np];
+		//fq = dist[nread];
+		nr5 = neighborList[n+4*Np];
+		fq = dist[nr5];
+		rho += fq;
+		m1 -= 11.0*fq;
+		m2 -= 4.0*fq;
+		jz = fq;
+		m8 = -4.0*fq;
+		m9 -= fq;
+		m10 += 2.0*fq;
+		m11 -= fq;
+		m12 += 2.0*fq;
+
+
+		// q = 6
+		//nread = neighborList[n+5*Np];
+		//fq = dist[nread];
+		nr6 = neighborList[n+5*Np];
+		fq = dist[nr6];
+		rho+= fq;
+		m1 -= 11.0*fq;
+		m2 -= 4.0*fq;
+		jz -= fq;
+		m8 += 4.0*fq;
+		m9 -= fq;
+		m10 += 2.0*fq;
+		m11 -= fq;
+		m12 += 2.0*fq;
+
+		// q=7
+		//nread = neighborList[n+6*Np];
+		//fq = dist[nread];
+		nr7 = neighborList[n+6*Np];
+		fq = dist[nr7];
+		rho += fq;
+		m1 += 8.0*fq;
+		m2 += fq;
+		jx += fq;
+		m4 += fq;
+		jy += fq;
+		m6 += fq;
+		m9  += fq;
+		m10 += fq;
+		m11 += fq;
+		m12 += fq;
+		m13 = fq;
+		m16 = fq;
+		m17 = -fq;
+
+		// q = 8
+		//nread = neighborList[n+7*Np];
+		//fq = dist[nread];
+		nr8 = neighborList[n+7*Np];
+		fq = dist[nr8];
+		rho += fq;
+		m1 += 8.0*fq;
+		m2 += fq;
+		jx -= fq;
+		m4 -= fq;
+		jy -= fq;
+		m6 -= fq;
+		m9 += fq;
+		m10 += fq;
+		m11 += fq;
+		m12 += fq;
+		m13 += fq;
+		m16 -= fq;
+		m17 += fq;
+
+		// q=9
+		//nread = neighborList[n+8*Np];
+		//fq = dist[nread];
+		nr9 = neighborList[n+8*Np];
+		fq = dist[nr9];
+		rho += fq;
+		m1 += 8.0*fq;
+		m2 += fq;
+		jx += fq;
+		m4 += fq;
+		jy -= fq;
+		m6 -= fq;
+		m9 += fq;
+		m10 += fq;
+		m11 += fq;
+		m12 += fq;
+		m13 -= fq;
+		m16 += fq;
+		m17 += fq;
+
+		// q = 10
+		//nread = neighborList[n+9*Np];
+		//fq = dist[nread];
+		nr10 = neighborList[n+9*Np];
+		fq = dist[nr10];
+		rho += fq;
+		m1 += 8.0*fq;
+		m2 += fq;
+		jx -= fq;
+		m4 -= fq;
+		jy += fq;
+		m6 += fq;
+		m9 += fq;
+		m10 += fq;
+		m11 += fq;
+		m12 += fq;
+		m13 -= fq;
+		m16 -= fq;
+		m17 -= fq;
+
+		// q=11
+		//nread = neighborList[n+10*Np];
+		//fq = dist[nread];
+		nr11 = neighborList[n+10*Np];
+		fq = dist[nr11];
+		rho += fq;
+		m1 += 8.0*fq;
+		m2 += fq;
+		jx += fq;
+		m4 += fq;
+		jz += fq;
+		m8 += fq;
+		m9 += fq;
+		m10 += fq;
+		m11 -= fq;
+		m12 -= fq;
+		m15 = fq;
+		m16 -= fq;
+		m18 = fq;
+
+		// q=12
+		//nread = neighborList[n+11*Np];
+		//fq = dist[nread];
+		nr12 = neighborList[n+11*Np];
+		fq = dist[nr12];
+		rho += fq;
+		m1 += 8.0*fq;
+		m2 += fq;
+		jx -= fq;
+		m4 -= fq;
+		jz -= fq;
+		m8 -= fq;
+		m9 += fq;
+		m10 += fq;
+		m11 -= fq;
+		m12 -= fq;
+		m15 += fq;
+		m16 += fq;
+		m18 -= fq;
+
+		// q=13
+		//nread = neighborList[n+12*Np];
+		//fq = dist[nread];
+		nr13 = neighborList[n+12*Np];
+		fq = dist[nr13];
+		rho += fq;
+		m1 += 8.0*fq;
+		m2 += fq;
+		jx += fq;
+		m4 += fq;
+		jz -= fq;
+		m8 -= fq;
+		m9 += fq;
+		m10 += fq;
+		m11 -= fq;
+		m12 -= fq;
+		m15 -= fq;
+		m16 -= fq;
+		m18 -= fq;
+
+		// q=14
+		//nread = neighborList[n+13*Np];
+		//fq = dist[nread];
+		nr14 = neighborList[n+13*Np];
+		fq = dist[nr14];
+		rho += fq;
+		m1 += 8.0*fq;
+		m2 += fq;
+		jx -= fq;
+		m4 -= fq;
+		jz += fq;
+		m8 += fq;
+		m9 += fq;
+		m10 += fq;
+		m11 -= fq;
+		m12 -= fq;
+		m15 -= fq;
+		m16 += fq;
+		m18 += fq;
+
+		// q=15
+		nread = neighborList[n+14*Np];
+		fq = dist[nread];
+		//fq = dist[17*Np+n];
+		rho += fq;
+		m1 += 8.0*fq;
+		m2 += fq;
+		jy += fq;
+		m6 += fq;
+		jz += fq;
+		m8 += fq;
+		m9 -= 2.0*fq;
+		m10 -= 2.0*fq;
+		m14 = fq;
+		m17 += fq;
+		m18 -= fq;
+
+		// q=16
+		nread = neighborList[n+15*Np];
+		fq = dist[nread];
+		//fq = dist[8*Np+n];
+		rho += fq;
+		m1 += 8.0*fq;
+		m2 += fq;
+		jy -= fq;
+		m6 -= fq;
+		jz -= fq;
+		m8 -= fq;
+		m9 -= 2.0*fq;
+		m10 -= 2.0*fq;
+		m14 += fq;
+		m17 -= fq;
+		m18 += fq;
+
+		// q=17
+		//fq = dist[18*Np+n];
+		nread = neighborList[n+16*Np];
+		fq = dist[nread];
+		rho += fq;
+		m1 += 8.0*fq;
+		m2 += fq;
+		jy += fq;
+		m6 += fq;
+		jz -= fq;
+		m8 -= fq;
+		m9 -= 2.0*fq;
+		m10 -= 2.0*fq;
+		m14 -= fq;
+		m17 += fq;
+		m18 += fq;
+
+		// q=18
+		nread = neighborList[n+17*Np];
+		fq = dist[nread];
+		//fq = dist[9*Np+n];
+		rho += fq;
+		m1 += 8.0*fq;
+		m2 += fq;
+		jy -= fq;
+		m6 -= fq;
+		jz += fq;
+		m8 += fq;
+		m9 -= 2.0*fq;
+		m10 -= 2.0*fq;
+		m14 -= fq;
+		m17 -= fq;
+		m18 -= fq;
+        //---------------------------------------------------------------------//
+
+        porosity = Poros[n];
+        perm = Perm[n];
+
+        c0 = 0.5*(1.0+porosity*0.5*mu_eff/perm);
+        if (porosity==1.0) c0 = 0.5;//i.e. apparent pore nodes
+        GeoFun = 1.75/sqrt(150.0*porosity*porosity*porosity);
+        c1 = porosity*0.5*GeoFun/sqrt(perm);
+        if (porosity==1.0) c1 = 0.0;//i.e. apparent pore nodes
+
+        vx = jx/rho0+0.5*porosity*Gx;
+        vy = jy/rho0+0.5*porosity*Gy;
+        vz = jz/rho0+0.5*porosity*Gz;
+        v_mag=sqrt(vx*vx+vy*vy+vz*vz);
+        ux = vx/(c0+sqrt(c0*c0+c1*v_mag));
+        uy = vy/(c0+sqrt(c0*c0+c1*v_mag));
+        uz = vz/(c0+sqrt(c0*c0+c1*v_mag));
+        u_mag=sqrt(ux*ux+uy*uy+uz*uz);
+
+        //Update the total force to include linear (Darcy) and nonlinear (Forchheimer) drags due to the porous medium
+        Fx = rho0*(-porosity*mu_eff/perm*ux - porosity*GeoFun/sqrt(perm)*u_mag*ux + porosity*Gx);
+        Fy = rho0*(-porosity*mu_eff/perm*uy - porosity*GeoFun/sqrt(perm)*u_mag*uy + porosity*Gy);
+        Fz = rho0*(-porosity*mu_eff/perm*uz - porosity*GeoFun/sqrt(perm)*u_mag*uz + porosity*Gz);
+        if (porosity==1.0){
+            Fx=rho0*Gx;
+            Fy=rho0*Gy;
+            Fz=rho0*Gz;
+        }
+
+        //Calculate pressure for MRT model
+        pressure=rho/3.f;
+
+        //-------------------- MRT collison where body force has NO higher-order terms -------------//
+		m1 = m1 + rlx_setA*((19*(ux*ux+uy*uy+uz*uz)*rho0/porosity - 11*rho) - m1);
+		m2 = m2 + rlx_setA*((3*rho - 5.5*(ux*ux+uy*uy+uz*uz)*rho0/porosity) - m2);
+        jx = jx + Fx;
+		m4 = m4 + rlx_setB*((-0.6666666666666666*ux*rho0)- m4)
+                + (1-0.5*rlx_setB)*(-0.6666666666666666*Fx);
+        jy = jy + Fy;
+		m6 = m6 + rlx_setB*((-0.6666666666666666*uy*rho0)- m6)
+                + (1-0.5*rlx_setB)*(-0.6666666666666666*Fy);
+        jz = jz + Fz;
+		m8 = m8 + rlx_setB*((-0.6666666666666666*uz*rho0)- m8)
+                + (1-0.5*rlx_setB)*(-0.6666666666666666*Fz);
+		m9 = m9 + rlx_setA*(((2*ux*ux-uy*uy-uz*uz)*rho0/porosity) - m9);
+		m10 = m10 + rlx_setA*( - m10);
+        //m10 = m10 + rlx_setA*(-0.5*rho0*((2*ux*ux-uy*uy-uz*uz)/porosity)- m10);
+		m11 = m11 + rlx_setA*(((uy*uy-uz*uz)*rho0/porosity) - m11);
+		m12 = m12 + rlx_setA*( - m12);
+        //m12 = m12 + rlx_setA*(-0.5*(rho0*(uy*uy-uz*uz)/porosity)- m12);
+		m13 = m13 + rlx_setA*( (ux*uy*rho0/porosity) - m13);
+		m14 = m14 + rlx_setA*( (uy*uz*rho0/porosity) - m14);
+		m15 = m15 + rlx_setA*( (ux*uz*rho0/porosity) - m15);
+		m16 = m16 + rlx_setB*( - m16);
+		m17 = m17 + rlx_setB*( - m17);
+		m18 = m18 + rlx_setB*( - m18);
+        //.......................................................................................................
+
+
+        //.................inverse transformation......................................................
+        // q=0
+		fq = mrt_V1*rho-mrt_V2*m1+mrt_V3*m2;
+		dist[n] = fq;
+
+		// q = 1
+		fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(jx-m4)+mrt_V6*(m9-m10);
+		//nread = neighborList[n+Np];
+		dist[nr2] = fq;
+
+		// q=2
+		fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(m4-jx)+mrt_V6*(m9-m10);
+		//nread = neighborList[n];
+		dist[nr1] = fq;
+
+		// q = 3
+		fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(jy-m6)+mrt_V7*(m10-m9)+mrt_V8*(m11-m12);
+		//nread = neighborList[n+3*Np];
+		dist[nr4] = fq;
+
+		// q = 4
+		fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(m6-jy)+mrt_V7*(m10-m9)+mrt_V8*(m11-m12);
+		//nread = neighborList[n+2*Np];
+		dist[nr3] = fq;
+
+		// q = 5
+		fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(jz-m8)+mrt_V7*(m10-m9)+mrt_V8*(m12-m11);
+		//nread = neighborList[n+5*Np];
+		dist[nr6] = fq;
+
+		// q = 6
+		fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(m8-jz)+mrt_V7*(m10-m9)+mrt_V8*(m12-m11);
+		//nread = neighborList[n+4*Np];
+		dist[nr5] = fq;
+
+		// q = 7
+		fq = mrt_V1*rho+mrt_V9*m1+mrt_V10*m2+0.1*(jx+jy)+0.025*(m4+m6)+
+				mrt_V7*m9+mrt_V11*m10+mrt_V8*m11+mrt_V12*m12+0.25*m13+0.125*(m16-m17);
+		//nread = neighborList[n+7*Np];
+		dist[nr8] = fq;
+
+		// q = 8
+		fq = mrt_V1*rho+mrt_V9*m1+mrt_V10*m2-0.1*(jx+jy)-0.025*(m4+m6) +mrt_V7*m9+mrt_V11*m10+mrt_V8*m11
+				+mrt_V12*m12+0.25*m13+0.125*(m17-m16);
+		//nread = neighborList[n+6*Np];
+		dist[nr7] = fq;
+
+		// q = 9
+		fq = mrt_V1*rho+mrt_V9*m1+mrt_V10*m2+0.1*(jx-jy)+0.025*(m4-m6)+
+				mrt_V7*m9+mrt_V11*m10+mrt_V8*m11+mrt_V12*m12-0.25*m13+0.125*(m16+m17);
+		//nread = neighborList[n+9*Np];
+		dist[nr10] = fq;
+
+		// q = 10
+		fq = mrt_V1*rho+mrt_V9*m1+mrt_V10*m2+0.1*(jy-jx)+0.025*(m6-m4)+
+				mrt_V7*m9+mrt_V11*m10+mrt_V8*m11+mrt_V12*m12-0.25*m13-0.125*(m16+m17);
+		//nread = neighborList[n+8*Np];
+		dist[nr9] = fq;
+
+		// q = 11
+		fq = mrt_V1*rho+mrt_V9*m1
+				+mrt_V10*m2+0.1*(jx+jz)+0.025*(m4+m8)
+				+mrt_V7*m9+mrt_V11*m10-mrt_V8*m11
+				-mrt_V12*m12+0.25*m15+0.125*(m18-m16);
+		//nread = neighborList[n+11*Np];
+		dist[nr12] = fq;
+
+		// q = 12
+		fq = mrt_V1*rho+mrt_V9*m1+mrt_V10*m2-0.1*(jx+jz)-0.025*(m4+m8)+
+				mrt_V7*m9+mrt_V11*m10-mrt_V8*m11-mrt_V12*m12+0.25*m15+0.125*(m16-m18);
+		//nread = neighborList[n+10*Np];
+		dist[nr11]= fq;
+
+		// q = 13
+		fq = mrt_V1*rho+mrt_V9*m1
+				+mrt_V10*m2+0.1*(jx-jz)+0.025*(m4-m8)
+				+mrt_V7*m9+mrt_V11*m10-mrt_V8*m11
+				-mrt_V12*m12-0.25*m15-0.125*(m16+m18);
+		//nread = neighborList[n+13*Np];
+		dist[nr14] = fq;
+
+		// q= 14
+		fq = mrt_V1*rho+mrt_V9*m1
+				+mrt_V10*m2+0.1*(jz-jx)+0.025*(m8-m4)
+				+mrt_V7*m9+mrt_V11*m10-mrt_V8*m11
+				-mrt_V12*m12-0.25*m15+0.125*(m16+m18);
+		//nread = neighborList[n+12*Np];
+		dist[nr13] = fq;
+
+
+		// q = 15
+		fq = mrt_V1*rho+mrt_V9*m1
+				+mrt_V10*m2+0.1*(jy+jz)+0.025*(m6+m8)
+				-mrt_V6*m9-mrt_V7*m10+0.25*m14+0.125*(m17-m18);
+		nread = neighborList[n+15*Np];
+		dist[nread] = fq;
+
+		// q = 16
+		fq =  mrt_V1*rho+mrt_V9*m1
+				+mrt_V10*m2-0.1*(jy+jz)-0.025*(m6+m8)
+				-mrt_V6*m9-mrt_V7*m10+0.25*m14+0.125*(m18-m17);
+		nread = neighborList[n+14*Np];
+		dist[nread] = fq;
+
+
+		// q = 17
+		fq = mrt_V1*rho+mrt_V9*m1
+				+mrt_V10*m2+0.1*(jy-jz)+0.025*(m6-m8)
+				-mrt_V6*m9-mrt_V7*m10-0.25*m14+0.125*(m17+m18);
+		nread = neighborList[n+17*Np];
+		dist[nread] = fq;
+
+		// q = 18
+		fq = mrt_V1*rho+mrt_V9*m1
+				+mrt_V10*m2+0.1*(jz-jy)+0.025*(m8-m6)
+				-mrt_V6*m9-mrt_V7*m10-0.25*m14-0.125*(m17+m18);
+		nread = neighborList[n+16*Np];
+		dist[nread] = fq;
+        //........................................................................
+
+        //Update velocity on device
+        Velocity[0*Np+n] = ux;
+        Velocity[1*Np+n] = uy;
+        Velocity[2*Np+n] = uz;
+        //Update pressure on device
+        Pressure[n] = pressure;
+	}
+}
+
+extern "C" void ScaLBL_D3Q19_AAeven_Greyscale_MRT(double *dist, int start, int finish, int Np, double rlx, double rlx_eff, double Gx, double Gy, double Gz,double *Poros,double *Perm, double *Velocity,double rho0,double *Pressure){
+
+	int n;
+	double vx,vy,vz,v_mag;
+    double ux,uy,uz,u_mag;
+    double pressure;//defined for this incompressible model
+	// conserved momemnts
+	double rho,jx,jy,jz;
+	// non-conserved moments
+	double m1,m2,m4,m6,m8,m9,m10,m11,m12,m13,m14,m15,m16,m17,m18;
+    double fq;
+	//double f0,f1,f2,f3,f4,f5,f6,f7,f8,f9,f10,f11,f12,f13,f14,f15,f16,f17,f18;
+    double GeoFun;//geometric function from Guo's PRE 66, 036304 (2002)
+    double porosity;
+    double perm;//voxel permeability
+    double c0, c1; //Guo's model parameters
+    double mu_eff = (1.0/rlx_eff-0.5)/3.0;//kinematic viscosity
+    double Fx, Fy, Fz;//The total body force including Brinkman force and user-specified (Gx,Gy,Gz)
+    double rlx_setA = rlx;
+    double rlx_setB = 8.f*(2.f-rlx_setA)/(8.f-rlx_setA);
+
+	const double mrt_V1=0.05263157894736842;
+	const double mrt_V2=0.012531328320802;
+	const double mrt_V3=0.04761904761904762;
+	const double mrt_V4=0.004594820384294068;
+	const double mrt_V5=0.01587301587301587;
+	const double mrt_V6=0.0555555555555555555555555;
+	const double mrt_V7=0.02777777777777778;
+	const double mrt_V8=0.08333333333333333;
+	const double mrt_V9=0.003341687552213868;
+	const double mrt_V10=0.003968253968253968;
+	const double mrt_V11=0.01388888888888889;
+	const double mrt_V12=0.04166666666666666;
+
+
+	for (int n=start; n<finish; n++){
+        //........................................................................
+        //					READ THE DISTRIBUTIONS
+        //		(read from opposite array due to previous swap operation)
+        //........................................................................
+        // q=0
+		fq = dist[n];
+		rho = fq;
+		m1  = -30.0*fq;
+		m2  = 12.0*fq;
+
+		// q=1
+		fq = dist[2*Np+n];
+		rho += fq;
+		m1 -= 11.0*fq;
+		m2 -= 4.0*fq;
+		jx = fq;
+		m4 = -4.0*fq;
+		m9 = 2.0*fq;
+		m10 = -4.0*fq;
+
+		// f2 = dist[10*Np+n];
+		fq = dist[1*Np+n];
+		rho += fq;
+		m1 -= 11.0*(fq);
+		m2 -= 4.0*(fq);
+		jx -= fq;
+		m4 += 4.0*(fq);
+		m9 += 2.0*(fq);
+		m10 -= 4.0*(fq);
+
+		// q=3
+		fq = dist[4*Np+n];
+		rho += fq;
+		m1 -= 11.0*fq;
+		m2 -= 4.0*fq;
+		jy = fq;
+		m6 = -4.0*fq;
+		m9 -= fq;
+		m10 += 2.0*fq;
+		m11 = fq;
+		m12 = -2.0*fq;
+
+		// q = 4
+		fq = dist[3*Np+n];
+		rho+= fq;
+		m1 -= 11.0*fq;
+		m2 -= 4.0*fq;
+		jy -= fq;
+		m6 += 4.0*fq;
+		m9 -= fq;
+		m10 += 2.0*fq;
+		m11 += fq;
+		m12 -= 2.0*fq;
+
+		// q=5
+		fq = dist[6*Np+n];
+		rho += fq;
+		m1 -= 11.0*fq;
+		m2 -= 4.0*fq;
+		jz = fq;
+		m8 = -4.0*fq;
+		m9 -= fq;
+		m10 += 2.0*fq;
+		m11 -= fq;
+		m12 += 2.0*fq;
+
+		// q = 6
+		fq = dist[5*Np+n];
+		rho+= fq;
+		m1 -= 11.0*fq;
+		m2 -= 4.0*fq;
+		jz -= fq;
+		m8 += 4.0*fq;
+		m9 -= fq;
+		m10 += 2.0*fq;
+		m11 -= fq;
+		m12 += 2.0*fq;
+
+		// q=7
+		fq = dist[8*Np+n];
+		rho += fq;
+		m1 += 8.0*fq;
+		m2 += fq;
+		jx += fq;
+		m4 += fq;
+		jy += fq;
+		m6 += fq;
+		m9  += fq;
+		m10 += fq;
+		m11 += fq;
+		m12 += fq;
+		m13 = fq;
+		m16 = fq;
+		m17 = -fq;
+
+		// q = 8
+		fq = dist[7*Np+n];
+		rho += fq;
+		m1 += 8.0*fq;
+		m2 += fq;
+		jx -= fq;
+		m4 -= fq;
+		jy -= fq;
+		m6 -= fq;
+		m9 += fq;
+		m10 += fq;
+		m11 += fq;
+		m12 += fq;
+		m13 += fq;
+		m16 -= fq;
+		m17 += fq;
+
+		// q=9
+		fq = dist[10*Np+n];
+		rho += fq;
+		m1 += 8.0*fq;
+		m2 += fq;
+		jx += fq;
+		m4 += fq;
+		jy -= fq;
+		m6 -= fq;
+		m9 += fq;
+		m10 += fq;
+		m11 += fq;
+		m12 += fq;
+		m13 -= fq;
+		m16 += fq;
+		m17 += fq;
+
+		// q = 10
+		fq = dist[9*Np+n];
+		rho += fq;
+		m1 += 8.0*fq;
+		m2 += fq;
+		jx -= fq;
+		m4 -= fq;
+		jy += fq;
+		m6 += fq;
+		m9 += fq;
+		m10 += fq;
+		m11 += fq;
+		m12 += fq;
+		m13 -= fq;
+		m16 -= fq;
+		m17 -= fq;
+
+		// q=11
+		fq = dist[12*Np+n];
+		rho += fq;
+		m1 += 8.0*fq;
+		m2 += fq;
+		jx += fq;
+		m4 += fq;
+		jz += fq;
+		m8 += fq;
+		m9 += fq;
+		m10 += fq;
+		m11 -= fq;
+		m12 -= fq;
+		m15 = fq;
+		m16 -= fq;
+		m18 = fq;
+
+		// q=12
+		fq = dist[11*Np+n];
+		rho += fq;
+		m1 += 8.0*fq;
+		m2 += fq;
+		jx -= fq;
+		m4 -= fq;
+		jz -= fq;
+		m8 -= fq;
+		m9 += fq;
+		m10 += fq;
+		m11 -= fq;
+		m12 -= fq;
+		m15 += fq;
+		m16 += fq;
+		m18 -= fq;
+
+		// q=13
+		fq = dist[14*Np+n];
+		rho += fq;
+		m1 += 8.0*fq;
+		m2 += fq;
+		jx += fq;
+		m4 += fq;
+		jz -= fq;
+		m8 -= fq;
+		m9 += fq;
+		m10 += fq;
+		m11 -= fq;
+		m12 -= fq;
+		m15 -= fq;
+		m16 -= fq;
+		m18 -= fq;
+
+		// q=14
+		fq = dist[13*Np+n];
+		rho += fq;
+		m1 += 8.0*fq;
+		m2 += fq;
+		jx -= fq;
+		m4 -= fq;
+		jz += fq;
+		m8 += fq;
+		m9 += fq;
+		m10 += fq;
+		m11 -= fq;
+		m12 -= fq;
+		m15 -= fq;
+		m16 += fq;
+		m18 += fq;
+
+		// q=15
+		fq = dist[16*Np+n];
+		rho += fq;
+		m1 += 8.0*fq;
+		m2 += fq;
+		jy += fq;
+		m6 += fq;
+		jz += fq;
+		m8 += fq;
+		m9 -= 2.0*fq;
+		m10 -= 2.0*fq;
+		m14 = fq;
+		m17 += fq;
+		m18 -= fq;
+
+		// q=16
+		fq = dist[15*Np+n];
+		rho += fq;
+		m1 += 8.0*fq;
+		m2 += fq;
+		jy -= fq;
+		m6 -= fq;
+		jz -= fq;
+		m8 -= fq;
+		m9 -= 2.0*fq;
+		m10 -= 2.0*fq;
+		m14 += fq;
+		m17 -= fq;
+		m18 += fq;
+
+		// q=17
+		fq = dist[18*Np+n];
+		rho += fq;
+		m1 += 8.0*fq;
+		m2 += fq;
+		jy += fq;
+		m6 += fq;
+		jz -= fq;
+		m8 -= fq;
+		m9 -= 2.0*fq;
+		m10 -= 2.0*fq;
+		m14 -= fq;
+		m17 += fq;
+		m18 += fq;
+
+		// q=18
+		fq = dist[17*Np+n];
+		rho += fq;
+		m1 += 8.0*fq;
+		m2 += fq;
+		jy -= fq;
+		m6 -= fq;
+		jz += fq;
+		m8 += fq;
+		m9 -= 2.0*fq;
+		m10 -= 2.0*fq;
+		m14 -= fq;
+		m17 -= fq;
+		m18 -= fq;
+        //---------------------------------------------------------------------//
+
+        porosity = Poros[n];
+        perm = Perm[n];
+
+        c0 = 0.5*(1.0+porosity*0.5*mu_eff/perm);
+        if (porosity==1.0) c0 = 0.5;//i.e. apparent pore nodes
+        GeoFun = 1.75/sqrt(150.0*porosity*porosity*porosity);
+        c1 = porosity*0.5*GeoFun/sqrt(perm);
+        if (porosity==1.0) c1 = 0.0;//i.e. apparent pore nodes
+
+        vx = jx/rho0+0.5*porosity*Gx;
+        vy = jy/rho0+0.5*porosity*Gy;
+        vz = jz/rho0+0.5*porosity*Gz;
+        v_mag=sqrt(vx*vx+vy*vy+vz*vz);
+        ux = vx/(c0+sqrt(c0*c0+c1*v_mag));
+        uy = vy/(c0+sqrt(c0*c0+c1*v_mag));
+        uz = vz/(c0+sqrt(c0*c0+c1*v_mag));
+        u_mag=sqrt(ux*ux+uy*uy+uz*uz);
+
+        //Update the total force to include linear (Darcy) and nonlinear (Forchheimer) drags due to the porous medium
+        Fx = rho0*(-porosity*mu_eff/perm*ux - porosity*GeoFun/sqrt(perm)*u_mag*ux + porosity*Gx);
+        Fy = rho0*(-porosity*mu_eff/perm*uy - porosity*GeoFun/sqrt(perm)*u_mag*uy + porosity*Gy);
+        Fz = rho0*(-porosity*mu_eff/perm*uz - porosity*GeoFun/sqrt(perm)*u_mag*uz + porosity*Gz);
+        if (porosity==1.0){
+            Fx=rho0*Gx;
+            Fy=rho0*Gy;
+            Fz=rho0*Gz;
+        }
+
+        //Calculate pressure for Incompressible-MRT model
+        pressure=rho/3.f;
+
+        //-------------------- IMRT collison where body force has NO higher-order terms -------------//
+		m1 = m1 + rlx_setA*((19*(ux*ux+uy*uy+uz*uz)*rho0/porosity - 11*rho) - m1);
+		m2 = m2 + rlx_setA*((3*rho - 5.5*(ux*ux+uy*uy+uz*uz)*rho0/porosity) - m2);
+        jx = jx + Fx;
+		m4 = m4 + rlx_setB*((-0.6666666666666666*ux*rho0)- m4)
+                + (1-0.5*rlx_setB)*(-0.6666666666666666*Fx);
+        jy = jy + Fy;
+		m6 = m6 + rlx_setB*((-0.6666666666666666*uy*rho0)- m6)
+                + (1-0.5*rlx_setB)*(-0.6666666666666666*Fy);
+        jz = jz + Fz;
+		m8 = m8 + rlx_setB*((-0.6666666666666666*uz*rho0)- m8)
+                + (1-0.5*rlx_setB)*(-0.6666666666666666*Fz);
+		m9 = m9 + rlx_setA*(((2*ux*ux-uy*uy-uz*uz)*rho0/porosity) - m9);
+		m10 = m10 + rlx_setA*( - m10);
+        //m10 = m10 + rlx_setA*(-0.5*rho0*((2*ux*ux-uy*uy-uz*uz)/porosity)- m10);
+		m11 = m11 + rlx_setA*(((uy*uy-uz*uz)*rho0/porosity) - m11);
+		m12 = m12 + rlx_setA*( - m12);
+        //m12 = m12 + rlx_setA*(-0.5*(rho0*(uy*uy-uz*uz)/porosity)- m12);
+		m13 = m13 + rlx_setA*( (ux*uy*rho0/porosity) - m13);
+		m14 = m14 + rlx_setA*( (uy*uz*rho0/porosity) - m14);
+		m15 = m15 + rlx_setA*( (ux*uz*rho0/porosity) - m15);
+		m16 = m16 + rlx_setB*( - m16);
+		m17 = m17 + rlx_setB*( - m17);
+		m18 = m18 + rlx_setB*( - m18);
+        //.......................................................................................................
+
+        //.................inverse transformation......................................................
+        // q=0
+		fq = mrt_V1*rho-mrt_V2*m1+mrt_V3*m2;
+		dist[n] = fq;
+
+		// q = 1
+		fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(jx-m4)+mrt_V6*(m9-m10);
+		dist[1*Np+n] = fq;
+
+		// q=2
+		fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(m4-jx)+mrt_V6*(m9-m10);
+		dist[2*Np+n] = fq;
+
+		// q = 3
+		fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(jy-m6)+mrt_V7*(m10-m9)+mrt_V8*(m11-m12);
+		dist[3*Np+n] = fq;
+
+		// q = 4
+		fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(m6-jy)+mrt_V7*(m10-m9)+mrt_V8*(m11-m12);
+		dist[4*Np+n] = fq;
+
+		// q = 5
+		fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(jz-m8)+mrt_V7*(m10-m9)+mrt_V8*(m12-m11);
+		dist[5*Np+n] = fq;
+
+		// q = 6
+		fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(m8-jz)+mrt_V7*(m10-m9)+mrt_V8*(m12-m11);
+		dist[6*Np+n] = fq;
+
+		// q = 7
+		fq = mrt_V1*rho+mrt_V9*m1+mrt_V10*m2+0.1*(jx+jy)+0.025*(m4+m6)+
+				mrt_V7*m9+mrt_V11*m10+mrt_V8*m11+mrt_V12*m12+0.25*m13+0.125*(m16-m17);
+		dist[7*Np+n] = fq;
+
+
+		// q = 8
+		fq = mrt_V1*rho+mrt_V9*m1+mrt_V10*m2-0.1*(jx+jy)-0.025*(m4+m6) +mrt_V7*m9+mrt_V11*m10+mrt_V8*m11
+				+mrt_V12*m12+0.25*m13+0.125*(m17-m16);
+		dist[8*Np+n] = fq;
+
+		// q = 9
+		fq = mrt_V1*rho+mrt_V9*m1+mrt_V10*m2+0.1*(jx-jy)+0.025*(m4-m6)+
+				mrt_V7*m9+mrt_V11*m10+mrt_V8*m11+mrt_V12*m12-0.25*m13+0.125*(m16+m17);
+		dist[9*Np+n] = fq;
+
+		// q = 10
+		fq = mrt_V1*rho+mrt_V9*m1+mrt_V10*m2+0.1*(jy-jx)+0.025*(m6-m4)+
+				mrt_V7*m9+mrt_V11*m10+mrt_V8*m11+mrt_V12*m12-0.25*m13-0.125*(m16+m17);
+		dist[10*Np+n] = fq;
+
+
+		// q = 11
+		fq = mrt_V1*rho+mrt_V9*m1
+				+mrt_V10*m2+0.1*(jx+jz)+0.025*(m4+m8)
+				+mrt_V7*m9+mrt_V11*m10-mrt_V8*m11
+				-mrt_V12*m12+0.25*m15+0.125*(m18-m16);
+		dist[11*Np+n] = fq;
+
+		// q = 12
+		fq = mrt_V1*rho+mrt_V9*m1+mrt_V10*m2-0.1*(jx+jz)-0.025*(m4+m8)+
+				mrt_V7*m9+mrt_V11*m10-mrt_V8*m11-mrt_V12*m12+0.25*m15+0.125*(m16-m18);
+		dist[12*Np+n] = fq;
+
+		// q = 13
+		fq = mrt_V1*rho+mrt_V9*m1
+				+mrt_V10*m2+0.1*(jx-jz)+0.025*(m4-m8)
+				+mrt_V7*m9+mrt_V11*m10-mrt_V8*m11
+				-mrt_V12*m12-0.25*m15-0.125*(m16+m18);
+		dist[13*Np+n] = fq;
+
+		// q= 14
+		fq = mrt_V1*rho+mrt_V9*m1
+				+mrt_V10*m2+0.1*(jz-jx)+0.025*(m8-m4)
+				+mrt_V7*m9+mrt_V11*m10-mrt_V8*m11
+				-mrt_V12*m12-0.25*m15+0.125*(m16+m18);
+
+		dist[14*Np+n] = fq;
+
+		// q = 15
+		fq = mrt_V1*rho+mrt_V9*m1
+				+mrt_V10*m2+0.1*(jy+jz)+0.025*(m6+m8)
+				-mrt_V6*m9-mrt_V7*m10+0.25*m14+0.125*(m17-m18);
+		dist[15*Np+n] = fq;
+
+		// q = 16
+		fq =  mrt_V1*rho+mrt_V9*m1
+				+mrt_V10*m2-0.1*(jy+jz)-0.025*(m6+m8)
+				-mrt_V6*m9-mrt_V7*m10+0.25*m14+0.125*(m18-m17);
+		dist[16*Np+n] = fq;
+
+
+		// q = 17
+		fq = mrt_V1*rho+mrt_V9*m1
+				+mrt_V10*m2+0.1*(jy-jz)+0.025*(m6-m8)
+				-mrt_V6*m9-mrt_V7*m10-0.25*m14+0.125*(m17+m18);
+		dist[17*Np+n] = fq;
+
+		// q = 18
+		fq = mrt_V1*rho+mrt_V9*m1
+				+mrt_V10*m2+0.1*(jz-jy)+0.025*(m8-m6)
+				-mrt_V6*m9-mrt_V7*m10-0.25*m14-0.125*(m17+m18);
+		dist[18*Np+n] = fq;
+        //........................................................................
+
+        //Update velocity on device
+        Velocity[0*Np+n] = ux;
+        Velocity[1*Np+n] = uy;
+        Velocity[2*Np+n] = uz;
+        //Update pressure on device
+        Pressure[n] = pressure;
+	}
+}
+
+
+extern "C" void ScaLBL_D3Q19_GreyIMRT_Init(double *dist, int Np, double Den)
+{
+	int n;
+	for (n=0; n<Np; n++){
+		dist[n] = Den - 0.6666666666666667;
+		dist[Np+n] = 0.055555555555555555;		//double(100*n)+1.f;
+		dist[2*Np+n] = 0.055555555555555555;	//double(100*n)+2.f;
+		dist[3*Np+n] = 0.055555555555555555;	//double(100*n)+3.f;
+		dist[4*Np+n] = 0.055555555555555555;	//double(100*n)+4.f;
+		dist[5*Np+n] = 0.055555555555555555;	//double(100*n)+5.f;
+		dist[6*Np+n] = 0.055555555555555555;	//double(100*n)+6.f;
+		dist[7*Np+n] = 0.0277777777777778;   //double(100*n)+7.f;
+		dist[8*Np+n] = 0.0277777777777778;   //double(100*n)+8.f;
+		dist[9*Np+n] = 0.0277777777777778;   //double(100*n)+9.f;
+		dist[10*Np+n] = 0.0277777777777778;  //double(100*n)+10.f;
+		dist[11*Np+n] = 0.0277777777777778;  //double(100*n)+11.f;
+		dist[12*Np+n] = 0.0277777777777778;  //double(100*n)+12.f;
+		dist[13*Np+n] = 0.0277777777777778;  //double(100*n)+13.f;
+		dist[14*Np+n] = 0.0277777777777778;  //double(100*n)+14.f;
+		dist[15*Np+n] = 0.0277777777777778;  //double(100*n)+15.f;
+		dist[16*Np+n] = 0.0277777777777778;  //double(100*n)+16.f;
+		dist[17*Np+n] = 0.0277777777777778;  //double(100*n)+17.f;
+		dist[18*Np+n] = 0.0277777777777778;  //double(100*n)+18.f;
+	}
+}
+
diff --git a/cpu/GreyscaleColor.cpp b/cpu/GreyscaleColor.cpp
new file mode 100644
index 00000000..48f84e09
--- /dev/null
+++ b/cpu/GreyscaleColor.cpp
@@ -0,0 +1,1366 @@
+#include <math.h>
+
+extern "C" void ScaLBL_D3Q19_AAodd_GreyscaleColor(int *neighborList, int *Map, double *dist, double *Aq, double *Bq, double *Den, 
+		double *Phi, double *GreySolidGrad, double *Poros,double *Perm,double *Velocity, 
+        double rhoA, double rhoB, double tauA, double tauB, double tauA_eff,double tauB_eff, double alpha, double beta,
+		double Gx, double Gy, double Gz, int strideY, int strideZ, int start, int finish, int Np){
+
+	int n,nn,ijk,nread;
+	int nr1,nr2,nr3,nr4,nr5,nr6;
+	int nr7,nr8,nr9,nr10;
+	int nr11,nr12,nr13,nr14;
+	//int nr15,nr16,nr17,nr18;
+	double fq;
+	// conserved momemnts
+	double rho,jx,jy,jz;
+	double vx,vy,vz,v_mag;
+    double ux,uy,uz,u_mag;
+	// non-conserved moments
+	double m1,m2,m4,m6,m8,m9,m10,m11,m12,m13,m14,m15,m16,m17,m18;
+	double m3,m5,m7;
+	double nA,nB; // number density
+	double a1,b1,a2,b2,nAB,delta;
+	double C,nx,ny,nz; //color gradient magnitude and direction
+	double phi,tau,rho0,rlx_setA,rlx_setB;
+
+    double GeoFun=0.0;//geometric function from Guo's PRE 66, 036304 (2002)
+    double porosity;
+    double perm;//voxel permeability
+    double c0, c1; //Guo's model parameters
+    double tau_eff;
+    double mu_eff;//kinematic viscosity
+    double nx_gs,ny_gs,nz_gs;//grey-solid color gradient
+    double Fx,Fy,Fz;
+
+	const double mrt_V1=0.05263157894736842;
+	const double mrt_V2=0.012531328320802;
+	const double mrt_V3=0.04761904761904762;
+	const double mrt_V4=0.004594820384294068;
+	const double mrt_V5=0.01587301587301587;
+	const double mrt_V6=0.0555555555555555555555555;
+	const double mrt_V7=0.02777777777777778;
+	const double mrt_V8=0.08333333333333333;
+	const double mrt_V9=0.003341687552213868;
+	const double mrt_V10=0.003968253968253968;
+	const double mrt_V11=0.01388888888888889;
+	const double mrt_V12=0.04166666666666666;
+
+	for (n=start; n<finish; n++){
+		// read the component number densities
+		nA = Den[n];
+		nB = Den[Np + n];
+        porosity = Poros[n];
+        perm = Perm[n];
+        nx_gs = GreySolidGrad[n+0*Np];
+        ny_gs = GreySolidGrad[n+1*Np];
+        nz_gs = GreySolidGrad[n+2*Np];
+
+		// compute phase indicator field
+		phi=(nA-nB)/(nA+nB);
+
+		// local density
+		rho0=rhoA + 0.5*(1.0-phi)*(rhoB-rhoA);
+		// local relaxation time
+		tau=tauA + 0.5*(1.0-phi)*(tauB-tauA);
+		tau_eff=tauA_eff + 0.5*(1.0-phi)*(tauB_eff-tauA_eff);
+		rlx_setA = 1.f/tau;
+		rlx_setB = 8.f*(2.f-rlx_setA)/(8.f-rlx_setA);
+        mu_eff = (tau_eff-0.5)/3.0;//kinematic viscosity
+		
+		// Get the 1D index based on regular data layout
+		ijk = Map[n];
+		//					COMPUTE THE COLOR GRADIENT
+		//........................................................................
+		//.................Read Phase Indicator Values............................
+		//........................................................................
+		nn = ijk-1;							// neighbor index (get convention)
+		m1 = Phi[nn];						// get neighbor for phi - 1
+		//........................................................................
+		nn = ijk+1;							// neighbor index (get convention)
+		m2 = Phi[nn];						// get neighbor for phi - 2
+		//........................................................................
+		nn = ijk-strideY;							// neighbor index (get convention)
+		m3 = Phi[nn];					// get neighbor for phi - 3
+		//........................................................................
+		nn = ijk+strideY;							// neighbor index (get convention)
+		m4 = Phi[nn];					// get neighbor for phi - 4
+		//........................................................................
+		nn = ijk-strideZ;						// neighbor index (get convention)
+		m5 = Phi[nn];					// get neighbor for phi - 5
+		//........................................................................
+		nn = ijk+strideZ;						// neighbor index (get convention)
+		m6 = Phi[nn];					// get neighbor for phi - 6
+		//........................................................................
+		nn = ijk-strideY-1;						// neighbor index (get convention)
+		m7 = Phi[nn];					// get neighbor for phi - 7
+		//........................................................................
+		nn = ijk+strideY+1;						// neighbor index (get convention)
+		m8 = Phi[nn];					// get neighbor for phi - 8
+		//........................................................................
+		nn = ijk+strideY-1;						// neighbor index (get convention)
+		m9 = Phi[nn];					// get neighbor for phi - 9
+		//........................................................................
+		nn = ijk-strideY+1;						// neighbor index (get convention)
+		m10 = Phi[nn];					// get neighbor for phi - 10
+		//........................................................................
+		nn = ijk-strideZ-1;						// neighbor index (get convention)
+		m11 = Phi[nn];					// get neighbor for phi - 11
+		//........................................................................
+		nn = ijk+strideZ+1;						// neighbor index (get convention)
+		m12 = Phi[nn];					// get neighbor for phi - 12
+		//........................................................................
+		nn = ijk+strideZ-1;						// neighbor index (get convention)
+		m13 = Phi[nn];					// get neighbor for phi - 13
+		//........................................................................
+		nn = ijk-strideZ+1;						// neighbor index (get convention)
+		m14 = Phi[nn];					// get neighbor for phi - 14
+		//........................................................................
+		nn = ijk-strideZ-strideY;					// neighbor index (get convention)
+		m15 = Phi[nn];					// get neighbor for phi - 15
+		//........................................................................
+		nn = ijk+strideZ+strideY;					// neighbor index (get convention)
+		m16 = Phi[nn];					// get neighbor for phi - 16
+		//........................................................................
+		nn = ijk+strideZ-strideY;					// neighbor index (get convention)
+		m17 = Phi[nn];					// get neighbor for phi - 17
+		//........................................................................
+		nn = ijk-strideZ+strideY;					// neighbor index (get convention)
+		m18 = Phi[nn];					// get neighbor for phi - 18
+		//............Compute the Color Gradient...................................
+		nx = -(m1-m2+0.5*(m7-m8+m9-m10+m11-m12+m13-m14));
+		ny = -(m3-m4+0.5*(m7-m8-m9+m10+m15-m16+m17-m18));
+		nz = -(m5-m6+0.5*(m11-m12-m13+m14+m15-m16-m17+m18));
+        //correct the normal color gradient by considering the effect of grey solid
+        nx += (1.0-porosity)*nx_gs; 
+        ny += (1.0-porosity)*ny_gs; 
+        nz += (1.0-porosity)*nz_gs; 
+
+		//...........Normalize the Color Gradient.................................
+		C = sqrt(nx*nx+ny*ny+nz*nz);
+		double ColorMag = C;
+		if (C==0.0) ColorMag=1.0;
+		nx = nx/ColorMag;
+		ny = ny/ColorMag;
+		nz = nz/ColorMag;		
+
+		// q=0
+		fq = dist[n];
+		rho = fq;
+		m1  = -30.0*fq;
+		m2  = 12.0*fq;
+
+		// q=1
+		//nread = neighborList[n]; // neighbor 2 
+		//fq = dist[nread]; // reading the f1 data into register fq		
+		nr1 = neighborList[n]; 
+		fq = dist[nr1]; // reading the f1 data into register fq
+		rho += fq;
+		m1 -= 11.0*fq;
+		m2 -= 4.0*fq;
+		jx = fq;
+		m4 = -4.0*fq;
+		m9 = 2.0*fq;
+		m10 = -4.0*fq;
+
+		// f2 = dist[10*Np+n];
+		//nread = neighborList[n+Np]; // neighbor 1 ( < 10Np => even part of dist)
+		//fq = dist[nread];  // reading the f2 data into register fq
+		nr2 = neighborList[n+Np]; // neighbor 1 ( < 10Np => even part of dist)
+		fq = dist[nr2];  // reading the f2 data into register fq
+		rho += fq;
+		m1 -= 11.0*(fq);
+		m2 -= 4.0*(fq);
+		jx -= fq;
+		m4 += 4.0*(fq);
+		m9 += 2.0*(fq);
+		m10 -= 4.0*(fq);
+
+		// q=3
+		//nread = neighborList[n+2*Np]; // neighbor 4
+		//fq = dist[nread];
+		nr3 = neighborList[n+2*Np]; // neighbor 4
+		fq = dist[nr3];
+		rho += fq;
+		m1 -= 11.0*fq;
+		m2 -= 4.0*fq;
+		jy = fq;
+		m6 = -4.0*fq;
+		m9 -= fq;
+		m10 += 2.0*fq;
+		m11 = fq;
+		m12 = -2.0*fq;
+
+		// q = 4
+		//nread = neighborList[n+3*Np]; // neighbor 3
+		//fq = dist[nread];
+		nr4 = neighborList[n+3*Np]; // neighbor 3
+		fq = dist[nr4];
+		rho+= fq;
+		m1 -= 11.0*fq;
+		m2 -= 4.0*fq;
+		jy -= fq;
+		m6 += 4.0*fq;
+		m9 -= fq;
+		m10 += 2.0*fq;
+		m11 += fq;
+		m12 -= 2.0*fq;
+
+		// q=5
+		//nread = neighborList[n+4*Np];
+		//fq = dist[nread];
+		nr5 = neighborList[n+4*Np];
+		fq = dist[nr5];
+		rho += fq;
+		m1 -= 11.0*fq;
+		m2 -= 4.0*fq;
+		jz = fq;
+		m8 = -4.0*fq;
+		m9 -= fq;
+		m10 += 2.0*fq;
+		m11 -= fq;
+		m12 += 2.0*fq;
+
+
+		// q = 6
+		//nread = neighborList[n+5*Np];
+		//fq = dist[nread];
+		nr6 = neighborList[n+5*Np];
+		fq = dist[nr6];
+		rho+= fq;
+		m1 -= 11.0*fq;
+		m2 -= 4.0*fq;
+		jz -= fq;
+		m8 += 4.0*fq;
+		m9 -= fq;
+		m10 += 2.0*fq;
+		m11 -= fq;
+		m12 += 2.0*fq;
+
+		// q=7
+		//nread = neighborList[n+6*Np];
+		//fq = dist[nread];
+		nr7 = neighborList[n+6*Np];
+		fq = dist[nr7];
+		rho += fq;
+		m1 += 8.0*fq;
+		m2 += fq;
+		jx += fq;
+		m4 += fq;
+		jy += fq;
+		m6 += fq;
+		m9  += fq;
+		m10 += fq;
+		m11 += fq;
+		m12 += fq;
+		m13 = fq;
+		m16 = fq;
+		m17 = -fq;
+
+		// q = 8
+		//nread = neighborList[n+7*Np];
+		//fq = dist[nread];
+		nr8 = neighborList[n+7*Np];
+		fq = dist[nr8];
+		rho += fq;
+		m1 += 8.0*fq;
+		m2 += fq;
+		jx -= fq;
+		m4 -= fq;
+		jy -= fq;
+		m6 -= fq;
+		m9 += fq;
+		m10 += fq;
+		m11 += fq;
+		m12 += fq;
+		m13 += fq;
+		m16 -= fq;
+		m17 += fq;
+
+		// q=9
+		//nread = neighborList[n+8*Np];
+		//fq = dist[nread];
+		nr9 = neighborList[n+8*Np];
+		fq = dist[nr9];
+		rho += fq;
+		m1 += 8.0*fq;
+		m2 += fq;
+		jx += fq;
+		m4 += fq;
+		jy -= fq;
+		m6 -= fq;
+		m9 += fq;
+		m10 += fq;
+		m11 += fq;
+		m12 += fq;
+		m13 -= fq;
+		m16 += fq;
+		m17 += fq;
+
+		// q = 10
+		//nread = neighborList[n+9*Np];
+		//fq = dist[nread];
+		nr10 = neighborList[n+9*Np];
+		fq = dist[nr10];
+		rho += fq;
+		m1 += 8.0*fq;
+		m2 += fq;
+		jx -= fq;
+		m4 -= fq;
+		jy += fq;
+		m6 += fq;
+		m9 += fq;
+		m10 += fq;
+		m11 += fq;
+		m12 += fq;
+		m13 -= fq;
+		m16 -= fq;
+		m17 -= fq;
+
+		// q=11
+		//nread = neighborList[n+10*Np];
+		//fq = dist[nread];
+		nr11 = neighborList[n+10*Np];
+		fq = dist[nr11];
+		rho += fq;
+		m1 += 8.0*fq;
+		m2 += fq;
+		jx += fq;
+		m4 += fq;
+		jz += fq;
+		m8 += fq;
+		m9 += fq;
+		m10 += fq;
+		m11 -= fq;
+		m12 -= fq;
+		m15 = fq;
+		m16 -= fq;
+		m18 = fq;
+
+		// q=12
+		//nread = neighborList[n+11*Np];
+		//fq = dist[nread];
+		nr12 = neighborList[n+11*Np];
+		fq = dist[nr12];
+		rho += fq;
+		m1 += 8.0*fq;
+		m2 += fq;
+		jx -= fq;
+		m4 -= fq;
+		jz -= fq;
+		m8 -= fq;
+		m9 += fq;
+		m10 += fq;
+		m11 -= fq;
+		m12 -= fq;
+		m15 += fq;
+		m16 += fq;
+		m18 -= fq;
+
+		// q=13
+		//nread = neighborList[n+12*Np];
+		//fq = dist[nread];
+		nr13 = neighborList[n+12*Np];
+		fq = dist[nr13];
+		rho += fq;
+		m1 += 8.0*fq;
+		m2 += fq;
+		jx += fq;
+		m4 += fq;
+		jz -= fq;
+		m8 -= fq;
+		m9 += fq;
+		m10 += fq;
+		m11 -= fq;
+		m12 -= fq;
+		m15 -= fq;
+		m16 -= fq;
+		m18 -= fq;
+
+		// q=14
+		//nread = neighborList[n+13*Np];
+		//fq = dist[nread];
+		nr14 = neighborList[n+13*Np];
+		fq = dist[nr14];
+		rho += fq;
+		m1 += 8.0*fq;
+		m2 += fq;
+		jx -= fq;
+		m4 -= fq;
+		jz += fq;
+		m8 += fq;
+		m9 += fq;
+		m10 += fq;
+		m11 -= fq;
+		m12 -= fq;
+		m15 -= fq;
+		m16 += fq;
+		m18 += fq;
+
+		// q=15
+		nread = neighborList[n+14*Np];
+		fq = dist[nread];
+		//fq = dist[17*Np+n];
+		rho += fq;
+		m1 += 8.0*fq;
+		m2 += fq;
+		jy += fq;
+		m6 += fq;
+		jz += fq;
+		m8 += fq;
+		m9 -= 2.0*fq;
+		m10 -= 2.0*fq;
+		m14 = fq;
+		m17 += fq;
+		m18 -= fq;
+
+		// q=16
+		nread = neighborList[n+15*Np];
+		fq = dist[nread];
+		//fq = dist[8*Np+n];
+		rho += fq;
+		m1 += 8.0*fq;
+		m2 += fq;
+		jy -= fq;
+		m6 -= fq;
+		jz -= fq;
+		m8 -= fq;
+		m9 -= 2.0*fq;
+		m10 -= 2.0*fq;
+		m14 += fq;
+		m17 -= fq;
+		m18 += fq;
+
+		// q=17
+		//fq = dist[18*Np+n];
+		nread = neighborList[n+16*Np];
+		fq = dist[nread];
+		rho += fq;
+		m1 += 8.0*fq;
+		m2 += fq;
+		jy += fq;
+		m6 += fq;
+		jz -= fq;
+		m8 -= fq;
+		m9 -= 2.0*fq;
+		m10 -= 2.0*fq;
+		m14 -= fq;
+		m17 += fq;
+		m18 += fq;
+
+		// q=18
+		nread = neighborList[n+17*Np];
+		fq = dist[nread];
+		//fq = dist[9*Np+n];
+		rho += fq;
+		m1 += 8.0*fq;
+		m2 += fq;
+		jy -= fq;
+		m6 -= fq;
+		jz += fq;
+		m8 += fq;
+		m9 -= 2.0*fq;
+		m10 -= 2.0*fq;
+		m14 -= fq;
+		m17 -= fq;
+		m18 -= fq;
+		
+        // Compute greyscale related parameters
+        c0 = 0.5*(1.0+porosity*0.5*mu_eff/perm);
+        if (porosity==1.0) c0 = 0.5;//i.e. apparent pore nodes
+        //GeoFun = 1.75/sqrt(150.0*porosity*porosity*porosity);
+        c1 = porosity*0.5*GeoFun/sqrt(perm);
+        if (porosity==1.0) c1 = 0.0;//i.e. apparent pore nodes
+
+        vx = jx/rho0+0.5*(porosity*Gx);
+        vy = jy/rho0+0.5*(porosity*Gy);
+        vz = jz/rho0+0.5*(porosity*Gz);
+        v_mag=sqrt(vx*vx+vy*vy+vz*vz);
+        ux = vx/(c0+sqrt(c0*c0+c1*v_mag));
+        uy = vy/(c0+sqrt(c0*c0+c1*v_mag));
+        uz = vz/(c0+sqrt(c0*c0+c1*v_mag));
+        u_mag=sqrt(ux*ux+uy*uy+uz*uz);
+
+        //Update the total force to include linear (Darcy) and nonlinear (Forchheimer) drags due to the porous medium
+        Fx = rho0*(-porosity*mu_eff/perm*ux - porosity*GeoFun/sqrt(perm)*u_mag*ux + porosity*Gx);
+        Fy = rho0*(-porosity*mu_eff/perm*uy - porosity*GeoFun/sqrt(perm)*u_mag*uy + porosity*Gy);
+        Fz = rho0*(-porosity*mu_eff/perm*uz - porosity*GeoFun/sqrt(perm)*u_mag*uz + porosity*Gz);
+        if (porosity==1.0){
+            Fx=rho0*(Gx);
+            Fy=rho0*(Gy);
+            Fz=rho0*(Gz);
+        }
+
+		// write the velocity 
+		Velocity[n] = ux;
+		Velocity[Np+n] = uy;
+		Velocity[2*Np+n] = uz;
+
+		//........................................................................
+		//..............carry out relaxation process..............................
+		//..........Toelke, Fruediger et. al. 2006................................
+		if (C == 0.0)	nx = ny = nz = 0.0;
+		m1 = m1 + rlx_setA*((19*(ux*ux+uy*uy+uz*uz)*rho0/porosity - 11*rho) -19*alpha*C - m1);
+		m2 = m2 + rlx_setA*((3*rho - 5.5*(ux*ux+uy*uy+uz*uz)*rho0/porosity)- m2);
+        jx = jx + Fx;
+		m4 = m4 + rlx_setB*((-0.6666666666666666*ux*rho0)- m4)
+                + (1-0.5*rlx_setB)*(-0.6666666666666666*Fx);
+        jy = jy + Fy;
+		m6 = m6 + rlx_setB*((-0.6666666666666666*uy*rho0)- m6)
+                + (1-0.5*rlx_setB)*(-0.6666666666666666*Fy);
+        jz = jz + Fz;
+		m8 = m8 + rlx_setB*((-0.6666666666666666*uz*rho0)- m8)
+                + (1-0.5*rlx_setB)*(-0.6666666666666666*Fz);
+		m9 = m9 + rlx_setA*(((2*ux*ux-uy*uy-uz*uz)*rho0/porosity) + 0.5*alpha*C*(2*nx*nx-ny*ny-nz*nz) - m9);
+		m10 = m10 + rlx_setA*( - m10);
+        //m10 = m10 + rlx_setA*(-0.5*rho0*((2*ux*ux-uy*uy-uz*uz)/porosity)- m10);
+		m11 = m11 + rlx_setA*(((uy*uy-uz*uz)*rho0/porosity) + 0.5*alpha*C*(ny*ny-nz*nz)- m11);
+		m12 = m12 + rlx_setA*( - m12);
+        //m12 = m12 + rlx_setA*(-0.5*(rho0*(uy*uy-uz*uz)/porosity)- m12);
+		m13 = m13 + rlx_setA*( (ux*uy*rho0/porosity) + 0.5*alpha*C*nx*ny - m13);
+		m14 = m14 + rlx_setA*( (uy*uz*rho0/porosity) + 0.5*alpha*C*ny*nz - m14);
+		m15 = m15 + rlx_setA*( (ux*uz*rho0/porosity) + 0.5*alpha*C*nx*nz - m15);
+		m16 = m16 + rlx_setB*( - m16);
+		m17 = m17 + rlx_setB*( - m17);
+		m18 = m18 + rlx_setB*( - m18);
+
+		//.................inverse transformation......................................................
+		// q=0
+		fq = mrt_V1*rho-mrt_V2*m1+mrt_V3*m2;
+		dist[n] = fq;
+
+		// q = 1
+		fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(jx-m4)+mrt_V6*(m9-m10);
+		//nread = neighborList[n+Np];
+		dist[nr2] = fq;
+
+		// q=2
+		fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(m4-jx)+mrt_V6*(m9-m10);
+		//nread = neighborList[n];
+		dist[nr1] = fq;
+
+		// q = 3
+		fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(jy-m6)+mrt_V7*(m10-m9)+mrt_V8*(m11-m12);
+		//nread = neighborList[n+3*Np];
+		dist[nr4] = fq;
+
+		// q = 4
+		fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(m6-jy)+mrt_V7*(m10-m9)+mrt_V8*(m11-m12);
+		//nread = neighborList[n+2*Np];
+		dist[nr3] = fq;
+
+		// q = 5
+		fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(jz-m8)+mrt_V7*(m10-m9)+mrt_V8*(m12-m11);
+		//nread = neighborList[n+5*Np];
+		dist[nr6] = fq;
+
+		// q = 6
+		fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(m8-jz)+mrt_V7*(m10-m9)+mrt_V8*(m12-m11);
+		//nread = neighborList[n+4*Np];
+		dist[nr5] = fq;
+
+		// q = 7
+		fq = mrt_V1*rho+mrt_V9*m1+mrt_V10*m2+0.1*(jx+jy)+0.025*(m4+m6)+
+				mrt_V7*m9+mrt_V11*m10+mrt_V8*m11+mrt_V12*m12+0.25*m13+0.125*(m16-m17);
+		//nread = neighborList[n+7*Np];
+		dist[nr8] = fq;
+
+		// q = 8
+		fq = mrt_V1*rho+mrt_V9*m1+mrt_V10*m2-0.1*(jx+jy)-0.025*(m4+m6) +mrt_V7*m9+mrt_V11*m10+mrt_V8*m11
+				+mrt_V12*m12+0.25*m13+0.125*(m17-m16);
+		//nread = neighborList[n+6*Np];
+		dist[nr7] = fq;
+
+		// q = 9
+		fq = mrt_V1*rho+mrt_V9*m1+mrt_V10*m2+0.1*(jx-jy)+0.025*(m4-m6)+
+				mrt_V7*m9+mrt_V11*m10+mrt_V8*m11+mrt_V12*m12-0.25*m13+0.125*(m16+m17);
+		//nread = neighborList[n+9*Np];
+		dist[nr10] = fq;
+
+		// q = 10
+		fq = mrt_V1*rho+mrt_V9*m1+mrt_V10*m2+0.1*(jy-jx)+0.025*(m6-m4)+
+				mrt_V7*m9+mrt_V11*m10+mrt_V8*m11+mrt_V12*m12-0.25*m13-0.125*(m16+m17);
+		//nread = neighborList[n+8*Np];
+		dist[nr9] = fq;
+
+		// q = 11
+		fq = mrt_V1*rho+mrt_V9*m1
+				+mrt_V10*m2+0.1*(jx+jz)+0.025*(m4+m8)
+				+mrt_V7*m9+mrt_V11*m10-mrt_V8*m11
+				-mrt_V12*m12+0.25*m15+0.125*(m18-m16);
+		//nread = neighborList[n+11*Np];
+		dist[nr12] = fq;
+
+		// q = 12
+		fq = mrt_V1*rho+mrt_V9*m1+mrt_V10*m2-0.1*(jx+jz)-0.025*(m4+m8)+
+				mrt_V7*m9+mrt_V11*m10-mrt_V8*m11-mrt_V12*m12+0.25*m15+0.125*(m16-m18);
+		//nread = neighborList[n+10*Np];
+		dist[nr11]= fq;
+
+		// q = 13
+		fq = mrt_V1*rho+mrt_V9*m1
+				+mrt_V10*m2+0.1*(jx-jz)+0.025*(m4-m8)
+				+mrt_V7*m9+mrt_V11*m10-mrt_V8*m11
+				-mrt_V12*m12-0.25*m15-0.125*(m16+m18);
+		//nread = neighborList[n+13*Np];
+		dist[nr14] = fq;
+
+		// q= 14
+		fq = mrt_V1*rho+mrt_V9*m1
+				+mrt_V10*m2+0.1*(jz-jx)+0.025*(m8-m4)
+				+mrt_V7*m9+mrt_V11*m10-mrt_V8*m11
+				-mrt_V12*m12-0.25*m15+0.125*(m16+m18);
+		//nread = neighborList[n+12*Np];
+		dist[nr13] = fq;
+
+
+		// q = 15
+		fq = mrt_V1*rho+mrt_V9*m1
+				+mrt_V10*m2+0.1*(jy+jz)+0.025*(m6+m8)
+				-mrt_V6*m9-mrt_V7*m10+0.25*m14+0.125*(m17-m18);
+		nread = neighborList[n+15*Np];
+		dist[nread] = fq;
+
+		// q = 16
+		fq =  mrt_V1*rho+mrt_V9*m1
+				+mrt_V10*m2-0.1*(jy+jz)-0.025*(m6+m8)
+				-mrt_V6*m9-mrt_V7*m10+0.25*m14+0.125*(m18-m17);
+		nread = neighborList[n+14*Np];
+		dist[nread] = fq;
+
+
+		// q = 17
+		fq = mrt_V1*rho+mrt_V9*m1
+				+mrt_V10*m2+0.1*(jy-jz)+0.025*(m6-m8)
+				-mrt_V6*m9-mrt_V7*m10-0.25*m14+0.125*(m17+m18);
+		nread = neighborList[n+17*Np];
+		dist[nread] = fq;
+
+		// q = 18
+		fq = mrt_V1*rho+mrt_V9*m1
+				+mrt_V10*m2+0.1*(jz-jy)+0.025*(m8-m6)
+				-mrt_V6*m9-mrt_V7*m10-0.25*m14-0.125*(m17+m18);
+		nread = neighborList[n+16*Np];
+		dist[nread] = fq;
+		//........................................................................
+
+		// Instantiate mass transport distributions
+		// Stationary value - distribution 0
+		nAB = 1.0/(nA+nB);
+		Aq[n] = 0.3333333333333333*nA;
+		Bq[n] = 0.3333333333333333*nB;
+
+		//...............................................
+		// q = 0,2,4
+		// Cq = {1,0,0}, {0,1,0}, {0,0,1}
+		delta = beta*nA*nB*nAB*0.1111111111111111*nx;
+		if (!(nA*nB*nAB>0)) delta=0;
+		a1 = nA*(0.1111111111111111*(1+4.5*ux))+delta;
+		b1 = nB*(0.1111111111111111*(1+4.5*ux))-delta;
+		a2 = nA*(0.1111111111111111*(1-4.5*ux))-delta;
+		b2 = nB*(0.1111111111111111*(1-4.5*ux))+delta;
+
+		// q = 1
+		//nread = neighborList[n+Np];
+		Aq[nr2] = a1;
+		Bq[nr2] = b1;
+		// q=2
+		//nread = neighborList[n];
+		Aq[nr1] = a2;
+		Bq[nr1] = b2;
+
+		//...............................................
+		// Cq = {0,1,0}
+		delta = beta*nA*nB*nAB*0.1111111111111111*ny;
+		if (!(nA*nB*nAB>0)) delta=0;
+		a1 = nA*(0.1111111111111111*(1+4.5*uy))+delta;
+		b1 = nB*(0.1111111111111111*(1+4.5*uy))-delta;
+		a2 = nA*(0.1111111111111111*(1-4.5*uy))-delta;
+		b2 = nB*(0.1111111111111111*(1-4.5*uy))+delta;
+
+		// q = 3
+		//nread = neighborList[n+3*Np];
+		Aq[nr4] = a1;
+		Bq[nr4] = b1;
+		// q = 4
+		//nread = neighborList[n+2*Np];
+		Aq[nr3] = a2;
+		Bq[nr3] = b2;
+
+		//...............................................
+		// q = 4
+		// Cq = {0,0,1}
+		delta = beta*nA*nB*nAB*0.1111111111111111*nz;
+		if (!(nA*nB*nAB>0)) delta=0;
+		a1 = nA*(0.1111111111111111*(1+4.5*uz))+delta;
+		b1 = nB*(0.1111111111111111*(1+4.5*uz))-delta;
+		a2 = nA*(0.1111111111111111*(1-4.5*uz))-delta;
+		b2 = nB*(0.1111111111111111*(1-4.5*uz))+delta;
+
+		// q = 5
+		//nread = neighborList[n+5*Np];
+		Aq[nr6] = a1;
+		Bq[nr6] = b1;
+		// q = 6
+		//nread = neighborList[n+4*Np];
+		Aq[nr5] = a2;
+		Bq[nr5] = b2;
+		//...............................................
+	}
+}
+
+extern "C" void ScaLBL_D3Q19_AAeven_GreyscaleColor(int *Map, double *dist, double *Aq, double *Bq, double *Den, 
+        double *Phi,double *GreySolidGrad, double *Poros,double *Perm,double *Velocity, 
+        double rhoA, double rhoB, double tauA, double tauB,double tauA_eff,double tauB_eff, double alpha, double beta,
+		double Gx, double Gy, double Gz, int strideY, int strideZ, int start, int finish, int Np){
+
+	int ijk,nn,n;
+	double fq;
+	// conserved momemnts
+	double rho,jx,jy,jz;
+	double vx,vy,vz,v_mag;
+    double ux,uy,uz,u_mag;
+	// non-conserved moments
+	double m1,m2,m4,m6,m8,m9,m10,m11,m12,m13,m14,m15,m16,m17,m18;
+	double m3,m5,m7;
+	double nA,nB; // number density
+	double a1,b1,a2,b2,nAB,delta;
+	double C,nx,ny,nz; //color gradient magnitude and direction
+	double phi,tau,rho0,rlx_setA,rlx_setB;
+
+    double GeoFun=0.0;//geometric function from Guo's PRE 66, 036304 (2002)
+    double porosity;
+    double perm;//voxel permeability
+    double c0, c1; //Guo's model parameters
+    double tau_eff;
+    double mu_eff;//kinematic viscosity
+    double nx_gs,ny_gs,nz_gs;//grey-solid color gradient
+    double Fx,Fy,Fz;
+
+	const double mrt_V1=0.05263157894736842;
+	const double mrt_V2=0.012531328320802;
+	const double mrt_V3=0.04761904761904762;
+	const double mrt_V4=0.004594820384294068;
+	const double mrt_V5=0.01587301587301587;
+	const double mrt_V6=0.0555555555555555555555555;
+	const double mrt_V7=0.02777777777777778;
+	const double mrt_V8=0.08333333333333333;
+	const double mrt_V9=0.003341687552213868;
+	const double mrt_V10=0.003968253968253968;
+	const double mrt_V11=0.01388888888888889;
+	const double mrt_V12=0.04166666666666666;
+
+	for (n=start; n<finish; n++){
+
+		// read the component number densities
+		nA = Den[n];
+		nB = Den[Np + n];
+        porosity = Poros[n];
+        perm = Perm[n];
+        nx_gs = GreySolidGrad[n+0*Np];
+        ny_gs = GreySolidGrad[n+1*Np];
+        nz_gs = GreySolidGrad[n+2*Np];
+
+		// compute phase indicator field
+		phi=(nA-nB)/(nA+nB);
+
+		// local density
+		rho0=rhoA + 0.5*(1.0-phi)*(rhoB-rhoA);
+		// local relaxation time
+		tau=tauA + 0.5*(1.0-phi)*(tauB-tauA);
+		tau_eff=tauA_eff + 0.5*(1.0-phi)*(tauB_eff-tauA_eff);
+		rlx_setA = 1.f/tau;
+		rlx_setB = 8.f*(2.f-rlx_setA)/(8.f-rlx_setA);
+        mu_eff = (tau_eff-0.5)/3.0;//kinematic viscosity
+
+		// Get the 1D index based on regular data layout
+		ijk = Map[n];
+		//					COMPUTE THE COLOR GRADIENT
+		//........................................................................
+		//.................Read Phase Indicator Values............................
+		//........................................................................
+		nn = ijk-1;							// neighbor index (get convention)
+		m1 = Phi[nn];						// get neighbor for phi - 1
+		//........................................................................
+		nn = ijk+1;							// neighbor index (get convention)
+		m2 = Phi[nn];						// get neighbor for phi - 2
+		//........................................................................
+		nn = ijk-strideY;							// neighbor index (get convention)
+		m3 = Phi[nn];					// get neighbor for phi - 3
+		//........................................................................
+		nn = ijk+strideY;							// neighbor index (get convention)
+		m4 = Phi[nn];					// get neighbor for phi - 4
+		//........................................................................
+		nn = ijk-strideZ;						// neighbor index (get convention)
+		m5 = Phi[nn];					// get neighbor for phi - 5
+		//........................................................................
+		nn = ijk+strideZ;						// neighbor index (get convention)
+		m6 = Phi[nn];					// get neighbor for phi - 6
+		//........................................................................
+		nn = ijk-strideY-1;						// neighbor index (get convention)
+		m7 = Phi[nn];					// get neighbor for phi - 7
+		//........................................................................
+		nn = ijk+strideY+1;						// neighbor index (get convention)
+		m8 = Phi[nn];					// get neighbor for phi - 8
+		//........................................................................
+		nn = ijk+strideY-1;						// neighbor index (get convention)
+		m9 = Phi[nn];					// get neighbor for phi - 9
+		//........................................................................
+		nn = ijk-strideY+1;						// neighbor index (get convention)
+		m10 = Phi[nn];					// get neighbor for phi - 10
+		//........................................................................
+		nn = ijk-strideZ-1;						// neighbor index (get convention)
+		m11 = Phi[nn];					// get neighbor for phi - 11
+		//........................................................................
+		nn = ijk+strideZ+1;						// neighbor index (get convention)
+		m12 = Phi[nn];					// get neighbor for phi - 12
+		//........................................................................
+		nn = ijk+strideZ-1;						// neighbor index (get convention)
+		m13 = Phi[nn];					// get neighbor for phi - 13
+		//........................................................................
+		nn = ijk-strideZ+1;						// neighbor index (get convention)
+		m14 = Phi[nn];					// get neighbor for phi - 14
+		//........................................................................
+		nn = ijk-strideZ-strideY;					// neighbor index (get convention)
+		m15 = Phi[nn];					// get neighbor for phi - 15
+		//........................................................................
+		nn = ijk+strideZ+strideY;					// neighbor index (get convention)
+		m16 = Phi[nn];					// get neighbor for phi - 16
+		//........................................................................
+		nn = ijk+strideZ-strideY;					// neighbor index (get convention)
+		m17 = Phi[nn];					// get neighbor for phi - 17
+		//........................................................................
+		nn = ijk-strideZ+strideY;					// neighbor index (get convention)
+		m18 = Phi[nn];					// get neighbor for phi - 18
+		//............Compute the Color Gradient...................................
+		nx = -(m1-m2+0.5*(m7-m8+m9-m10+m11-m12+m13-m14));
+		ny = -(m3-m4+0.5*(m7-m8-m9+m10+m15-m16+m17-m18));
+		nz = -(m5-m6+0.5*(m11-m12-m13+m14+m15-m16-m17+m18));
+        //correct the normal color gradient by considering the effect of grey solid
+        nx += (1.0-porosity)*nx_gs; 
+        ny += (1.0-porosity)*ny_gs; 
+        nz += (1.0-porosity)*nz_gs; 
+
+		//...........Normalize the Color Gradient.................................
+		C = sqrt(nx*nx+ny*ny+nz*nz);
+		double ColorMag = C;
+		if (C==0.0) ColorMag=1.0;
+		nx = nx/ColorMag;
+		ny = ny/ColorMag;
+		nz = nz/ColorMag;		
+
+		// q=0
+		fq = dist[n];
+		rho = fq;
+		m1  = -30.0*fq;
+		m2  = 12.0*fq;
+
+		// q=1
+		fq = dist[2*Np+n];
+		rho += fq;
+		m1 -= 11.0*fq;
+		m2 -= 4.0*fq;
+		jx = fq;
+		m4 = -4.0*fq;
+		m9 = 2.0*fq;
+		m10 = -4.0*fq;
+
+		// f2 = dist[10*Np+n];
+		fq = dist[1*Np+n];
+		rho += fq;
+		m1 -= 11.0*(fq);
+		m2 -= 4.0*(fq);
+		jx -= fq;
+		m4 += 4.0*(fq);
+		m9 += 2.0*(fq);
+		m10 -= 4.0*(fq);
+
+		// q=3
+		fq = dist[4*Np+n];
+		rho += fq;
+		m1 -= 11.0*fq;
+		m2 -= 4.0*fq;
+		jy = fq;
+		m6 = -4.0*fq;
+		m9 -= fq;
+		m10 += 2.0*fq;
+		m11 = fq;
+		m12 = -2.0*fq;
+
+		// q = 4
+		fq = dist[3*Np+n];
+		rho+= fq;
+		m1 -= 11.0*fq;
+		m2 -= 4.0*fq;
+		jy -= fq;
+		m6 += 4.0*fq;
+		m9 -= fq;
+		m10 += 2.0*fq;
+		m11 += fq;
+		m12 -= 2.0*fq;
+
+		// q=5
+		fq = dist[6*Np+n];
+		rho += fq;
+		m1 -= 11.0*fq;
+		m2 -= 4.0*fq;
+		jz = fq;
+		m8 = -4.0*fq;
+		m9 -= fq;
+		m10 += 2.0*fq;
+		m11 -= fq;
+		m12 += 2.0*fq;
+
+		// q = 6
+		fq = dist[5*Np+n];
+		rho+= fq;
+		m1 -= 11.0*fq;
+		m2 -= 4.0*fq;
+		jz -= fq;
+		m8 += 4.0*fq;
+		m9 -= fq;
+		m10 += 2.0*fq;
+		m11 -= fq;
+		m12 += 2.0*fq;
+
+		// q=7
+		fq = dist[8*Np+n];
+		rho += fq;
+		m1 += 8.0*fq;
+		m2 += fq;
+		jx += fq;
+		m4 += fq;
+		jy += fq;
+		m6 += fq;
+		m9  += fq;
+		m10 += fq;
+		m11 += fq;
+		m12 += fq;
+		m13 = fq;
+		m16 = fq;
+		m17 = -fq;
+
+		// q = 8
+		fq = dist[7*Np+n];
+		rho += fq;
+		m1 += 8.0*fq;
+		m2 += fq;
+		jx -= fq;
+		m4 -= fq;
+		jy -= fq;
+		m6 -= fq;
+		m9 += fq;
+		m10 += fq;
+		m11 += fq;
+		m12 += fq;
+		m13 += fq;
+		m16 -= fq;
+		m17 += fq;
+
+		// q=9
+		fq = dist[10*Np+n];
+		rho += fq;
+		m1 += 8.0*fq;
+		m2 += fq;
+		jx += fq;
+		m4 += fq;
+		jy -= fq;
+		m6 -= fq;
+		m9 += fq;
+		m10 += fq;
+		m11 += fq;
+		m12 += fq;
+		m13 -= fq;
+		m16 += fq;
+		m17 += fq;
+
+		// q = 10
+		fq = dist[9*Np+n];
+		rho += fq;
+		m1 += 8.0*fq;
+		m2 += fq;
+		jx -= fq;
+		m4 -= fq;
+		jy += fq;
+		m6 += fq;
+		m9 += fq;
+		m10 += fq;
+		m11 += fq;
+		m12 += fq;
+		m13 -= fq;
+		m16 -= fq;
+		m17 -= fq;
+
+		// q=11
+		fq = dist[12*Np+n];
+		rho += fq;
+		m1 += 8.0*fq;
+		m2 += fq;
+		jx += fq;
+		m4 += fq;
+		jz += fq;
+		m8 += fq;
+		m9 += fq;
+		m10 += fq;
+		m11 -= fq;
+		m12 -= fq;
+		m15 = fq;
+		m16 -= fq;
+		m18 = fq;
+
+		// q=12
+		fq = dist[11*Np+n];
+		rho += fq;
+		m1 += 8.0*fq;
+		m2 += fq;
+		jx -= fq;
+		m4 -= fq;
+		jz -= fq;
+		m8 -= fq;
+		m9 += fq;
+		m10 += fq;
+		m11 -= fq;
+		m12 -= fq;
+		m15 += fq;
+		m16 += fq;
+		m18 -= fq;
+
+		// q=13
+		fq = dist[14*Np+n];
+		rho += fq;
+		m1 += 8.0*fq;
+		m2 += fq;
+		jx += fq;
+		m4 += fq;
+		jz -= fq;
+		m8 -= fq;
+		m9 += fq;
+		m10 += fq;
+		m11 -= fq;
+		m12 -= fq;
+		m15 -= fq;
+		m16 -= fq;
+		m18 -= fq;
+
+		// q=14
+		fq = dist[13*Np+n];
+		rho += fq;
+		m1 += 8.0*fq;
+		m2 += fq;
+		jx -= fq;
+		m4 -= fq;
+		jz += fq;
+		m8 += fq;
+		m9 += fq;
+		m10 += fq;
+		m11 -= fq;
+		m12 -= fq;
+		m15 -= fq;
+		m16 += fq;
+		m18 += fq;
+
+		// q=15
+		fq = dist[16*Np+n];
+		rho += fq;
+		m1 += 8.0*fq;
+		m2 += fq;
+		jy += fq;
+		m6 += fq;
+		jz += fq;
+		m8 += fq;
+		m9 -= 2.0*fq;
+		m10 -= 2.0*fq;
+		m14 = fq;
+		m17 += fq;
+		m18 -= fq;
+
+		// q=16
+		fq = dist[15*Np+n];
+		rho += fq;
+		m1 += 8.0*fq;
+		m2 += fq;
+		jy -= fq;
+		m6 -= fq;
+		jz -= fq;
+		m8 -= fq;
+		m9 -= 2.0*fq;
+		m10 -= 2.0*fq;
+		m14 += fq;
+		m17 -= fq;
+		m18 += fq;
+
+		// q=17
+		fq = dist[18*Np+n];
+		rho += fq;
+		m1 += 8.0*fq;
+		m2 += fq;
+		jy += fq;
+		m6 += fq;
+		jz -= fq;
+		m8 -= fq;
+		m9 -= 2.0*fq;
+		m10 -= 2.0*fq;
+		m14 -= fq;
+		m17 += fq;
+		m18 += fq;
+
+		// q=18
+		fq = dist[17*Np+n];
+		rho += fq;
+		m1 += 8.0*fq;
+		m2 += fq;
+		jy -= fq;
+		m6 -= fq;
+		jz += fq;
+		m8 += fq;
+		m9 -= 2.0*fq;
+		m10 -= 2.0*fq;
+		m14 -= fq;
+		m17 -= fq;
+		m18 -= fq;
+
+        // Compute greyscale related parameters
+        c0 = 0.5*(1.0+porosity*0.5*mu_eff/perm);
+        if (porosity==1.0) c0 = 0.5;//i.e. apparent pore nodes
+        //GeoFun = 1.75/sqrt(150.0*porosity*porosity*porosity);
+        c1 = porosity*0.5*GeoFun/sqrt(perm);
+        if (porosity==1.0) c1 = 0.0;//i.e. apparent pore nodes
+
+        vx = jx/rho0+0.5*(porosity*Gx);
+        vy = jy/rho0+0.5*(porosity*Gy);
+        vz = jz/rho0+0.5*(porosity*Gz);
+        v_mag=sqrt(vx*vx+vy*vy+vz*vz);
+        ux = vx/(c0+sqrt(c0*c0+c1*v_mag));
+        uy = vy/(c0+sqrt(c0*c0+c1*v_mag));
+        uz = vz/(c0+sqrt(c0*c0+c1*v_mag));
+        u_mag=sqrt(ux*ux+uy*uy+uz*uz);
+
+        //Update the total force to include linear (Darcy) and nonlinear (Forchheimer) drags due to the porous medium
+        Fx = rho0*(-porosity*mu_eff/perm*ux - porosity*GeoFun/sqrt(perm)*u_mag*ux + porosity*Gx);
+        Fy = rho0*(-porosity*mu_eff/perm*uy - porosity*GeoFun/sqrt(perm)*u_mag*uy + porosity*Gy);
+        Fz = rho0*(-porosity*mu_eff/perm*uz - porosity*GeoFun/sqrt(perm)*u_mag*uz + porosity*Gz);
+        if (porosity==1.0){
+            Fx=rho0*(Gx);
+            Fy=rho0*(Gy);
+            Fz=rho0*(Gz);
+        }
+
+		// write the velocity 
+		Velocity[n] = ux;
+		Velocity[Np+n] = uy;
+		Velocity[2*Np+n] = uz;
+
+		//........................................................................
+		//..............carry out relaxation process..............................
+		//..........Toelke, Fruediger et. al. 2006................................
+		if (C == 0.0)	nx = ny = nz = 0.0;
+		m1 = m1 + rlx_setA*((19*(ux*ux+uy*uy+uz*uz)*rho0/porosity - 11*rho) -19*alpha*C - m1);
+		m2 = m2 + rlx_setA*((3*rho - 5.5*(ux*ux+uy*uy+uz*uz)*rho0/porosity)- m2);
+        jx = jx + Fx;
+		m4 = m4 + rlx_setB*((-0.6666666666666666*ux*rho0)- m4)
+                + (1-0.5*rlx_setB)*(-0.6666666666666666*Fx);
+        jy = jy + Fy;
+		m6 = m6 + rlx_setB*((-0.6666666666666666*uy*rho0)- m6)
+                + (1-0.5*rlx_setB)*(-0.6666666666666666*Fy);
+        jz = jz + Fz;
+		m8 = m8 + rlx_setB*((-0.6666666666666666*uz*rho0)- m8)
+                + (1-0.5*rlx_setB)*(-0.6666666666666666*Fz);
+		m9 = m9 + rlx_setA*(((2*ux*ux-uy*uy-uz*uz)*rho0/porosity) + 0.5*alpha*C*(2*nx*nx-ny*ny-nz*nz) - m9);
+		m10 = m10 + rlx_setA*( - m10);
+        //m10 = m10 + rlx_setA*(-0.5*rho0*((2*ux*ux-uy*uy-uz*uz)/porosity)- m10);
+		m11 = m11 + rlx_setA*(((uy*uy-uz*uz)*rho0/porosity) + 0.5*alpha*C*(ny*ny-nz*nz)- m11);
+		m12 = m12 + rlx_setA*( - m12);
+        //m12 = m12 + rlx_setA*(-0.5*(rho0*(uy*uy-uz*uz)/porosity)- m12);
+		m13 = m13 + rlx_setA*( (ux*uy*rho0/porosity) + 0.5*alpha*C*nx*ny - m13);
+		m14 = m14 + rlx_setA*( (uy*uz*rho0/porosity) + 0.5*alpha*C*ny*nz - m14);
+		m15 = m15 + rlx_setA*( (ux*uz*rho0/porosity) + 0.5*alpha*C*nx*nz - m15);
+		m16 = m16 + rlx_setB*( - m16);
+		m17 = m17 + rlx_setB*( - m17);
+		m18 = m18 + rlx_setB*( - m18);
+
+		//.................inverse transformation......................................................
+		// q=0
+		fq = mrt_V1*rho-mrt_V2*m1+mrt_V3*m2;
+		dist[n] = fq;
+
+		// q = 1
+		fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(jx-m4)+mrt_V6*(m9-m10);
+		dist[1*Np+n] = fq;
+
+		// q=2
+		fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(m4-jx)+mrt_V6*(m9-m10);
+		dist[2*Np+n] = fq;
+
+		// q = 3
+		fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(jy-m6)+mrt_V7*(m10-m9)+mrt_V8*(m11-m12);
+		dist[3*Np+n] = fq;
+
+		// q = 4
+		fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(m6-jy)+mrt_V7*(m10-m9)+mrt_V8*(m11-m12);
+		dist[4*Np+n] = fq;
+
+		// q = 5
+		fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(jz-m8)+mrt_V7*(m10-m9)+mrt_V8*(m12-m11);
+		dist[5*Np+n] = fq;
+
+		// q = 6
+		fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(m8-jz)+mrt_V7*(m10-m9)+mrt_V8*(m12-m11);
+		dist[6*Np+n] = fq;
+
+		// q = 7
+		fq = mrt_V1*rho+mrt_V9*m1+mrt_V10*m2+0.1*(jx+jy)+0.025*(m4+m6)+
+				mrt_V7*m9+mrt_V11*m10+mrt_V8*m11+mrt_V12*m12+0.25*m13+0.125*(m16-m17);
+		dist[7*Np+n] = fq;
+
+
+		// q = 8
+		fq = mrt_V1*rho+mrt_V9*m1+mrt_V10*m2-0.1*(jx+jy)-0.025*(m4+m6) +mrt_V7*m9+mrt_V11*m10+mrt_V8*m11
+				+mrt_V12*m12+0.25*m13+0.125*(m17-m16);
+		dist[8*Np+n] = fq;
+
+		// q = 9
+		fq = mrt_V1*rho+mrt_V9*m1+mrt_V10*m2+0.1*(jx-jy)+0.025*(m4-m6)+
+				mrt_V7*m9+mrt_V11*m10+mrt_V8*m11+mrt_V12*m12-0.25*m13+0.125*(m16+m17);
+		dist[9*Np+n] = fq;
+
+		// q = 10
+		fq = mrt_V1*rho+mrt_V9*m1+mrt_V10*m2+0.1*(jy-jx)+0.025*(m6-m4)+
+				mrt_V7*m9+mrt_V11*m10+mrt_V8*m11+mrt_V12*m12-0.25*m13-0.125*(m16+m17);
+		dist[10*Np+n] = fq;
+
+
+		// q = 11
+		fq = mrt_V1*rho+mrt_V9*m1
+				+mrt_V10*m2+0.1*(jx+jz)+0.025*(m4+m8)
+				+mrt_V7*m9+mrt_V11*m10-mrt_V8*m11
+				-mrt_V12*m12+0.25*m15+0.125*(m18-m16);
+		dist[11*Np+n] = fq;
+
+		// q = 12
+		fq = mrt_V1*rho+mrt_V9*m1+mrt_V10*m2-0.1*(jx+jz)-0.025*(m4+m8)+
+				mrt_V7*m9+mrt_V11*m10-mrt_V8*m11-mrt_V12*m12+0.25*m15+0.125*(m16-m18);
+		dist[12*Np+n] = fq;
+
+		// q = 13
+		fq = mrt_V1*rho+mrt_V9*m1
+				+mrt_V10*m2+0.1*(jx-jz)+0.025*(m4-m8)
+				+mrt_V7*m9+mrt_V11*m10-mrt_V8*m11
+				-mrt_V12*m12-0.25*m15-0.125*(m16+m18);
+		dist[13*Np+n] = fq;
+
+		// q= 14
+		fq = mrt_V1*rho+mrt_V9*m1
+				+mrt_V10*m2+0.1*(jz-jx)+0.025*(m8-m4)
+				+mrt_V7*m9+mrt_V11*m10-mrt_V8*m11
+				-mrt_V12*m12-0.25*m15+0.125*(m16+m18);
+
+		dist[14*Np+n] = fq;
+
+		// q = 15
+		fq = mrt_V1*rho+mrt_V9*m1
+				+mrt_V10*m2+0.1*(jy+jz)+0.025*(m6+m8)
+				-mrt_V6*m9-mrt_V7*m10+0.25*m14+0.125*(m17-m18);
+		dist[15*Np+n] = fq;
+
+		// q = 16
+		fq =  mrt_V1*rho+mrt_V9*m1
+				+mrt_V10*m2-0.1*(jy+jz)-0.025*(m6+m8)
+				-mrt_V6*m9-mrt_V7*m10+0.25*m14+0.125*(m18-m17);
+		dist[16*Np+n] = fq;
+
+
+		// q = 17
+		fq = mrt_V1*rho+mrt_V9*m1
+				+mrt_V10*m2+0.1*(jy-jz)+0.025*(m6-m8)
+				-mrt_V6*m9-mrt_V7*m10-0.25*m14+0.125*(m17+m18);
+		dist[17*Np+n] = fq;
+
+		// q = 18
+		fq = mrt_V1*rho+mrt_V9*m1
+				+mrt_V10*m2+0.1*(jz-jy)+0.025*(m8-m6)
+				-mrt_V6*m9-mrt_V7*m10-0.25*m14-0.125*(m17+m18);
+		dist[18*Np+n] = fq;
+		//........................................................................
+
+		// Instantiate mass transport distributions
+		// Stationary value - distribution 0
+		nAB = 1.0/(nA+nB);
+		Aq[n] = 0.3333333333333333*nA;
+		Bq[n] = 0.3333333333333333*nB;
+
+		//...............................................
+		// q = 0,2,4
+		// Cq = {1,0,0}, {0,1,0}, {0,0,1}
+		delta = beta*nA*nB*nAB*0.1111111111111111*nx;
+		if (!(nA*nB*nAB>0)) delta=0;
+		a1 = nA*(0.1111111111111111*(1+4.5*ux))+delta;
+		b1 = nB*(0.1111111111111111*(1+4.5*ux))-delta;
+		a2 = nA*(0.1111111111111111*(1-4.5*ux))-delta;
+		b2 = nB*(0.1111111111111111*(1-4.5*ux))+delta;
+
+		Aq[1*Np+n] = a1;
+		Bq[1*Np+n] = b1;
+		Aq[2*Np+n] = a2;
+		Bq[2*Np+n] = b2;
+
+		//...............................................
+		// q = 2
+		// Cq = {0,1,0}
+		delta = beta*nA*nB*nAB*0.1111111111111111*ny;
+		if (!(nA*nB*nAB>0)) delta=0;
+		a1 = nA*(0.1111111111111111*(1+4.5*uy))+delta;
+		b1 = nB*(0.1111111111111111*(1+4.5*uy))-delta;
+		a2 = nA*(0.1111111111111111*(1-4.5*uy))-delta;
+		b2 = nB*(0.1111111111111111*(1-4.5*uy))+delta;
+
+		Aq[3*Np+n] = a1;
+		Bq[3*Np+n] = b1;
+		Aq[4*Np+n] = a2;
+		Bq[4*Np+n] = b2;
+		//...............................................
+		// q = 4
+		// Cq = {0,0,1}
+		delta = beta*nA*nB*nAB*0.1111111111111111*nz;
+		if (!(nA*nB*nAB>0)) delta=0;
+		a1 = nA*(0.1111111111111111*(1+4.5*uz))+delta;
+		b1 = nB*(0.1111111111111111*(1+4.5*uz))-delta;
+		a2 = nA*(0.1111111111111111*(1-4.5*uz))-delta;
+		b2 = nB*(0.1111111111111111*(1-4.5*uz))+delta;
+
+		Aq[5*Np+n] = a1;
+		Bq[5*Np+n] = b1;
+		Aq[6*Np+n] = a2;
+		Bq[6*Np+n] = b2;
+		//...............................................
+	}
+}
+
+
+//extern "C" void ScaLBL_D3Q19_GreyscaleColor_Init(double *dist, double *Porosity, int Np){
+//	int n;
+//    double porosity;
+//	for (n=0; n<Np; n++){
+//        porosity = Porosity[n];
+//        if (porosity==0.0) porosity=1.f;
+//		dist[n] = 0.3333333333333333/porosity;
+//		dist[Np+n] = 0.055555555555555555/porosity;		//double(100*n)+1.f;
+//		dist[2*Np+n] = 0.055555555555555555/porosity;	//double(100*n)+2.f;
+//		dist[3*Np+n] = 0.055555555555555555/porosity;	//double(100*n)+3.f;
+//		dist[4*Np+n] = 0.055555555555555555/porosity;	//double(100*n)+4.f;
+//		dist[5*Np+n] = 0.055555555555555555/porosity;	//double(100*n)+5.f;
+//		dist[6*Np+n] = 0.055555555555555555/porosity;	//double(100*n)+6.f;
+//		dist[7*Np+n] = 0.0277777777777778/porosity;   //double(100*n)+7.f;
+//		dist[8*Np+n] = 0.0277777777777778/porosity;   //double(100*n)+8.f;
+//		dist[9*Np+n] = 0.0277777777777778/porosity;   //double(100*n)+9.f;
+//		dist[10*Np+n] = 0.0277777777777778/porosity;  //double(100*n)+10.f;
+//		dist[11*Np+n] = 0.0277777777777778/porosity;  //double(100*n)+11.f;
+//		dist[12*Np+n] = 0.0277777777777778/porosity;  //double(100*n)+12.f;
+//		dist[13*Np+n] = 0.0277777777777778/porosity;  //double(100*n)+13.f;
+//		dist[14*Np+n] = 0.0277777777777778/porosity;  //double(100*n)+14.f;
+//		dist[15*Np+n] = 0.0277777777777778/porosity;  //double(100*n)+15.f;
+//		dist[16*Np+n] = 0.0277777777777778/porosity;  //double(100*n)+16.f;
+//		dist[17*Np+n] = 0.0277777777777778/porosity;  //double(100*n)+17.f;
+//		dist[18*Np+n] = 0.0277777777777778/porosity;  //double(100*n)+18.f;
+//	}
+//}
+
+
diff --git a/gpu/D3Q19.cu b/gpu/D3Q19.cu
index a2d3b877..d31712b1 100644
--- a/gpu/D3Q19.cu
+++ b/gpu/D3Q19.cu
@@ -282,37 +282,6 @@ __global__ void dvc_ScaLBL_D3Q19_Init(double *dist, int Np)
 	}
 }
 
-__global__ void dvc_ScaLBL_D3Q19_GreyIMRT_Init(double *dist, int Np, double Den)
-{
-	int n;
-	int S = Np/NBLOCKS/NTHREADS + 1;
-	for (int s=0; s<S; s++){
-		//........Get 1-D index for this thread....................
-		n = S*blockIdx.x*blockDim.x + s*blockDim.x + threadIdx.x;
-		if (n<Np ){
-			dist[n] = Den - 0.6666666666666667;
-			dist[Np+n] = 0.055555555555555555;		//double(100*n)+1.f;
-			dist[2*Np+n] = 0.055555555555555555;	//double(100*n)+2.f;
-			dist[3*Np+n] = 0.055555555555555555;	//double(100*n)+3.f;
-			dist[4*Np+n] = 0.055555555555555555;	//double(100*n)+4.f;
-			dist[5*Np+n] = 0.055555555555555555;	//double(100*n)+5.f;
-			dist[6*Np+n] = 0.055555555555555555;	//double(100*n)+6.f;
-			dist[7*Np+n] = 0.0277777777777778;   //double(100*n)+7.f;
-			dist[8*Np+n] = 0.0277777777777778;   //double(100*n)+8.f;
-			dist[9*Np+n] = 0.0277777777777778;   //double(100*n)+9.f;
-			dist[10*Np+n] = 0.0277777777777778;  //double(100*n)+10.f;
-			dist[11*Np+n] = 0.0277777777777778;  //double(100*n)+11.f;
-			dist[12*Np+n] = 0.0277777777777778;  //double(100*n)+12.f;
-			dist[13*Np+n] = 0.0277777777777778;  //double(100*n)+13.f;
-			dist[14*Np+n] = 0.0277777777777778;  //double(100*n)+14.f;
-			dist[15*Np+n] = 0.0277777777777778;  //double(100*n)+15.f;
-			dist[16*Np+n] = 0.0277777777777778;  //double(100*n)+16.f;
-			dist[17*Np+n] = 0.0277777777777778;  //double(100*n)+17.f;
-			dist[18*Np+n] = 0.0277777777777778;  //double(100*n)+18.f;
-		}
-	}
-}
-
 //*************************************************************************
 __global__  void dvc_ScaLBL_D3Q19_Swap_Compact(int *neighborList, double *disteven, double *distodd, int Np, int q){
 	int n,nn;
@@ -2410,13 +2379,6 @@ extern "C" void ScaLBL_D3Q19_Init(double *dist, int Np){
 	}
 }
 
-extern "C" void ScaLBL_D3Q19_GreyIMRT_Init(double *dist, int Np, double Den){
-	dvc_ScaLBL_D3Q19_GreyIMRT_Init<<<NBLOCKS,NTHREADS >>>(dist, Np, Den);
-	cudaError_t err = cudaGetLastError();
-	if (cudaSuccess != err){
-		printf("CUDA error in ScaLBL_D3Q19_GreyIMRT_Init: %s \n",cudaGetErrorString(err));
-	}
-}
 
 extern "C" void ScaLBL_D3Q19_Swap(char *ID, double *disteven, double *distodd, int Nx, int Ny, int Nz){
 	dvc_ScaLBL_D3Q19_Swap<<<NBLOCKS,NTHREADS >>>(ID, disteven, distodd, Nx, Ny, Nz);
diff --git a/gpu/Greyscale.cu b/gpu/Greyscale.cu
index 7aa9fff9..89738dd7 100644
--- a/gpu/Greyscale.cu
+++ b/gpu/Greyscale.cu
@@ -928,9 +928,9 @@ __global__ void dvc_ScaLBL_D3Q19_AAeven_Greyscale_IMRT(double *dist, int start,
             pressure=0.5/porosity*(pressure-0.5*Den*u_mag*u_mag/porosity);
 
 //            //..............carry out relaxation process...............................................
-//            m1 = m1 + rlx_setA*((-30*Den+19*(ux*ux+uy*uy+uz*uz)/porosity + 57*pressure*porosity) - m1) 
+//            m1 = m1 + rlx_setA*((-30*Den+19*Den*(ux*ux+uy*uy+uz*uz)/porosity + 57*pressure*porosity) - m1) 
 //                    + (1-0.5*rlx_setA)*38*(Fx*ux+Fy*uy+Fz*uz)/porosity;
-//            m2 = m2 + rlx_setA*((12*Den - 5.5*(ux*ux+uy*uy+uz*uz)/porosity-27*pressure*porosity) - m2)
+//            m2 = m2 + rlx_setA*((12*Den - 5.5*Den*(ux*ux+uy*uy+uz*uz)/porosity-27*pressure*porosity) - m2)
 //                    + (1-0.5*rlx_setA)*11*(-Fx*ux-Fy*uy-Fz*uz)/porosity;
 //            jx = jx + Fx;
 //            m4 = m4 + rlx_setB*((-0.6666666666666666*ux*Den) - m4)
@@ -962,8 +962,8 @@ __global__ void dvc_ScaLBL_D3Q19_AAeven_Greyscale_IMRT(double *dist, int start,
 
             //-------------------- IMRT collison where body force has NO higher-order terms -------------//
             //..............carry out relaxation process...............................................
-            m1 = m1 + rlx_setA*((-30*Den+19*(ux*ux+uy*uy+uz*uz)/porosity + 57*pressure*porosity) - m1);
-            m2 = m2 + rlx_setA*((12*Den - 5.5*(ux*ux+uy*uy+uz*uz)/porosity-27*pressure*porosity) - m2);
+            m1 = m1 + rlx_setA*((-30*Den+19*Den*(ux*ux+uy*uy+uz*uz)/porosity + 57*pressure*porosity) - m1);
+            m2 = m2 + rlx_setA*((12*Den - 5.5*Den*(ux*ux+uy*uy+uz*uz)/porosity-27*pressure*porosity) - m2);
             jx = jx + Fx;
             m4 = m4 + rlx_setB*((-0.6666666666666666*ux*Den) - m4)
                     + (1-0.5*rlx_setB)*(-0.6666666666666666*Fx);
@@ -1441,9 +1441,9 @@ __global__ void dvc_ScaLBL_D3Q19_AAodd_Greyscale_IMRT(int *neighborList, double
             pressure=0.5/porosity*(pressure-0.5*Den*u_mag*u_mag/porosity);
 
 //            //..............carry out relaxation process...............................................
-//            m1 = m1 + rlx_setA*((-30*Den+19*(ux*ux+uy*uy+uz*uz)/porosity + 57*pressure*porosity) - m1) 
+//            m1 = m1 + rlx_setA*((-30*Den+19*Den*(ux*ux+uy*uy+uz*uz)/porosity + 57*pressure*porosity) - m1) 
 //                    + (1-0.5*rlx_setA)*38*(Fx*ux+Fy*uy+Fz*uz)/porosity;
-//            m2 = m2 + rlx_setA*((12*Den - 5.5*(ux*ux+uy*uy+uz*uz)/porosity-27*pressure*porosity) - m2)
+//            m2 = m2 + rlx_setA*((12*Den - 5.5*Den*(ux*ux+uy*uy+uz*uz)/porosity-27*pressure*porosity) - m2)
 //                    + (1-0.5*rlx_setA)*11*(-Fx*ux-Fy*uy-Fz*uz)/porosity;
 //            jx = jx + Fx;
 //            m4 = m4 + rlx_setB*((-0.6666666666666666*ux*Den) - m4)
@@ -1475,8 +1475,8 @@ __global__ void dvc_ScaLBL_D3Q19_AAodd_Greyscale_IMRT(int *neighborList, double
            
             //-------------------- IMRT collison where body force has NO higher-order terms -------------//
             //..............carry out relaxation process...............................................
-            m1 = m1 + rlx_setA*((-30*Den+19*(ux*ux+uy*uy+uz*uz)/porosity + 57*pressure*porosity) - m1);
-            m2 = m2 + rlx_setA*((12*Den - 5.5*(ux*ux+uy*uy+uz*uz)/porosity-27*pressure*porosity) - m2);
+            m1 = m1 + rlx_setA*((-30*Den+19*Den*(ux*ux+uy*uy+uz*uz)/porosity + 57*pressure*porosity) - m1);
+            m2 = m2 + rlx_setA*((12*Den - 5.5*Den*(ux*ux+uy*uy+uz*uz)/porosity-27*pressure*porosity) - m2);
             jx = jx + Fx;
             m4 = m4 + rlx_setB*((-0.6666666666666666*ux*Den) - m4)
                     + (1-0.5*rlx_setB)*(-0.6666666666666666*Fx);
@@ -1606,6 +1606,1087 @@ __global__ void dvc_ScaLBL_D3Q19_AAodd_Greyscale_IMRT(int *neighborList, double
 	}
 }
 
+__global__ void dvc_ScaLBL_D3Q19_AAodd_Greyscale_MRT(int *neighborList, double *dist, int start, int finish, int Np, double rlx,  double rlx_eff, double Gx, double Gy, double Gz,
+                                                 double *Poros,double *Perm, double *Velocity,double rho0, double *Pressure){
+
+	int n, nread;
+	int nr1,nr2,nr3,nr4,nr5,nr6;
+	int nr7,nr8,nr9,nr10;
+	int nr11,nr12,nr13,nr14;
+	double vx,vy,vz,v_mag;
+    double ux,uy,uz,u_mag;
+    double pressure;//defined for this incompressible model
+	// conserved momemnts
+	double rho,jx,jy,jz;
+	// non-conserved moments
+	double m1,m2,m4,m6,m8,m9,m10,m11,m12,m13,m14,m15,m16,m17,m18;
+    double fq;
+	//double f0,f1,f2,f3,f4,f5,f6,f7,f8,f9,f10,f11,f12,f13,f14,f15,f16,f17,f18;
+    double GeoFun;//geometric function from Guo's PRE 66, 036304 (2002)
+    double porosity;
+    double perm;//voxel permeability
+    double c0, c1; //Guo's model parameters
+    double mu_eff = (1.0/rlx_eff-0.5)/3.0;//kinematic viscosity
+    double Fx, Fy, Fz;//The total body force including Brinkman force and user-specified (Gx,Gy,Gz)
+    double rlx_setA = rlx;
+    double rlx_setB = 8.f*(2.f-rlx_setA)/(8.f-rlx_setA);
+
+	const double mrt_V1=0.05263157894736842;
+	const double mrt_V2=0.012531328320802;
+	const double mrt_V3=0.04761904761904762;
+	const double mrt_V4=0.004594820384294068;
+	const double mrt_V5=0.01587301587301587;
+	const double mrt_V6=0.0555555555555555555555555;
+	const double mrt_V7=0.02777777777777778;
+	const double mrt_V8=0.08333333333333333;
+	const double mrt_V9=0.003341687552213868;
+	const double mrt_V10=0.003968253968253968;
+	const double mrt_V11=0.01388888888888889;
+	const double mrt_V12=0.04166666666666666;
+
+	int S = Np/NBLOCKS/NTHREADS + 1;
+	for (int s=0; s<S; s++){
+	    //........Get 1-D index for this thread....................
+	    n = S*blockIdx.x*blockDim.x + s*blockDim.x + threadIdx.x + start;
+
+		if ( n<finish ){		
+
+            //........................................................................
+            //					READ THE DISTRIBUTIONS
+            //		(read from opposite array due to previous swap operation)
+            //........................................................................
+            // q=0
+			fq = dist[n];
+			rho = fq;
+			m1  = -30.0*fq;
+			m2  = 12.0*fq;
+
+			// q=1
+			//nread = neighborList[n]; // neighbor 2 
+			//fq = dist[nread]; // reading the f1 data into register fq		
+			nr1 = neighborList[n]; 
+			fq = dist[nr1]; // reading the f1 data into register fq
+			rho += fq;
+			m1 -= 11.0*fq;
+			m2 -= 4.0*fq;
+			jx = fq;
+			m4 = -4.0*fq;
+			m9 = 2.0*fq;
+			m10 = -4.0*fq;
+
+			// f2 = dist[10*Np+n];
+			//nread = neighborList[n+Np]; // neighbor 1 ( < 10Np => even part of dist)
+			//fq = dist[nread];  // reading the f2 data into register fq
+			nr2 = neighborList[n+Np]; // neighbor 1 ( < 10Np => even part of dist)
+			fq = dist[nr2];  // reading the f2 data into register fq
+			rho += fq;
+			m1 -= 11.0*(fq);
+			m2 -= 4.0*(fq);
+			jx -= fq;
+			m4 += 4.0*(fq);
+			m9 += 2.0*(fq);
+			m10 -= 4.0*(fq);
+
+			// q=3
+			//nread = neighborList[n+2*Np]; // neighbor 4
+			//fq = dist[nread];
+			nr3 = neighborList[n+2*Np]; // neighbor 4
+			fq = dist[nr3];
+			rho += fq;
+			m1 -= 11.0*fq;
+			m2 -= 4.0*fq;
+			jy = fq;
+			m6 = -4.0*fq;
+			m9 -= fq;
+			m10 += 2.0*fq;
+			m11 = fq;
+			m12 = -2.0*fq;
+
+			// q = 4
+			//nread = neighborList[n+3*Np]; // neighbor 3
+			//fq = dist[nread];
+			nr4 = neighborList[n+3*Np]; // neighbor 3
+			fq = dist[nr4];
+			rho+= fq;
+			m1 -= 11.0*fq;
+			m2 -= 4.0*fq;
+			jy -= fq;
+			m6 += 4.0*fq;
+			m9 -= fq;
+			m10 += 2.0*fq;
+			m11 += fq;
+			m12 -= 2.0*fq;
+
+			// q=5
+			//nread = neighborList[n+4*Np];
+			//fq = dist[nread];
+			nr5 = neighborList[n+4*Np];
+			fq = dist[nr5];
+			rho += fq;
+			m1 -= 11.0*fq;
+			m2 -= 4.0*fq;
+			jz = fq;
+			m8 = -4.0*fq;
+			m9 -= fq;
+			m10 += 2.0*fq;
+			m11 -= fq;
+			m12 += 2.0*fq;
+
+
+			// q = 6
+			//nread = neighborList[n+5*Np];
+			//fq = dist[nread];
+			nr6 = neighborList[n+5*Np];
+			fq = dist[nr6];
+			rho+= fq;
+			m1 -= 11.0*fq;
+			m2 -= 4.0*fq;
+			jz -= fq;
+			m8 += 4.0*fq;
+			m9 -= fq;
+			m10 += 2.0*fq;
+			m11 -= fq;
+			m12 += 2.0*fq;
+
+			// q=7
+			//nread = neighborList[n+6*Np];
+			//fq = dist[nread];
+			nr7 = neighborList[n+6*Np];
+			fq = dist[nr7];
+			rho += fq;
+			m1 += 8.0*fq;
+			m2 += fq;
+			jx += fq;
+			m4 += fq;
+			jy += fq;
+			m6 += fq;
+			m9  += fq;
+			m10 += fq;
+			m11 += fq;
+			m12 += fq;
+			m13 = fq;
+			m16 = fq;
+			m17 = -fq;
+
+			// q = 8
+			//nread = neighborList[n+7*Np];
+			//fq = dist[nread];
+			nr8 = neighborList[n+7*Np];
+			fq = dist[nr8];
+			rho += fq;
+			m1 += 8.0*fq;
+			m2 += fq;
+			jx -= fq;
+			m4 -= fq;
+			jy -= fq;
+			m6 -= fq;
+			m9 += fq;
+			m10 += fq;
+			m11 += fq;
+			m12 += fq;
+			m13 += fq;
+			m16 -= fq;
+			m17 += fq;
+
+			// q=9
+			//nread = neighborList[n+8*Np];
+			//fq = dist[nread];
+			nr9 = neighborList[n+8*Np];
+			fq = dist[nr9];
+			rho += fq;
+			m1 += 8.0*fq;
+			m2 += fq;
+			jx += fq;
+			m4 += fq;
+			jy -= fq;
+			m6 -= fq;
+			m9 += fq;
+			m10 += fq;
+			m11 += fq;
+			m12 += fq;
+			m13 -= fq;
+			m16 += fq;
+			m17 += fq;
+
+			// q = 10
+			//nread = neighborList[n+9*Np];
+			//fq = dist[nread];
+			nr10 = neighborList[n+9*Np];
+			fq = dist[nr10];
+			rho += fq;
+			m1 += 8.0*fq;
+			m2 += fq;
+			jx -= fq;
+			m4 -= fq;
+			jy += fq;
+			m6 += fq;
+			m9 += fq;
+			m10 += fq;
+			m11 += fq;
+			m12 += fq;
+			m13 -= fq;
+			m16 -= fq;
+			m17 -= fq;
+
+			// q=11
+			//nread = neighborList[n+10*Np];
+			//fq = dist[nread];
+			nr11 = neighborList[n+10*Np];
+			fq = dist[nr11];
+			rho += fq;
+			m1 += 8.0*fq;
+			m2 += fq;
+			jx += fq;
+			m4 += fq;
+			jz += fq;
+			m8 += fq;
+			m9 += fq;
+			m10 += fq;
+			m11 -= fq;
+			m12 -= fq;
+			m15 = fq;
+			m16 -= fq;
+			m18 = fq;
+
+			// q=12
+			//nread = neighborList[n+11*Np];
+			//fq = dist[nread];
+			nr12 = neighborList[n+11*Np];
+			fq = dist[nr12];
+			rho += fq;
+			m1 += 8.0*fq;
+			m2 += fq;
+			jx -= fq;
+			m4 -= fq;
+			jz -= fq;
+			m8 -= fq;
+			m9 += fq;
+			m10 += fq;
+			m11 -= fq;
+			m12 -= fq;
+			m15 += fq;
+			m16 += fq;
+			m18 -= fq;
+
+			// q=13
+			//nread = neighborList[n+12*Np];
+			//fq = dist[nread];
+			nr13 = neighborList[n+12*Np];
+			fq = dist[nr13];
+			rho += fq;
+			m1 += 8.0*fq;
+			m2 += fq;
+			jx += fq;
+			m4 += fq;
+			jz -= fq;
+			m8 -= fq;
+			m9 += fq;
+			m10 += fq;
+			m11 -= fq;
+			m12 -= fq;
+			m15 -= fq;
+			m16 -= fq;
+			m18 -= fq;
+
+			// q=14
+			//nread = neighborList[n+13*Np];
+			//fq = dist[nread];
+			nr14 = neighborList[n+13*Np];
+			fq = dist[nr14];
+			rho += fq;
+			m1 += 8.0*fq;
+			m2 += fq;
+			jx -= fq;
+			m4 -= fq;
+			jz += fq;
+			m8 += fq;
+			m9 += fq;
+			m10 += fq;
+			m11 -= fq;
+			m12 -= fq;
+			m15 -= fq;
+			m16 += fq;
+			m18 += fq;
+
+			// q=15
+			nread = neighborList[n+14*Np];
+			fq = dist[nread];
+			//fq = dist[17*Np+n];
+			rho += fq;
+			m1 += 8.0*fq;
+			m2 += fq;
+			jy += fq;
+			m6 += fq;
+			jz += fq;
+			m8 += fq;
+			m9 -= 2.0*fq;
+			m10 -= 2.0*fq;
+			m14 = fq;
+			m17 += fq;
+			m18 -= fq;
+
+			// q=16
+			nread = neighborList[n+15*Np];
+			fq = dist[nread];
+			//fq = dist[8*Np+n];
+			rho += fq;
+			m1 += 8.0*fq;
+			m2 += fq;
+			jy -= fq;
+			m6 -= fq;
+			jz -= fq;
+			m8 -= fq;
+			m9 -= 2.0*fq;
+			m10 -= 2.0*fq;
+			m14 += fq;
+			m17 -= fq;
+			m18 += fq;
+
+			// q=17
+			//fq = dist[18*Np+n];
+			nread = neighborList[n+16*Np];
+			fq = dist[nread];
+			rho += fq;
+			m1 += 8.0*fq;
+			m2 += fq;
+			jy += fq;
+			m6 += fq;
+			jz -= fq;
+			m8 -= fq;
+			m9 -= 2.0*fq;
+			m10 -= 2.0*fq;
+			m14 -= fq;
+			m17 += fq;
+			m18 += fq;
+
+			// q=18
+			nread = neighborList[n+17*Np];
+			fq = dist[nread];
+			//fq = dist[9*Np+n];
+			rho += fq;
+			m1 += 8.0*fq;
+			m2 += fq;
+			jy -= fq;
+			m6 -= fq;
+			jz += fq;
+			m8 += fq;
+			m9 -= 2.0*fq;
+			m10 -= 2.0*fq;
+			m14 -= fq;
+			m17 -= fq;
+			m18 -= fq;
+            //---------------------------------------------------------------------//
+
+            porosity = Poros[n];
+            perm = Perm[n];
+
+            c0 = 0.5*(1.0+porosity*0.5*mu_eff/perm);
+            if (porosity==1.0) c0 = 0.5;//i.e. apparent pore nodes
+            GeoFun = 1.75/sqrt(150.0*porosity*porosity*porosity);
+            c1 = porosity*0.5*GeoFun/sqrt(perm);
+            if (porosity==1.0) c1 = 0.0;//i.e. apparent pore nodes
+
+            vx = jx/rho0+0.5*porosity*Gx;
+            vy = jy/rho0+0.5*porosity*Gy;
+            vz = jz/rho0+0.5*porosity*Gz;
+            v_mag=sqrt(vx*vx+vy*vy+vz*vz);
+            ux = vx/(c0+sqrt(c0*c0+c1*v_mag));
+            uy = vy/(c0+sqrt(c0*c0+c1*v_mag));
+            uz = vz/(c0+sqrt(c0*c0+c1*v_mag));
+            u_mag=sqrt(ux*ux+uy*uy+uz*uz);
+
+            //Update the total force to include linear (Darcy) and nonlinear (Forchheimer) drags due to the porous medium
+            Fx = rho0*(-porosity*mu_eff/perm*ux - porosity*GeoFun/sqrt(perm)*u_mag*ux + porosity*Gx);
+            Fy = rho0*(-porosity*mu_eff/perm*uy - porosity*GeoFun/sqrt(perm)*u_mag*uy + porosity*Gy);
+            Fz = rho0*(-porosity*mu_eff/perm*uz - porosity*GeoFun/sqrt(perm)*u_mag*uz + porosity*Gz);
+            if (porosity==1.0){
+                Fx=rho0*Gx;
+                Fy=rho0*Gy;
+                Fz=rho0*Gz;
+            }
+
+            //Calculate pressure for MRT model
+            pressure=rho/3.f;
+
+            //-------------------- MRT collison where body force has NO higher-order terms -------------//
+			m1 = m1 + rlx_setA*((19*(ux*ux+uy*uy+uz*uz)*rho0/porosity - 11*rho) - m1);
+			m2 = m2 + rlx_setA*((3*rho - 5.5*(ux*ux+uy*uy+uz*uz)*rho0/porosity) - m2);
+            jx = jx + Fx;
+			m4 = m4 + rlx_setB*((-0.6666666666666666*ux*rho0)- m4)
+                    + (1-0.5*rlx_setB)*(-0.6666666666666666*Fx);
+            jy = jy + Fy;
+			m6 = m6 + rlx_setB*((-0.6666666666666666*uy*rho0)- m6)
+                    + (1-0.5*rlx_setB)*(-0.6666666666666666*Fy);
+            jz = jz + Fz;
+			m8 = m8 + rlx_setB*((-0.6666666666666666*uz*rho0)- m8)
+                    + (1-0.5*rlx_setB)*(-0.6666666666666666*Fz);
+			m9 = m9 + rlx_setA*(((2*ux*ux-uy*uy-uz*uz)*rho0/porosity) - m9);
+			m10 = m10 + rlx_setA*( - m10);
+            //m10 = m10 + rlx_setA*(-0.5*rho0*((2*ux*ux-uy*uy-uz*uz)/porosity)- m10);
+			m11 = m11 + rlx_setA*(((uy*uy-uz*uz)*rho0/porosity) - m11);
+			m12 = m12 + rlx_setA*( - m12);
+            //m12 = m12 + rlx_setA*(-0.5*(rho0*(uy*uy-uz*uz)/porosity)- m12);
+			m13 = m13 + rlx_setA*( (ux*uy*rho0/porosity) - m13);
+			m14 = m14 + rlx_setA*( (uy*uz*rho0/porosity) - m14);
+			m15 = m15 + rlx_setA*( (ux*uz*rho0/porosity) - m15);
+			m16 = m16 + rlx_setB*( - m16);
+			m17 = m17 + rlx_setB*( - m17);
+			m18 = m18 + rlx_setB*( - m18);
+            //.......................................................................................................
+
+
+            //.................inverse transformation......................................................
+            // q=0
+			fq = mrt_V1*rho-mrt_V2*m1+mrt_V3*m2;
+			dist[n] = fq;
+
+			// q = 1
+			fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(jx-m4)+mrt_V6*(m9-m10);
+			//nread = neighborList[n+Np];
+			dist[nr2] = fq;
+
+			// q=2
+			fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(m4-jx)+mrt_V6*(m9-m10);
+			//nread = neighborList[n];
+			dist[nr1] = fq;
+
+			// q = 3
+			fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(jy-m6)+mrt_V7*(m10-m9)+mrt_V8*(m11-m12);
+			//nread = neighborList[n+3*Np];
+			dist[nr4] = fq;
+
+			// q = 4
+			fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(m6-jy)+mrt_V7*(m10-m9)+mrt_V8*(m11-m12);
+			//nread = neighborList[n+2*Np];
+			dist[nr3] = fq;
+
+			// q = 5
+			fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(jz-m8)+mrt_V7*(m10-m9)+mrt_V8*(m12-m11);
+			//nread = neighborList[n+5*Np];
+			dist[nr6] = fq;
+
+			// q = 6
+			fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(m8-jz)+mrt_V7*(m10-m9)+mrt_V8*(m12-m11);
+			//nread = neighborList[n+4*Np];
+			dist[nr5] = fq;
+
+			// q = 7
+			fq = mrt_V1*rho+mrt_V9*m1+mrt_V10*m2+0.1*(jx+jy)+0.025*(m4+m6)+
+					mrt_V7*m9+mrt_V11*m10+mrt_V8*m11+mrt_V12*m12+0.25*m13+0.125*(m16-m17);
+			//nread = neighborList[n+7*Np];
+			dist[nr8] = fq;
+
+			// q = 8
+			fq = mrt_V1*rho+mrt_V9*m1+mrt_V10*m2-0.1*(jx+jy)-0.025*(m4+m6) +mrt_V7*m9+mrt_V11*m10+mrt_V8*m11
+					+mrt_V12*m12+0.25*m13+0.125*(m17-m16);
+			//nread = neighborList[n+6*Np];
+			dist[nr7] = fq;
+
+			// q = 9
+			fq = mrt_V1*rho+mrt_V9*m1+mrt_V10*m2+0.1*(jx-jy)+0.025*(m4-m6)+
+					mrt_V7*m9+mrt_V11*m10+mrt_V8*m11+mrt_V12*m12-0.25*m13+0.125*(m16+m17);
+			//nread = neighborList[n+9*Np];
+			dist[nr10] = fq;
+
+			// q = 10
+			fq = mrt_V1*rho+mrt_V9*m1+mrt_V10*m2+0.1*(jy-jx)+0.025*(m6-m4)+
+					mrt_V7*m9+mrt_V11*m10+mrt_V8*m11+mrt_V12*m12-0.25*m13-0.125*(m16+m17);
+			//nread = neighborList[n+8*Np];
+			dist[nr9] = fq;
+
+			// q = 11
+			fq = mrt_V1*rho+mrt_V9*m1
+					+mrt_V10*m2+0.1*(jx+jz)+0.025*(m4+m8)
+					+mrt_V7*m9+mrt_V11*m10-mrt_V8*m11
+					-mrt_V12*m12+0.25*m15+0.125*(m18-m16);
+			//nread = neighborList[n+11*Np];
+			dist[nr12] = fq;
+
+			// q = 12
+			fq = mrt_V1*rho+mrt_V9*m1+mrt_V10*m2-0.1*(jx+jz)-0.025*(m4+m8)+
+					mrt_V7*m9+mrt_V11*m10-mrt_V8*m11-mrt_V12*m12+0.25*m15+0.125*(m16-m18);
+			//nread = neighborList[n+10*Np];
+			dist[nr11]= fq;
+
+			// q = 13
+			fq = mrt_V1*rho+mrt_V9*m1
+					+mrt_V10*m2+0.1*(jx-jz)+0.025*(m4-m8)
+					+mrt_V7*m9+mrt_V11*m10-mrt_V8*m11
+					-mrt_V12*m12-0.25*m15-0.125*(m16+m18);
+			//nread = neighborList[n+13*Np];
+			dist[nr14] = fq;
+
+			// q= 14
+			fq = mrt_V1*rho+mrt_V9*m1
+					+mrt_V10*m2+0.1*(jz-jx)+0.025*(m8-m4)
+					+mrt_V7*m9+mrt_V11*m10-mrt_V8*m11
+					-mrt_V12*m12-0.25*m15+0.125*(m16+m18);
+			//nread = neighborList[n+12*Np];
+			dist[nr13] = fq;
+
+
+			// q = 15
+			fq = mrt_V1*rho+mrt_V9*m1
+					+mrt_V10*m2+0.1*(jy+jz)+0.025*(m6+m8)
+					-mrt_V6*m9-mrt_V7*m10+0.25*m14+0.125*(m17-m18);
+			nread = neighborList[n+15*Np];
+			dist[nread] = fq;
+
+			// q = 16
+			fq =  mrt_V1*rho+mrt_V9*m1
+					+mrt_V10*m2-0.1*(jy+jz)-0.025*(m6+m8)
+					-mrt_V6*m9-mrt_V7*m10+0.25*m14+0.125*(m18-m17);
+			nread = neighborList[n+14*Np];
+			dist[nread] = fq;
+
+
+			// q = 17
+			fq = mrt_V1*rho+mrt_V9*m1
+					+mrt_V10*m2+0.1*(jy-jz)+0.025*(m6-m8)
+					-mrt_V6*m9-mrt_V7*m10-0.25*m14+0.125*(m17+m18);
+			nread = neighborList[n+17*Np];
+			dist[nread] = fq;
+
+			// q = 18
+			fq = mrt_V1*rho+mrt_V9*m1
+					+mrt_V10*m2+0.1*(jz-jy)+0.025*(m8-m6)
+					-mrt_V6*m9-mrt_V7*m10-0.25*m14-0.125*(m17+m18);
+			nread = neighborList[n+16*Np];
+			dist[nread] = fq;
+            //........................................................................
+
+            //Update velocity on device
+            Velocity[0*Np+n] = ux;
+            Velocity[1*Np+n] = uy;
+            Velocity[2*Np+n] = uz;
+            //Update pressure on device
+            Pressure[n] = pressure;
+		}
+	}
+}
+
+__global__ void dvc_ScaLBL_D3Q19_AAeven_Greyscale_MRT(double *dist, int start, int finish, int Np, double rlx,  double rlx_eff, double Gx, double Gy, double Gz,
+                                                  double *Poros,double *Perm, double *Velocity,double rho0, double *Pressure){
+
+	int n;
+	double vx,vy,vz,v_mag;
+    double ux,uy,uz,u_mag;
+    double pressure;//defined for this incompressible model
+	// conserved momemnts
+	double rho,jx,jy,jz;
+	// non-conserved moments
+	double m1,m2,m4,m6,m8,m9,m10,m11,m12,m13,m14,m15,m16,m17,m18;
+    double fq;
+	//double f0,f1,f2,f3,f4,f5,f6,f7,f8,f9,f10,f11,f12,f13,f14,f15,f16,f17,f18;
+    double GeoFun;//geometric function from Guo's PRE 66, 036304 (2002)
+    double porosity;
+    double perm;//voxel permeability
+    double c0, c1; //Guo's model parameters
+    double mu_eff = (1.0/rlx_eff-0.5)/3.0;//kinematic viscosity
+    double Fx, Fy, Fz;//The total body force including Brinkman force and user-specified (Gx,Gy,Gz)
+    double rlx_setA = rlx;
+    double rlx_setB = 8.f*(2.f-rlx_setA)/(8.f-rlx_setA);
+
+	const double mrt_V1=0.05263157894736842;
+	const double mrt_V2=0.012531328320802;
+	const double mrt_V3=0.04761904761904762;
+	const double mrt_V4=0.004594820384294068;
+	const double mrt_V5=0.01587301587301587;
+	const double mrt_V6=0.0555555555555555555555555;
+	const double mrt_V7=0.02777777777777778;
+	const double mrt_V8=0.08333333333333333;
+	const double mrt_V9=0.003341687552213868;
+	const double mrt_V10=0.003968253968253968;
+	const double mrt_V11=0.01388888888888889;
+	const double mrt_V12=0.04166666666666666;
+
+
+	int S = Np/NBLOCKS/NTHREADS + 1;
+	for (int s=0; s<S; s++){
+	    //........Get 1-D index for this thread....................
+	    n = S*blockIdx.x*blockDim.x + s*blockDim.x + threadIdx.x + start;
+
+		if ( n<finish ){
+
+            //........................................................................
+            //					READ THE DISTRIBUTIONS
+            //		(read from opposite array due to previous swap operation)
+            //........................................................................
+            // q=0
+			fq = dist[n];
+			rho = fq;
+			m1  = -30.0*fq;
+			m2  = 12.0*fq;
+
+			// q=1
+			fq = dist[2*Np+n];
+			rho += fq;
+			m1 -= 11.0*fq;
+			m2 -= 4.0*fq;
+			jx = fq;
+			m4 = -4.0*fq;
+			m9 = 2.0*fq;
+			m10 = -4.0*fq;
+
+			// f2 = dist[10*Np+n];
+			fq = dist[1*Np+n];
+			rho += fq;
+			m1 -= 11.0*(fq);
+			m2 -= 4.0*(fq);
+			jx -= fq;
+			m4 += 4.0*(fq);
+			m9 += 2.0*(fq);
+			m10 -= 4.0*(fq);
+
+			// q=3
+			fq = dist[4*Np+n];
+			rho += fq;
+			m1 -= 11.0*fq;
+			m2 -= 4.0*fq;
+			jy = fq;
+			m6 = -4.0*fq;
+			m9 -= fq;
+			m10 += 2.0*fq;
+			m11 = fq;
+			m12 = -2.0*fq;
+
+			// q = 4
+			fq = dist[3*Np+n];
+			rho+= fq;
+			m1 -= 11.0*fq;
+			m2 -= 4.0*fq;
+			jy -= fq;
+			m6 += 4.0*fq;
+			m9 -= fq;
+			m10 += 2.0*fq;
+			m11 += fq;
+			m12 -= 2.0*fq;
+
+			// q=5
+			fq = dist[6*Np+n];
+			rho += fq;
+			m1 -= 11.0*fq;
+			m2 -= 4.0*fq;
+			jz = fq;
+			m8 = -4.0*fq;
+			m9 -= fq;
+			m10 += 2.0*fq;
+			m11 -= fq;
+			m12 += 2.0*fq;
+
+			// q = 6
+			fq = dist[5*Np+n];
+			rho+= fq;
+			m1 -= 11.0*fq;
+			m2 -= 4.0*fq;
+			jz -= fq;
+			m8 += 4.0*fq;
+			m9 -= fq;
+			m10 += 2.0*fq;
+			m11 -= fq;
+			m12 += 2.0*fq;
+
+			// q=7
+			fq = dist[8*Np+n];
+			rho += fq;
+			m1 += 8.0*fq;
+			m2 += fq;
+			jx += fq;
+			m4 += fq;
+			jy += fq;
+			m6 += fq;
+			m9  += fq;
+			m10 += fq;
+			m11 += fq;
+			m12 += fq;
+			m13 = fq;
+			m16 = fq;
+			m17 = -fq;
+
+			// q = 8
+			fq = dist[7*Np+n];
+			rho += fq;
+			m1 += 8.0*fq;
+			m2 += fq;
+			jx -= fq;
+			m4 -= fq;
+			jy -= fq;
+			m6 -= fq;
+			m9 += fq;
+			m10 += fq;
+			m11 += fq;
+			m12 += fq;
+			m13 += fq;
+			m16 -= fq;
+			m17 += fq;
+
+			// q=9
+			fq = dist[10*Np+n];
+			rho += fq;
+			m1 += 8.0*fq;
+			m2 += fq;
+			jx += fq;
+			m4 += fq;
+			jy -= fq;
+			m6 -= fq;
+			m9 += fq;
+			m10 += fq;
+			m11 += fq;
+			m12 += fq;
+			m13 -= fq;
+			m16 += fq;
+			m17 += fq;
+
+			// q = 10
+			fq = dist[9*Np+n];
+			rho += fq;
+			m1 += 8.0*fq;
+			m2 += fq;
+			jx -= fq;
+			m4 -= fq;
+			jy += fq;
+			m6 += fq;
+			m9 += fq;
+			m10 += fq;
+			m11 += fq;
+			m12 += fq;
+			m13 -= fq;
+			m16 -= fq;
+			m17 -= fq;
+
+			// q=11
+			fq = dist[12*Np+n];
+			rho += fq;
+			m1 += 8.0*fq;
+			m2 += fq;
+			jx += fq;
+			m4 += fq;
+			jz += fq;
+			m8 += fq;
+			m9 += fq;
+			m10 += fq;
+			m11 -= fq;
+			m12 -= fq;
+			m15 = fq;
+			m16 -= fq;
+			m18 = fq;
+
+			// q=12
+			fq = dist[11*Np+n];
+			rho += fq;
+			m1 += 8.0*fq;
+			m2 += fq;
+			jx -= fq;
+			m4 -= fq;
+			jz -= fq;
+			m8 -= fq;
+			m9 += fq;
+			m10 += fq;
+			m11 -= fq;
+			m12 -= fq;
+			m15 += fq;
+			m16 += fq;
+			m18 -= fq;
+
+			// q=13
+			fq = dist[14*Np+n];
+			rho += fq;
+			m1 += 8.0*fq;
+			m2 += fq;
+			jx += fq;
+			m4 += fq;
+			jz -= fq;
+			m8 -= fq;
+			m9 += fq;
+			m10 += fq;
+			m11 -= fq;
+			m12 -= fq;
+			m15 -= fq;
+			m16 -= fq;
+			m18 -= fq;
+
+			// q=14
+			fq = dist[13*Np+n];
+			rho += fq;
+			m1 += 8.0*fq;
+			m2 += fq;
+			jx -= fq;
+			m4 -= fq;
+			jz += fq;
+			m8 += fq;
+			m9 += fq;
+			m10 += fq;
+			m11 -= fq;
+			m12 -= fq;
+			m15 -= fq;
+			m16 += fq;
+			m18 += fq;
+
+			// q=15
+			fq = dist[16*Np+n];
+			rho += fq;
+			m1 += 8.0*fq;
+			m2 += fq;
+			jy += fq;
+			m6 += fq;
+			jz += fq;
+			m8 += fq;
+			m9 -= 2.0*fq;
+			m10 -= 2.0*fq;
+			m14 = fq;
+			m17 += fq;
+			m18 -= fq;
+
+			// q=16
+			fq = dist[15*Np+n];
+			rho += fq;
+			m1 += 8.0*fq;
+			m2 += fq;
+			jy -= fq;
+			m6 -= fq;
+			jz -= fq;
+			m8 -= fq;
+			m9 -= 2.0*fq;
+			m10 -= 2.0*fq;
+			m14 += fq;
+			m17 -= fq;
+			m18 += fq;
+
+			// q=17
+			fq = dist[18*Np+n];
+			rho += fq;
+			m1 += 8.0*fq;
+			m2 += fq;
+			jy += fq;
+			m6 += fq;
+			jz -= fq;
+			m8 -= fq;
+			m9 -= 2.0*fq;
+			m10 -= 2.0*fq;
+			m14 -= fq;
+			m17 += fq;
+			m18 += fq;
+
+			// q=18
+			fq = dist[17*Np+n];
+			rho += fq;
+			m1 += 8.0*fq;
+			m2 += fq;
+			jy -= fq;
+			m6 -= fq;
+			jz += fq;
+			m8 += fq;
+			m9 -= 2.0*fq;
+			m10 -= 2.0*fq;
+			m14 -= fq;
+			m17 -= fq;
+			m18 -= fq;
+            //---------------------------------------------------------------------//
+
+            porosity = Poros[n];
+            perm = Perm[n];
+
+            c0 = 0.5*(1.0+porosity*0.5*mu_eff/perm);
+            if (porosity==1.0) c0 = 0.5;//i.e. apparent pore nodes
+            GeoFun = 1.75/sqrt(150.0*porosity*porosity*porosity);
+            c1 = porosity*0.5*GeoFun/sqrt(perm);
+            if (porosity==1.0) c1 = 0.0;//i.e. apparent pore nodes
+
+            vx = jx/rho0+0.5*porosity*Gx;
+            vy = jy/rho0+0.5*porosity*Gy;
+            vz = jz/rho0+0.5*porosity*Gz;
+            v_mag=sqrt(vx*vx+vy*vy+vz*vz);
+            ux = vx/(c0+sqrt(c0*c0+c1*v_mag));
+            uy = vy/(c0+sqrt(c0*c0+c1*v_mag));
+            uz = vz/(c0+sqrt(c0*c0+c1*v_mag));
+            u_mag=sqrt(ux*ux+uy*uy+uz*uz);
+
+            //Update the total force to include linear (Darcy) and nonlinear (Forchheimer) drags due to the porous medium
+            Fx = rho0*(-porosity*mu_eff/perm*ux - porosity*GeoFun/sqrt(perm)*u_mag*ux + porosity*Gx);
+            Fy = rho0*(-porosity*mu_eff/perm*uy - porosity*GeoFun/sqrt(perm)*u_mag*uy + porosity*Gy);
+            Fz = rho0*(-porosity*mu_eff/perm*uz - porosity*GeoFun/sqrt(perm)*u_mag*uz + porosity*Gz);
+            if (porosity==1.0){
+                Fx=rho0*Gx;
+                Fy=rho0*Gy;
+                Fz=rho0*Gz;
+            }
+
+            //Calculate pressure for Incompressible-MRT model
+            pressure=rho/3.f;
+
+            //-------------------- IMRT collison where body force has NO higher-order terms -------------//
+			m1 = m1 + rlx_setA*((19*(ux*ux+uy*uy+uz*uz)*rho0/porosity - 11*rho) - m1);
+			m2 = m2 + rlx_setA*((3*rho - 5.5*(ux*ux+uy*uy+uz*uz)*rho0/porosity) - m2);
+            jx = jx + Fx;
+			m4 = m4 + rlx_setB*((-0.6666666666666666*ux*rho0)- m4)
+                    + (1-0.5*rlx_setB)*(-0.6666666666666666*Fx);
+            jy = jy + Fy;
+			m6 = m6 + rlx_setB*((-0.6666666666666666*uy*rho0)- m6)
+                    + (1-0.5*rlx_setB)*(-0.6666666666666666*Fy);
+            jz = jz + Fz;
+			m8 = m8 + rlx_setB*((-0.6666666666666666*uz*rho0)- m8)
+                    + (1-0.5*rlx_setB)*(-0.6666666666666666*Fz);
+			m9 = m9 + rlx_setA*(((2*ux*ux-uy*uy-uz*uz)*rho0/porosity) - m9);
+			m10 = m10 + rlx_setA*( - m10);
+            //m10 = m10 + rlx_setA*(-0.5*rho0*((2*ux*ux-uy*uy-uz*uz)/porosity)- m10);
+			m11 = m11 + rlx_setA*(((uy*uy-uz*uz)*rho0/porosity) - m11);
+			m12 = m12 + rlx_setA*( - m12);
+            //m12 = m12 + rlx_setA*(-0.5*(rho0*(uy*uy-uz*uz)/porosity)- m12);
+			m13 = m13 + rlx_setA*( (ux*uy*rho0/porosity) - m13);
+			m14 = m14 + rlx_setA*( (uy*uz*rho0/porosity) - m14);
+			m15 = m15 + rlx_setA*( (ux*uz*rho0/porosity) - m15);
+			m16 = m16 + rlx_setB*( - m16);
+			m17 = m17 + rlx_setB*( - m17);
+			m18 = m18 + rlx_setB*( - m18);
+            //.......................................................................................................
+
+            //.................inverse transformation......................................................
+            // q=0
+			fq = mrt_V1*rho-mrt_V2*m1+mrt_V3*m2;
+			dist[n] = fq;
+
+			// q = 1
+			fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(jx-m4)+mrt_V6*(m9-m10);
+			dist[1*Np+n] = fq;
+
+			// q=2
+			fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(m4-jx)+mrt_V6*(m9-m10);
+			dist[2*Np+n] = fq;
+
+			// q = 3
+			fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(jy-m6)+mrt_V7*(m10-m9)+mrt_V8*(m11-m12);
+			dist[3*Np+n] = fq;
+
+			// q = 4
+			fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(m6-jy)+mrt_V7*(m10-m9)+mrt_V8*(m11-m12);
+			dist[4*Np+n] = fq;
+
+			// q = 5
+			fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(jz-m8)+mrt_V7*(m10-m9)+mrt_V8*(m12-m11);
+			dist[5*Np+n] = fq;
+
+			// q = 6
+			fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(m8-jz)+mrt_V7*(m10-m9)+mrt_V8*(m12-m11);
+			dist[6*Np+n] = fq;
+
+			// q = 7
+			fq = mrt_V1*rho+mrt_V9*m1+mrt_V10*m2+0.1*(jx+jy)+0.025*(m4+m6)+
+					mrt_V7*m9+mrt_V11*m10+mrt_V8*m11+mrt_V12*m12+0.25*m13+0.125*(m16-m17);
+			dist[7*Np+n] = fq;
+
+
+			// q = 8
+			fq = mrt_V1*rho+mrt_V9*m1+mrt_V10*m2-0.1*(jx+jy)-0.025*(m4+m6) +mrt_V7*m9+mrt_V11*m10+mrt_V8*m11
+					+mrt_V12*m12+0.25*m13+0.125*(m17-m16);
+			dist[8*Np+n] = fq;
+
+			// q = 9
+			fq = mrt_V1*rho+mrt_V9*m1+mrt_V10*m2+0.1*(jx-jy)+0.025*(m4-m6)+
+					mrt_V7*m9+mrt_V11*m10+mrt_V8*m11+mrt_V12*m12-0.25*m13+0.125*(m16+m17);
+			dist[9*Np+n] = fq;
+
+			// q = 10
+			fq = mrt_V1*rho+mrt_V9*m1+mrt_V10*m2+0.1*(jy-jx)+0.025*(m6-m4)+
+					mrt_V7*m9+mrt_V11*m10+mrt_V8*m11+mrt_V12*m12-0.25*m13-0.125*(m16+m17);
+			dist[10*Np+n] = fq;
+
+
+			// q = 11
+			fq = mrt_V1*rho+mrt_V9*m1
+					+mrt_V10*m2+0.1*(jx+jz)+0.025*(m4+m8)
+					+mrt_V7*m9+mrt_V11*m10-mrt_V8*m11
+					-mrt_V12*m12+0.25*m15+0.125*(m18-m16);
+			dist[11*Np+n] = fq;
+
+			// q = 12
+			fq = mrt_V1*rho+mrt_V9*m1+mrt_V10*m2-0.1*(jx+jz)-0.025*(m4+m8)+
+					mrt_V7*m9+mrt_V11*m10-mrt_V8*m11-mrt_V12*m12+0.25*m15+0.125*(m16-m18);
+			dist[12*Np+n] = fq;
+
+			// q = 13
+			fq = mrt_V1*rho+mrt_V9*m1
+					+mrt_V10*m2+0.1*(jx-jz)+0.025*(m4-m8)
+					+mrt_V7*m9+mrt_V11*m10-mrt_V8*m11
+					-mrt_V12*m12-0.25*m15-0.125*(m16+m18);
+			dist[13*Np+n] = fq;
+
+			// q= 14
+			fq = mrt_V1*rho+mrt_V9*m1
+					+mrt_V10*m2+0.1*(jz-jx)+0.025*(m8-m4)
+					+mrt_V7*m9+mrt_V11*m10-mrt_V8*m11
+					-mrt_V12*m12-0.25*m15+0.125*(m16+m18);
+
+			dist[14*Np+n] = fq;
+
+			// q = 15
+			fq = mrt_V1*rho+mrt_V9*m1
+					+mrt_V10*m2+0.1*(jy+jz)+0.025*(m6+m8)
+					-mrt_V6*m9-mrt_V7*m10+0.25*m14+0.125*(m17-m18);
+			dist[15*Np+n] = fq;
+
+			// q = 16
+			fq =  mrt_V1*rho+mrt_V9*m1
+					+mrt_V10*m2-0.1*(jy+jz)-0.025*(m6+m8)
+					-mrt_V6*m9-mrt_V7*m10+0.25*m14+0.125*(m18-m17);
+			dist[16*Np+n] = fq;
+
+
+			// q = 17
+			fq = mrt_V1*rho+mrt_V9*m1
+					+mrt_V10*m2+0.1*(jy-jz)+0.025*(m6-m8)
+					-mrt_V6*m9-mrt_V7*m10-0.25*m14+0.125*(m17+m18);
+			dist[17*Np+n] = fq;
+
+			// q = 18
+			fq = mrt_V1*rho+mrt_V9*m1
+					+mrt_V10*m2+0.1*(jz-jy)+0.025*(m8-m6)
+					-mrt_V6*m9-mrt_V7*m10-0.25*m14-0.125*(m17+m18);
+			dist[18*Np+n] = fq;
+            //........................................................................
+
+            //Update velocity on device
+            Velocity[0*Np+n] = ux;
+            Velocity[1*Np+n] = uy;
+            Velocity[2*Np+n] = uz;
+            //Update pressure on device
+            Pressure[n] = pressure;
+
+		}
+	}
+}
+
+
+__global__ void dvc_ScaLBL_D3Q19_GreyIMRT_Init(double *dist, int Np, double Den)
+{
+	int n;
+	int S = Np/NBLOCKS/NTHREADS + 1;
+	for (int s=0; s<S; s++){
+		//........Get 1-D index for this thread....................
+		n = S*blockIdx.x*blockDim.x + s*blockDim.x + threadIdx.x;
+		if (n<Np ){
+			dist[n] = Den - 0.6666666666666667;
+			dist[Np+n] = 0.055555555555555555;		//double(100*n)+1.f;
+			dist[2*Np+n] = 0.055555555555555555;	//double(100*n)+2.f;
+			dist[3*Np+n] = 0.055555555555555555;	//double(100*n)+3.f;
+			dist[4*Np+n] = 0.055555555555555555;	//double(100*n)+4.f;
+			dist[5*Np+n] = 0.055555555555555555;	//double(100*n)+5.f;
+			dist[6*Np+n] = 0.055555555555555555;	//double(100*n)+6.f;
+			dist[7*Np+n] = 0.0277777777777778;   //double(100*n)+7.f;
+			dist[8*Np+n] = 0.0277777777777778;   //double(100*n)+8.f;
+			dist[9*Np+n] = 0.0277777777777778;   //double(100*n)+9.f;
+			dist[10*Np+n] = 0.0277777777777778;  //double(100*n)+10.f;
+			dist[11*Np+n] = 0.0277777777777778;  //double(100*n)+11.f;
+			dist[12*Np+n] = 0.0277777777777778;  //double(100*n)+12.f;
+			dist[13*Np+n] = 0.0277777777777778;  //double(100*n)+13.f;
+			dist[14*Np+n] = 0.0277777777777778;  //double(100*n)+14.f;
+			dist[15*Np+n] = 0.0277777777777778;  //double(100*n)+15.f;
+			dist[16*Np+n] = 0.0277777777777778;  //double(100*n)+16.f;
+			dist[17*Np+n] = 0.0277777777777778;  //double(100*n)+17.f;
+			dist[18*Np+n] = 0.0277777777777778;  //double(100*n)+18.f;
+		}
+	}
+}
+
 
 extern "C" void ScaLBL_D3Q19_AAeven_Greyscale(double *dist, int start, int finish, int Np, double rlx, double rlx_eff, double Fx, double Fy, double Fz,double *Poros,double *Perm, double *Velocity,double *Pressure){
 	
@@ -1647,3 +2728,30 @@ extern "C" void ScaLBL_D3Q19_AAodd_Greyscale_IMRT(int *neighborList, double *dis
 	}
 }
 
+extern "C" void ScaLBL_D3Q19_AAodd_Greyscale_MRT(int *neighborList, double *dist, int start, int finish, int Np, double rlx, double rlx_eff, double Fx, double Fy, double Fz,double *Poros,double *Perm, double *Velocity,double rho0,double *Pressure){
+
+    dvc_ScaLBL_D3Q19_AAodd_Greyscale_MRT<<<NBLOCKS,NTHREADS >>>(neighborList,dist,start,finish,Np,rlx,rlx_eff,Fx,Fy,Fz,Poros,Perm,Velocity,rho0,Pressure);
+
+    cudaError_t err = cudaGetLastError();
+	if (cudaSuccess != err){
+		printf("CUDA error in ScaLBL_D3Q19_AAodd_Greyscale_MRT: %s \n",cudaGetErrorString(err));
+	}
+}
+
+extern "C" void ScaLBL_D3Q19_AAeven_Greyscale_MRT(double *dist, int start, int finish, int Np, double rlx, double rlx_eff, double Fx, double Fy, double Fz,double *Poros,double *Perm, double *Velocity,double rho0,double *Pressure){
+	
+    dvc_ScaLBL_D3Q19_AAeven_Greyscale_MRT<<<NBLOCKS,NTHREADS >>>(dist,start,finish,Np,rlx,rlx_eff,Fx,Fy,Fz,Poros,Perm,Velocity,rho0,Pressure);
+
+    cudaError_t err = cudaGetLastError();
+	if (cudaSuccess != err){
+		printf("CUDA error in ScaLBL_D3Q19_AAeven_Greyscale_MRT: %s \n",cudaGetErrorString(err));
+	}
+}
+
+extern "C" void ScaLBL_D3Q19_GreyIMRT_Init(double *dist, int Np, double Den){
+	dvc_ScaLBL_D3Q19_GreyIMRT_Init<<<NBLOCKS,NTHREADS >>>(dist, Np, Den);
+	cudaError_t err = cudaGetLastError();
+	if (cudaSuccess != err){
+		printf("CUDA error in ScaLBL_D3Q19_GreyIMRT_Init: %s \n",cudaGetErrorString(err));
+	}
+}
diff --git a/gpu/GreyscaleColor.cu b/gpu/GreyscaleColor.cu
new file mode 100644
index 00000000..2af5760b
--- /dev/null
+++ b/gpu/GreyscaleColor.cu
@@ -0,0 +1,2993 @@
+#include <stdio.h>
+#include <math.h>
+
+#define NBLOCKS 1024
+#define NTHREADS 256
+
+//Model-1 & 4
+__global__ void dvc_ScaLBL_D3Q19_AAodd_GreyscaleColor(int *neighborList, int *Map, double *dist, double *Aq, double *Bq, double *Den,
+		 double *Phi, double *GreySolidGrad, double *Poros,double *Perm, double *Velocity, 
+         double rhoA, double rhoB, double tauA, double tauB,double tauA_eff,double tauB_eff,double alpha, double beta,
+		double Gx, double Gy, double Gz, int strideY, int strideZ, int start, int finish, int Np){
+
+	int n,nn,ijk,nread;
+	int nr1,nr2,nr3,nr4,nr5,nr6;
+	int nr7,nr8,nr9,nr10;
+	int nr11,nr12,nr13,nr14;
+	//int nr15,nr16,nr17,nr18;
+	double fq;
+	// conserved momemnts
+	double rho,jx,jy,jz;
+	double vx,vy,vz,v_mag;
+    double ux,uy,uz,u_mag;
+	// non-conserved moments
+	double m1,m2,m4,m6,m8,m9,m10,m11,m12,m13,m14,m15,m16,m17,m18;
+	double m3,m5,m7;
+	double nA,nB; // number density
+	double a1,b1,a2,b2,nAB,delta;
+	double C,nx,ny,nz; //color gradient magnitude and direction
+	double phi,tau,rho0,rlx_setA,rlx_setB;
+
+    double GeoFun=0.0;//geometric function from Guo's PRE 66, 036304 (2002)
+    double porosity;
+    double perm;//voxel permeability
+    double c0, c1; //Guo's model parameters
+    double tau_eff;
+    double mu_eff;//kinematic viscosity
+    double nx_gs,ny_gs,nz_gs;//grey-solid color gradient
+    double nx_phase,ny_phase,nz_phase,C_phase;
+    double Fx,Fy,Fz;
+
+	const double mrt_V1=0.05263157894736842;
+	const double mrt_V2=0.012531328320802;
+	const double mrt_V3=0.04761904761904762;
+	const double mrt_V4=0.004594820384294068;
+	const double mrt_V5=0.01587301587301587;
+	const double mrt_V6=0.0555555555555555555555555;
+	const double mrt_V7=0.02777777777777778;
+	const double mrt_V8=0.08333333333333333;
+	const double mrt_V9=0.003341687552213868;
+	const double mrt_V10=0.003968253968253968;
+	const double mrt_V11=0.01388888888888889;
+	const double mrt_V12=0.04166666666666666;
+
+	int S = Np/NBLOCKS/NTHREADS + 1;
+	for (int s=0; s<S; s++){
+		//........Get 1-D index for this thread....................
+		n =  S*blockIdx.x*blockDim.x + s*blockDim.x + threadIdx.x + start;
+		if (n<finish) {
+			// read the component number densities
+			nA = Den[n];
+			nB = Den[Np + n];
+
+            porosity = Poros[n];
+            perm = Perm[n];
+            nx_gs = GreySolidGrad[n+0*Np];
+            ny_gs = GreySolidGrad[n+1*Np];
+            nz_gs = GreySolidGrad[n+2*Np];
+
+			// compute phase indicator field
+			phi=(nA-nB)/(nA+nB);
+
+			// local density
+			rho0=rhoA + 0.5*(1.0-phi)*(rhoB-rhoA);
+			// local relaxation time
+			tau=tauA + 0.5*(1.0-phi)*(tauB-tauA);
+			tau_eff=tauA_eff + 0.5*(1.0-phi)*(tauB_eff-tauA_eff);
+			rlx_setA = 1.f/tau;
+			rlx_setB = 8.f*(2.f-rlx_setA)/(8.f-rlx_setA);
+            mu_eff = (tau_eff-0.5)/3.0;//kinematic viscosity
+			
+			// Get the 1D index based on regular data layout
+			ijk = Map[n];
+			//					COMPUTE THE COLOR GRADIENT
+			//........................................................................
+			//.................Read Phase Indicator Values............................
+			//........................................................................
+			nn = ijk-1;							// neighbor index (get convention)
+			m1 = Phi[nn];						// get neighbor for phi - 1
+			//........................................................................
+			nn = ijk+1;							// neighbor index (get convention)
+			m2 = Phi[nn];						// get neighbor for phi - 2
+			//........................................................................
+			nn = ijk-strideY;							// neighbor index (get convention)
+			m3 = Phi[nn];					// get neighbor for phi - 3
+			//........................................................................
+			nn = ijk+strideY;							// neighbor index (get convention)
+			m4 = Phi[nn];					// get neighbor for phi - 4
+			//........................................................................
+			nn = ijk-strideZ;						// neighbor index (get convention)
+			m5 = Phi[nn];					// get neighbor for phi - 5
+			//........................................................................
+			nn = ijk+strideZ;						// neighbor index (get convention)
+			m6 = Phi[nn];					// get neighbor for phi - 6
+			//........................................................................
+			nn = ijk-strideY-1;						// neighbor index (get convention)
+			m7 = Phi[nn];					// get neighbor for phi - 7
+			//........................................................................
+			nn = ijk+strideY+1;						// neighbor index (get convention)
+			m8 = Phi[nn];					// get neighbor for phi - 8
+			//........................................................................
+			nn = ijk+strideY-1;						// neighbor index (get convention)
+			m9 = Phi[nn];					// get neighbor for phi - 9
+			//........................................................................
+			nn = ijk-strideY+1;						// neighbor index (get convention)
+			m10 = Phi[nn];					// get neighbor for phi - 10
+			//........................................................................
+			nn = ijk-strideZ-1;						// neighbor index (get convention)
+			m11 = Phi[nn];					// get neighbor for phi - 11
+			//........................................................................
+			nn = ijk+strideZ+1;						// neighbor index (get convention)
+			m12 = Phi[nn];					// get neighbor for phi - 12
+			//........................................................................
+			nn = ijk+strideZ-1;						// neighbor index (get convention)
+			m13 = Phi[nn];					// get neighbor for phi - 13
+			//........................................................................
+			nn = ijk-strideZ+1;						// neighbor index (get convention)
+			m14 = Phi[nn];					// get neighbor for phi - 14
+			//........................................................................
+			nn = ijk-strideZ-strideY;					// neighbor index (get convention)
+			m15 = Phi[nn];					// get neighbor for phi - 15
+			//........................................................................
+			nn = ijk+strideZ+strideY;					// neighbor index (get convention)
+			m16 = Phi[nn];					// get neighbor for phi - 16
+			//........................................................................
+			nn = ijk+strideZ-strideY;					// neighbor index (get convention)
+			m17 = Phi[nn];					// get neighbor for phi - 17
+			//........................................................................
+			nn = ijk-strideZ+strideY;					// neighbor index (get convention)
+			m18 = Phi[nn];					// get neighbor for phi - 18
+			//............Compute the Color Gradient...................................
+			nx_phase = -(m1-m2+0.5*(m7-m8+m9-m10+m11-m12+m13-m14));
+			ny_phase = -(m3-m4+0.5*(m7-m8-m9+m10+m15-m16+m17-m18));
+			nz_phase = -(m5-m6+0.5*(m11-m12-m13+m14+m15-m16-m17+m18));
+			C_phase = sqrt(nx_phase*nx_phase+ny_phase*ny_phase+nz_phase*nz_phase);
+
+            //correct the normal color gradient by considering the effect of grey solid
+            nx = nx_phase + (1.0-porosity)*nx_gs; 
+            ny = ny_phase + (1.0-porosity)*ny_gs; 
+            nz = nz_phase + (1.0-porosity)*nz_gs; 
+            if (C_phase==0.0){
+                nx = nx_phase; 
+                ny = ny_phase;
+                nz = nz_phase;
+            }
+
+			//...........Normalize the Color Gradient.................................
+			C = sqrt(nx*nx+ny*ny+nz*nz);
+			double ColorMag = C;
+			if (C==0.0) ColorMag=1.0;
+			nx = nx/ColorMag;
+			ny = ny/ColorMag;
+			nz = nz/ColorMag;		
+
+			// q=0
+			fq = dist[n];
+			rho = fq;
+			m1  = -30.0*fq;
+			m2  = 12.0*fq;
+
+			// q=1
+			//nread = neighborList[n]; // neighbor 2 
+			//fq = dist[nread]; // reading the f1 data into register fq		
+			nr1 = neighborList[n]; 
+			fq = dist[nr1]; // reading the f1 data into register fq
+			rho += fq;
+			m1 -= 11.0*fq;
+			m2 -= 4.0*fq;
+			jx = fq;
+			m4 = -4.0*fq;
+			m9 = 2.0*fq;
+			m10 = -4.0*fq;
+
+			// f2 = dist[10*Np+n];
+			//nread = neighborList[n+Np]; // neighbor 1 ( < 10Np => even part of dist)
+			//fq = dist[nread];  // reading the f2 data into register fq
+			nr2 = neighborList[n+Np]; // neighbor 1 ( < 10Np => even part of dist)
+			fq = dist[nr2];  // reading the f2 data into register fq
+			rho += fq;
+			m1 -= 11.0*(fq);
+			m2 -= 4.0*(fq);
+			jx -= fq;
+			m4 += 4.0*(fq);
+			m9 += 2.0*(fq);
+			m10 -= 4.0*(fq);
+
+			// q=3
+			//nread = neighborList[n+2*Np]; // neighbor 4
+			//fq = dist[nread];
+			nr3 = neighborList[n+2*Np]; // neighbor 4
+			fq = dist[nr3];
+			rho += fq;
+			m1 -= 11.0*fq;
+			m2 -= 4.0*fq;
+			jy = fq;
+			m6 = -4.0*fq;
+			m9 -= fq;
+			m10 += 2.0*fq;
+			m11 = fq;
+			m12 = -2.0*fq;
+
+			// q = 4
+			//nread = neighborList[n+3*Np]; // neighbor 3
+			//fq = dist[nread];
+			nr4 = neighborList[n+3*Np]; // neighbor 3
+			fq = dist[nr4];
+			rho+= fq;
+			m1 -= 11.0*fq;
+			m2 -= 4.0*fq;
+			jy -= fq;
+			m6 += 4.0*fq;
+			m9 -= fq;
+			m10 += 2.0*fq;
+			m11 += fq;
+			m12 -= 2.0*fq;
+
+			// q=5
+			//nread = neighborList[n+4*Np];
+			//fq = dist[nread];
+			nr5 = neighborList[n+4*Np];
+			fq = dist[nr5];
+			rho += fq;
+			m1 -= 11.0*fq;
+			m2 -= 4.0*fq;
+			jz = fq;
+			m8 = -4.0*fq;
+			m9 -= fq;
+			m10 += 2.0*fq;
+			m11 -= fq;
+			m12 += 2.0*fq;
+
+
+			// q = 6
+			//nread = neighborList[n+5*Np];
+			//fq = dist[nread];
+			nr6 = neighborList[n+5*Np];
+			fq = dist[nr6];
+			rho+= fq;
+			m1 -= 11.0*fq;
+			m2 -= 4.0*fq;
+			jz -= fq;
+			m8 += 4.0*fq;
+			m9 -= fq;
+			m10 += 2.0*fq;
+			m11 -= fq;
+			m12 += 2.0*fq;
+
+			// q=7
+			//nread = neighborList[n+6*Np];
+			//fq = dist[nread];
+			nr7 = neighborList[n+6*Np];
+			fq = dist[nr7];
+			rho += fq;
+			m1 += 8.0*fq;
+			m2 += fq;
+			jx += fq;
+			m4 += fq;
+			jy += fq;
+			m6 += fq;
+			m9  += fq;
+			m10 += fq;
+			m11 += fq;
+			m12 += fq;
+			m13 = fq;
+			m16 = fq;
+			m17 = -fq;
+
+			// q = 8
+			//nread = neighborList[n+7*Np];
+			//fq = dist[nread];
+			nr8 = neighborList[n+7*Np];
+			fq = dist[nr8];
+			rho += fq;
+			m1 += 8.0*fq;
+			m2 += fq;
+			jx -= fq;
+			m4 -= fq;
+			jy -= fq;
+			m6 -= fq;
+			m9 += fq;
+			m10 += fq;
+			m11 += fq;
+			m12 += fq;
+			m13 += fq;
+			m16 -= fq;
+			m17 += fq;
+
+			// q=9
+			//nread = neighborList[n+8*Np];
+			//fq = dist[nread];
+			nr9 = neighborList[n+8*Np];
+			fq = dist[nr9];
+			rho += fq;
+			m1 += 8.0*fq;
+			m2 += fq;
+			jx += fq;
+			m4 += fq;
+			jy -= fq;
+			m6 -= fq;
+			m9 += fq;
+			m10 += fq;
+			m11 += fq;
+			m12 += fq;
+			m13 -= fq;
+			m16 += fq;
+			m17 += fq;
+
+			// q = 10
+			//nread = neighborList[n+9*Np];
+			//fq = dist[nread];
+			nr10 = neighborList[n+9*Np];
+			fq = dist[nr10];
+			rho += fq;
+			m1 += 8.0*fq;
+			m2 += fq;
+			jx -= fq;
+			m4 -= fq;
+			jy += fq;
+			m6 += fq;
+			m9 += fq;
+			m10 += fq;
+			m11 += fq;
+			m12 += fq;
+			m13 -= fq;
+			m16 -= fq;
+			m17 -= fq;
+
+			// q=11
+			//nread = neighborList[n+10*Np];
+			//fq = dist[nread];
+			nr11 = neighborList[n+10*Np];
+			fq = dist[nr11];
+			rho += fq;
+			m1 += 8.0*fq;
+			m2 += fq;
+			jx += fq;
+			m4 += fq;
+			jz += fq;
+			m8 += fq;
+			m9 += fq;
+			m10 += fq;
+			m11 -= fq;
+			m12 -= fq;
+			m15 = fq;
+			m16 -= fq;
+			m18 = fq;
+
+			// q=12
+			//nread = neighborList[n+11*Np];
+			//fq = dist[nread];
+			nr12 = neighborList[n+11*Np];
+			fq = dist[nr12];
+			rho += fq;
+			m1 += 8.0*fq;
+			m2 += fq;
+			jx -= fq;
+			m4 -= fq;
+			jz -= fq;
+			m8 -= fq;
+			m9 += fq;
+			m10 += fq;
+			m11 -= fq;
+			m12 -= fq;
+			m15 += fq;
+			m16 += fq;
+			m18 -= fq;
+
+			// q=13
+			//nread = neighborList[n+12*Np];
+			//fq = dist[nread];
+			nr13 = neighborList[n+12*Np];
+			fq = dist[nr13];
+			rho += fq;
+			m1 += 8.0*fq;
+			m2 += fq;
+			jx += fq;
+			m4 += fq;
+			jz -= fq;
+			m8 -= fq;
+			m9 += fq;
+			m10 += fq;
+			m11 -= fq;
+			m12 -= fq;
+			m15 -= fq;
+			m16 -= fq;
+			m18 -= fq;
+
+			// q=14
+			//nread = neighborList[n+13*Np];
+			//fq = dist[nread];
+			nr14 = neighborList[n+13*Np];
+			fq = dist[nr14];
+			rho += fq;
+			m1 += 8.0*fq;
+			m2 += fq;
+			jx -= fq;
+			m4 -= fq;
+			jz += fq;
+			m8 += fq;
+			m9 += fq;
+			m10 += fq;
+			m11 -= fq;
+			m12 -= fq;
+			m15 -= fq;
+			m16 += fq;
+			m18 += fq;
+
+			// q=15
+			nread = neighborList[n+14*Np];
+			fq = dist[nread];
+			//fq = dist[17*Np+n];
+			rho += fq;
+			m1 += 8.0*fq;
+			m2 += fq;
+			jy += fq;
+			m6 += fq;
+			jz += fq;
+			m8 += fq;
+			m9 -= 2.0*fq;
+			m10 -= 2.0*fq;
+			m14 = fq;
+			m17 += fq;
+			m18 -= fq;
+
+			// q=16
+			nread = neighborList[n+15*Np];
+			fq = dist[nread];
+			//fq = dist[8*Np+n];
+			rho += fq;
+			m1 += 8.0*fq;
+			m2 += fq;
+			jy -= fq;
+			m6 -= fq;
+			jz -= fq;
+			m8 -= fq;
+			m9 -= 2.0*fq;
+			m10 -= 2.0*fq;
+			m14 += fq;
+			m17 -= fq;
+			m18 += fq;
+
+			// q=17
+			//fq = dist[18*Np+n];
+			nread = neighborList[n+16*Np];
+			fq = dist[nread];
+			rho += fq;
+			m1 += 8.0*fq;
+			m2 += fq;
+			jy += fq;
+			m6 += fq;
+			jz -= fq;
+			m8 -= fq;
+			m9 -= 2.0*fq;
+			m10 -= 2.0*fq;
+			m14 -= fq;
+			m17 += fq;
+			m18 += fq;
+
+			// q=18
+			nread = neighborList[n+17*Np];
+			fq = dist[nread];
+			//fq = dist[9*Np+n];
+			rho += fq;
+			m1 += 8.0*fq;
+			m2 += fq;
+			jy -= fq;
+			m6 -= fq;
+			jz += fq;
+			m8 += fq;
+			m9 -= 2.0*fq;
+			m10 -= 2.0*fq;
+			m14 -= fq;
+			m17 -= fq;
+			m18 -= fq;
+			
+            // Compute greyscale related parameters
+            c0 = 0.5*(1.0+porosity*0.5*mu_eff/perm);
+            if (porosity==1.0) c0 = 0.5;//i.e. apparent pore nodes
+            //GeoFun = 1.75/sqrt(150.0*porosity*porosity*porosity);
+            c1 = porosity*0.5*GeoFun/sqrt(perm);
+            if (porosity==1.0) c1 = 0.0;//i.e. apparent pore nodes
+
+            vx = jx/rho0+0.5*(porosity*Gx);
+            vy = jy/rho0+0.5*(porosity*Gy);
+            vz = jz/rho0+0.5*(porosity*Gz);
+            v_mag=sqrt(vx*vx+vy*vy+vz*vz);
+            ux = vx/(c0+sqrt(c0*c0+c1*v_mag));
+            uy = vy/(c0+sqrt(c0*c0+c1*v_mag));
+            uz = vz/(c0+sqrt(c0*c0+c1*v_mag));
+            u_mag=sqrt(ux*ux+uy*uy+uz*uz);
+
+            //Update the total force to include linear (Darcy) and nonlinear (Forchheimer) drags due to the porous medium
+            Fx = rho0*(-porosity*mu_eff/perm*ux - porosity*GeoFun/sqrt(perm)*u_mag*ux + porosity*Gx);
+            Fy = rho0*(-porosity*mu_eff/perm*uy - porosity*GeoFun/sqrt(perm)*u_mag*uy + porosity*Gy);
+            Fz = rho0*(-porosity*mu_eff/perm*uz - porosity*GeoFun/sqrt(perm)*u_mag*uz + porosity*Gz);
+            if (porosity==1.0){
+                Fx=rho0*(Gx);
+                Fy=rho0*(Gy);
+                Fz=rho0*(Gz);
+            }
+
+			// write the velocity 
+			Velocity[n] = ux;
+			Velocity[Np+n] = uy;
+			Velocity[2*Np+n] = uz;
+
+			//........................................................................
+			//..............carry out relaxation process..............................
+			//..........Toelke, Fruediger et. al. 2006................................
+            //---------------- NO higher-order force -------------------------------//
+			if (C == 0.0)	nx = ny = nz = 0.0;
+			m1 = m1 + rlx_setA*((19*(ux*ux+uy*uy+uz*uz)*rho0/porosity - 11*rho) -19*alpha*C - m1);
+			m2 = m2 + rlx_setA*((3*rho - 5.5*(ux*ux+uy*uy+uz*uz)*rho0/porosity)- m2);
+            jx = jx + Fx;
+			m4 = m4 + rlx_setB*((-0.6666666666666666*ux*rho0)- m4)
+                    + (1-0.5*rlx_setB)*(-0.6666666666666666*Fx);
+            jy = jy + Fy;
+			m6 = m6 + rlx_setB*((-0.6666666666666666*uy*rho0)- m6)
+                    + (1-0.5*rlx_setB)*(-0.6666666666666666*Fy);
+            jz = jz + Fz;
+			m8 = m8 + rlx_setB*((-0.6666666666666666*uz*rho0)- m8)
+                    + (1-0.5*rlx_setB)*(-0.6666666666666666*Fz);
+			m9 = m9 + rlx_setA*(((2*ux*ux-uy*uy-uz*uz)*rho0/porosity) + 0.5*alpha*C*(2*nx*nx-ny*ny-nz*nz) - m9);
+			m10 = m10 + rlx_setA*( - m10);
+            //m10 = m10 + rlx_setA*(-0.5*rho0*((2*ux*ux-uy*uy-uz*uz)/porosity)- m10);
+			m11 = m11 + rlx_setA*(((uy*uy-uz*uz)*rho0/porosity) + 0.5*alpha*C*(ny*ny-nz*nz)- m11);
+			m12 = m12 + rlx_setA*( - m12);
+            //m12 = m12 + rlx_setA*(-0.5*(rho0*(uy*uy-uz*uz)/porosity)- m12);
+			m13 = m13 + rlx_setA*( (ux*uy*rho0/porosity) + 0.5*alpha*C*nx*ny - m13);
+			m14 = m14 + rlx_setA*( (uy*uz*rho0/porosity) + 0.5*alpha*C*ny*nz - m14);
+			m15 = m15 + rlx_setA*( (ux*uz*rho0/porosity) + 0.5*alpha*C*nx*nz - m15);
+			m16 = m16 + rlx_setB*( - m16);
+			m17 = m17 + rlx_setB*( - m17);
+			m18 = m18 + rlx_setB*( - m18);
+            //----------------------------------------------------------------------//
+
+            //----------------With higher-order force ------------------------------//
+			//if (C == 0.0)	nx = ny = nz = 0.0;
+			//m1 = m1 + rlx_setA*((19*(ux*ux+uy*uy+uz*uz)*rho0/porosity - 11*rho) -19*alpha*C - m1)
+            //        + (1-0.5*rlx_setA)*38*(Fx*ux+Fy*uy+Fz*uz)/porosity;
+			//m2 = m2 + rlx_setA*((3*rho - 5.5*(ux*ux+uy*uy+uz*uz)*rho0/porosity)- m2)
+            //        + (1-0.5*rlx_setA)*11*(-Fx*ux-Fy*uy-Fz*uz)/porosity;
+            //jx = jx + Fx;
+			//m4 = m4 + rlx_setB*((-0.6666666666666666*ux*rho0)- m4)
+            //        + (1-0.5*rlx_setB)*(-0.6666666666666666*Fx);
+            //jy = jy + Fy;
+			//m6 = m6 + rlx_setB*((-0.6666666666666666*uy*rho0)- m6)
+            //        + (1-0.5*rlx_setB)*(-0.6666666666666666*Fy);
+            //jz = jz + Fz;
+			//m8 = m8 + rlx_setB*((-0.6666666666666666*uz*rho0)- m8)
+            //        + (1-0.5*rlx_setB)*(-0.6666666666666666*Fz);
+			//m9 = m9 + rlx_setA*(((2*ux*ux-uy*uy-uz*uz)*rho0/porosity) + 0.5*alpha*C*(2*nx*nx-ny*ny-nz*nz) - m9)
+            //        + (1-0.5*rlx_setA)*(4*Fx*ux-2*Fy*uy-2*Fz*uz)/porosity;
+			////m10 = m10 + rlx_setA*( - m10);
+            //m10 = m10 + rlx_setA*(-0.5*rho0*((2*ux*ux-uy*uy-uz*uz)/porosity)- m10)
+            //          + (1-0.5*rlx_setA)*(-2*Fx*ux+Fy*uy+Fz*uz)/porosity;
+			//m11 = m11 + rlx_setA*(((uy*uy-uz*uz)*rho0/porosity) + 0.5*alpha*C*(ny*ny-nz*nz)- m11)
+            //          + (1-0.5*rlx_setA)*(2*Fy*uy-2*Fz*uz)/porosity;
+			////m12 = m12 + rlx_setA*( - m12);
+            //m12 = m12 + rlx_setA*(-0.5*(rho0*(uy*uy-uz*uz)/porosity)- m12)
+            //          + (1-0.5*rlx_setA)*(-Fy*uy+Fz*uz)/porosity;
+			//m13 = m13 + rlx_setA*( (ux*uy*rho0/porosity) + 0.5*alpha*C*nx*ny - m13);
+            //          + (1-0.5*rlx_setA)*(Fy*ux+Fx*uy)/porosity;
+			//m14 = m14 + rlx_setA*( (uy*uz*rho0/porosity) + 0.5*alpha*C*ny*nz - m14);
+            //          + (1-0.5*rlx_setA)*(Fz*uy+Fy*uz)/porosity;
+			//m15 = m15 + rlx_setA*( (ux*uz*rho0/porosity) + 0.5*alpha*C*nx*nz - m15);
+            //          + (1-0.5*rlx_setA)*(Fz*ux+Fx*uz)/porosity;
+			//m16 = m16 + rlx_setB*( - m16);
+			//m17 = m17 + rlx_setB*( - m17);
+			//m18 = m18 + rlx_setB*( - m18);
+            //----------------------------------------------------------------------//
+
+			//.................inverse transformation......................................................
+			// q=0
+			fq = mrt_V1*rho-mrt_V2*m1+mrt_V3*m2;
+			dist[n] = fq;
+
+			// q = 1
+			fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(jx-m4)+mrt_V6*(m9-m10);
+			//nread = neighborList[n+Np];
+			dist[nr2] = fq;
+
+			// q=2
+			fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(m4-jx)+mrt_V6*(m9-m10);
+			//nread = neighborList[n];
+			dist[nr1] = fq;
+
+			// q = 3
+			fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(jy-m6)+mrt_V7*(m10-m9)+mrt_V8*(m11-m12);
+			//nread = neighborList[n+3*Np];
+			dist[nr4] = fq;
+
+			// q = 4
+			fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(m6-jy)+mrt_V7*(m10-m9)+mrt_V8*(m11-m12);
+			//nread = neighborList[n+2*Np];
+			dist[nr3] = fq;
+
+			// q = 5
+			fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(jz-m8)+mrt_V7*(m10-m9)+mrt_V8*(m12-m11);
+			//nread = neighborList[n+5*Np];
+			dist[nr6] = fq;
+
+			// q = 6
+			fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(m8-jz)+mrt_V7*(m10-m9)+mrt_V8*(m12-m11);
+			//nread = neighborList[n+4*Np];
+			dist[nr5] = fq;
+
+			// q = 7
+			fq = mrt_V1*rho+mrt_V9*m1+mrt_V10*m2+0.1*(jx+jy)+0.025*(m4+m6)+
+					mrt_V7*m9+mrt_V11*m10+mrt_V8*m11+mrt_V12*m12+0.25*m13+0.125*(m16-m17);
+			//nread = neighborList[n+7*Np];
+			dist[nr8] = fq;
+
+			// q = 8
+			fq = mrt_V1*rho+mrt_V9*m1+mrt_V10*m2-0.1*(jx+jy)-0.025*(m4+m6) +mrt_V7*m9+mrt_V11*m10+mrt_V8*m11
+					+mrt_V12*m12+0.25*m13+0.125*(m17-m16);
+			//nread = neighborList[n+6*Np];
+			dist[nr7] = fq;
+
+			// q = 9
+			fq = mrt_V1*rho+mrt_V9*m1+mrt_V10*m2+0.1*(jx-jy)+0.025*(m4-m6)+
+					mrt_V7*m9+mrt_V11*m10+mrt_V8*m11+mrt_V12*m12-0.25*m13+0.125*(m16+m17);
+			//nread = neighborList[n+9*Np];
+			dist[nr10] = fq;
+
+			// q = 10
+			fq = mrt_V1*rho+mrt_V9*m1+mrt_V10*m2+0.1*(jy-jx)+0.025*(m6-m4)+
+					mrt_V7*m9+mrt_V11*m10+mrt_V8*m11+mrt_V12*m12-0.25*m13-0.125*(m16+m17);
+			//nread = neighborList[n+8*Np];
+			dist[nr9] = fq;
+
+			// q = 11
+			fq = mrt_V1*rho+mrt_V9*m1
+					+mrt_V10*m2+0.1*(jx+jz)+0.025*(m4+m8)
+					+mrt_V7*m9+mrt_V11*m10-mrt_V8*m11
+					-mrt_V12*m12+0.25*m15+0.125*(m18-m16);
+			//nread = neighborList[n+11*Np];
+			dist[nr12] = fq;
+
+			// q = 12
+			fq = mrt_V1*rho+mrt_V9*m1+mrt_V10*m2-0.1*(jx+jz)-0.025*(m4+m8)+
+					mrt_V7*m9+mrt_V11*m10-mrt_V8*m11-mrt_V12*m12+0.25*m15+0.125*(m16-m18);
+			//nread = neighborList[n+10*Np];
+			dist[nr11]= fq;
+
+			// q = 13
+			fq = mrt_V1*rho+mrt_V9*m1
+					+mrt_V10*m2+0.1*(jx-jz)+0.025*(m4-m8)
+					+mrt_V7*m9+mrt_V11*m10-mrt_V8*m11
+					-mrt_V12*m12-0.25*m15-0.125*(m16+m18);
+			//nread = neighborList[n+13*Np];
+			dist[nr14] = fq;
+
+			// q= 14
+			fq = mrt_V1*rho+mrt_V9*m1
+					+mrt_V10*m2+0.1*(jz-jx)+0.025*(m8-m4)
+					+mrt_V7*m9+mrt_V11*m10-mrt_V8*m11
+					-mrt_V12*m12-0.25*m15+0.125*(m16+m18);
+			//nread = neighborList[n+12*Np];
+			dist[nr13] = fq;
+
+
+			// q = 15
+			fq = mrt_V1*rho+mrt_V9*m1
+					+mrt_V10*m2+0.1*(jy+jz)+0.025*(m6+m8)
+					-mrt_V6*m9-mrt_V7*m10+0.25*m14+0.125*(m17-m18);
+			nread = neighborList[n+15*Np];
+			dist[nread] = fq;
+
+			// q = 16
+			fq =  mrt_V1*rho+mrt_V9*m1
+					+mrt_V10*m2-0.1*(jy+jz)-0.025*(m6+m8)
+					-mrt_V6*m9-mrt_V7*m10+0.25*m14+0.125*(m18-m17);
+			nread = neighborList[n+14*Np];
+			dist[nread] = fq;
+
+
+			// q = 17
+			fq = mrt_V1*rho+mrt_V9*m1
+					+mrt_V10*m2+0.1*(jy-jz)+0.025*(m6-m8)
+					-mrt_V6*m9-mrt_V7*m10-0.25*m14+0.125*(m17+m18);
+			nread = neighborList[n+17*Np];
+			dist[nread] = fq;
+
+			// q = 18
+			fq = mrt_V1*rho+mrt_V9*m1
+					+mrt_V10*m2+0.1*(jz-jy)+0.025*(m8-m6)
+					-mrt_V6*m9-mrt_V7*m10-0.25*m14-0.125*(m17+m18);
+			nread = neighborList[n+16*Np];
+			dist[nread] = fq;
+			//........................................................................
+
+			// Instantiate mass transport distributions
+			// Stationary value - distribution 0
+			nAB = 1.0/(nA+nB);
+			Aq[n] = 0.3333333333333333*nA;
+			Bq[n] = 0.3333333333333333*nB;
+
+			//...............................................
+			// q = 0,2,4
+			// Cq = {1,0,0}, {0,1,0}, {0,0,1}
+			delta = beta*nA*nB*nAB*0.1111111111111111*nx;
+			if (!(nA*nB*nAB>0)) delta=0;
+			a1 = nA*(0.1111111111111111*(1+4.5*ux))+delta;
+			b1 = nB*(0.1111111111111111*(1+4.5*ux))-delta;
+			a2 = nA*(0.1111111111111111*(1-4.5*ux))-delta;
+			b2 = nB*(0.1111111111111111*(1-4.5*ux))+delta;
+
+			// q = 1
+			//nread = neighborList[n+Np];
+			Aq[nr2] = a1;
+			Bq[nr2] = b1;
+			// q=2
+			//nread = neighborList[n];
+			Aq[nr1] = a2;
+			Bq[nr1] = b2;
+
+			//...............................................
+			// Cq = {0,1,0}
+			delta = beta*nA*nB*nAB*0.1111111111111111*ny;
+			if (!(nA*nB*nAB>0)) delta=0;
+			a1 = nA*(0.1111111111111111*(1+4.5*uy))+delta;
+			b1 = nB*(0.1111111111111111*(1+4.5*uy))-delta;
+			a2 = nA*(0.1111111111111111*(1-4.5*uy))-delta;
+			b2 = nB*(0.1111111111111111*(1-4.5*uy))+delta;
+
+			// q = 3
+			//nread = neighborList[n+3*Np];
+			Aq[nr4] = a1;
+			Bq[nr4] = b1;
+			// q = 4
+			//nread = neighborList[n+2*Np];
+			Aq[nr3] = a2;
+			Bq[nr3] = b2;
+
+			//...............................................
+			// q = 4
+			// Cq = {0,0,1}
+			delta = beta*nA*nB*nAB*0.1111111111111111*nz;
+			if (!(nA*nB*nAB>0)) delta=0;
+			a1 = nA*(0.1111111111111111*(1+4.5*uz))+delta;
+			b1 = nB*(0.1111111111111111*(1+4.5*uz))-delta;
+			a2 = nA*(0.1111111111111111*(1-4.5*uz))-delta;
+			b2 = nB*(0.1111111111111111*(1-4.5*uz))+delta;
+
+			// q = 5
+			//nread = neighborList[n+5*Np];
+			Aq[nr6] = a1;
+			Bq[nr6] = b1;
+			// q = 6
+			//nread = neighborList[n+4*Np];
+			Aq[nr5] = a2;
+			Bq[nr5] = b2;
+			//...............................................
+		}
+	}
+}
+
+//Model-1 & 4
+__global__  void dvc_ScaLBL_D3Q19_AAeven_GreyscaleColor(int *Map, double *dist, double *Aq, double *Bq, double *Den, 
+        double *Phi, double *GreySolidGrad, double *Poros,double *Perm, double *Velocity, 
+        double rhoA, double rhoB, double tauA, double tauB,double tauA_eff,double tauB_eff, double alpha, double beta,
+		double Gx, double Gy, double Gz, int strideY, int strideZ, int start, int finish, int Np){
+	int ijk,nn,n;
+	double fq;
+	// conserved momemnts
+	double rho,jx,jy,jz;
+	double vx,vy,vz,v_mag;
+    double ux,uy,uz,u_mag;
+	// non-conserved moments
+	double m1,m2,m4,m6,m8,m9,m10,m11,m12,m13,m14,m15,m16,m17,m18;
+	double m3,m5,m7;
+	double nA,nB; // number density
+	double a1,b1,a2,b2,nAB,delta;
+	double C,nx,ny,nz; //color gradient magnitude and direction
+	double phi,tau,rho0,rlx_setA,rlx_setB;
+
+    double GeoFun=0.0;//geometric function from Guo's PRE 66, 036304 (2002)
+    double porosity;
+    double perm;//voxel permeability
+    double c0, c1; //Guo's model parameters
+    double tau_eff;
+    double mu_eff;//kinematic viscosity
+    double nx_gs,ny_gs,nz_gs;//grey-solid color gradient
+    double nx_phase,ny_phase,nz_phase,C_phase;
+    double Fx,Fy,Fz;
+
+	const double mrt_V1=0.05263157894736842;
+	const double mrt_V2=0.012531328320802;
+	const double mrt_V3=0.04761904761904762;
+	const double mrt_V4=0.004594820384294068;
+	const double mrt_V5=0.01587301587301587;
+	const double mrt_V6=0.0555555555555555555555555;
+	const double mrt_V7=0.02777777777777778;
+	const double mrt_V8=0.08333333333333333;
+	const double mrt_V9=0.003341687552213868;
+	const double mrt_V10=0.003968253968253968;
+	const double mrt_V11=0.01388888888888889;
+	const double mrt_V12=0.04166666666666666;
+
+	int S = Np/NBLOCKS/NTHREADS + 1;
+	for (int s=0; s<S; s++){
+		//........Get 1-D index for this thread....................
+		n =  S*blockIdx.x*blockDim.x + s*blockDim.x + threadIdx.x + start;
+		if (n<finish) {
+
+			// read the component number densities
+			nA = Den[n];
+			nB = Den[Np + n];
+            porosity = Poros[n];
+            perm = Perm[n];
+            nx_gs = GreySolidGrad[n+0*Np];
+            ny_gs = GreySolidGrad[n+1*Np];
+            nz_gs = GreySolidGrad[n+2*Np];
+
+			// compute phase indicator field
+			phi=(nA-nB)/(nA+nB);
+
+			// local density
+			rho0=rhoA + 0.5*(1.0-phi)*(rhoB-rhoA);
+			// local relaxation time
+			tau=tauA + 0.5*(1.0-phi)*(tauB-tauA);
+			tau_eff=tauA_eff + 0.5*(1.0-phi)*(tauB_eff-tauA_eff);
+			rlx_setA = 1.f/tau;
+			rlx_setB = 8.f*(2.f-rlx_setA)/(8.f-rlx_setA);
+            mu_eff = (tau_eff-0.5)/3.0;//kinematic viscosity
+
+			// Get the 1D index based on regular data layout
+			ijk = Map[n];
+			//					COMPUTE THE COLOR GRADIENT
+			//........................................................................
+			//.................Read Phase Indicator Values............................
+			//........................................................................
+			nn = ijk-1;							// neighbor index (get convention)
+			m1 = Phi[nn];						// get neighbor for phi - 1
+			//........................................................................
+			nn = ijk+1;							// neighbor index (get convention)
+			m2 = Phi[nn];						// get neighbor for phi - 2
+			//........................................................................
+			nn = ijk-strideY;							// neighbor index (get convention)
+			m3 = Phi[nn];					// get neighbor for phi - 3
+			//........................................................................
+			nn = ijk+strideY;							// neighbor index (get convention)
+			m4 = Phi[nn];					// get neighbor for phi - 4
+			//........................................................................
+			nn = ijk-strideZ;						// neighbor index (get convention)
+			m5 = Phi[nn];					// get neighbor for phi - 5
+			//........................................................................
+			nn = ijk+strideZ;						// neighbor index (get convention)
+			m6 = Phi[nn];					// get neighbor for phi - 6
+			//........................................................................
+			nn = ijk-strideY-1;						// neighbor index (get convention)
+			m7 = Phi[nn];					// get neighbor for phi - 7
+			//........................................................................
+			nn = ijk+strideY+1;						// neighbor index (get convention)
+			m8 = Phi[nn];					// get neighbor for phi - 8
+			//........................................................................
+			nn = ijk+strideY-1;						// neighbor index (get convention)
+			m9 = Phi[nn];					// get neighbor for phi - 9
+			//........................................................................
+			nn = ijk-strideY+1;						// neighbor index (get convention)
+			m10 = Phi[nn];					// get neighbor for phi - 10
+			//........................................................................
+			nn = ijk-strideZ-1;						// neighbor index (get convention)
+			m11 = Phi[nn];					// get neighbor for phi - 11
+			//........................................................................
+			nn = ijk+strideZ+1;						// neighbor index (get convention)
+			m12 = Phi[nn];					// get neighbor for phi - 12
+			//........................................................................
+			nn = ijk+strideZ-1;						// neighbor index (get convention)
+			m13 = Phi[nn];					// get neighbor for phi - 13
+			//........................................................................
+			nn = ijk-strideZ+1;						// neighbor index (get convention)
+			m14 = Phi[nn];					// get neighbor for phi - 14
+			//........................................................................
+			nn = ijk-strideZ-strideY;					// neighbor index (get convention)
+			m15 = Phi[nn];					// get neighbor for phi - 15
+			//........................................................................
+			nn = ijk+strideZ+strideY;					// neighbor index (get convention)
+			m16 = Phi[nn];					// get neighbor for phi - 16
+			//........................................................................
+			nn = ijk+strideZ-strideY;					// neighbor index (get convention)
+			m17 = Phi[nn];					// get neighbor for phi - 17
+			//........................................................................
+			nn = ijk-strideZ+strideY;					// neighbor index (get convention)
+			m18 = Phi[nn];					// get neighbor for phi - 18
+			//............Compute the Color Gradient...................................
+			nx_phase = -(m1-m2+0.5*(m7-m8+m9-m10+m11-m12+m13-m14));
+			ny_phase = -(m3-m4+0.5*(m7-m8-m9+m10+m15-m16+m17-m18));
+			nz_phase = -(m5-m6+0.5*(m11-m12-m13+m14+m15-m16-m17+m18));
+			C_phase = sqrt(nx_phase*nx_phase+ny_phase*ny_phase+nz_phase*nz_phase);
+
+            //correct the normal color gradient by considering the effect of grey solid
+            nx = nx_phase + (1.0-porosity)*nx_gs; 
+            ny = ny_phase + (1.0-porosity)*ny_gs; 
+            nz = nz_phase + (1.0-porosity)*nz_gs; 
+            if (C_phase==0.0){
+                nx = nx_phase; 
+                ny = ny_phase;
+                nz = nz_phase;
+            }
+
+			//...........Normalize the Color Gradient.................................
+			C = sqrt(nx*nx+ny*ny+nz*nz);
+			double ColorMag = C;
+			if (C==0.0) ColorMag=1.0;
+			nx = nx/ColorMag;
+			ny = ny/ColorMag;
+			nz = nz/ColorMag;		
+
+			// q=0
+			fq = dist[n];
+			rho = fq;
+			m1  = -30.0*fq;
+			m2  = 12.0*fq;
+
+			// q=1
+			fq = dist[2*Np+n];
+			rho += fq;
+			m1 -= 11.0*fq;
+			m2 -= 4.0*fq;
+			jx = fq;
+			m4 = -4.0*fq;
+			m9 = 2.0*fq;
+			m10 = -4.0*fq;
+
+			// f2 = dist[10*Np+n];
+			fq = dist[1*Np+n];
+			rho += fq;
+			m1 -= 11.0*(fq);
+			m2 -= 4.0*(fq);
+			jx -= fq;
+			m4 += 4.0*(fq);
+			m9 += 2.0*(fq);
+			m10 -= 4.0*(fq);
+
+			// q=3
+			fq = dist[4*Np+n];
+			rho += fq;
+			m1 -= 11.0*fq;
+			m2 -= 4.0*fq;
+			jy = fq;
+			m6 = -4.0*fq;
+			m9 -= fq;
+			m10 += 2.0*fq;
+			m11 = fq;
+			m12 = -2.0*fq;
+
+			// q = 4
+			fq = dist[3*Np+n];
+			rho+= fq;
+			m1 -= 11.0*fq;
+			m2 -= 4.0*fq;
+			jy -= fq;
+			m6 += 4.0*fq;
+			m9 -= fq;
+			m10 += 2.0*fq;
+			m11 += fq;
+			m12 -= 2.0*fq;
+
+			// q=5
+			fq = dist[6*Np+n];
+			rho += fq;
+			m1 -= 11.0*fq;
+			m2 -= 4.0*fq;
+			jz = fq;
+			m8 = -4.0*fq;
+			m9 -= fq;
+			m10 += 2.0*fq;
+			m11 -= fq;
+			m12 += 2.0*fq;
+
+			// q = 6
+			fq = dist[5*Np+n];
+			rho+= fq;
+			m1 -= 11.0*fq;
+			m2 -= 4.0*fq;
+			jz -= fq;
+			m8 += 4.0*fq;
+			m9 -= fq;
+			m10 += 2.0*fq;
+			m11 -= fq;
+			m12 += 2.0*fq;
+
+			// q=7
+			fq = dist[8*Np+n];
+			rho += fq;
+			m1 += 8.0*fq;
+			m2 += fq;
+			jx += fq;
+			m4 += fq;
+			jy += fq;
+			m6 += fq;
+			m9  += fq;
+			m10 += fq;
+			m11 += fq;
+			m12 += fq;
+			m13 = fq;
+			m16 = fq;
+			m17 = -fq;
+
+			// q = 8
+			fq = dist[7*Np+n];
+			rho += fq;
+			m1 += 8.0*fq;
+			m2 += fq;
+			jx -= fq;
+			m4 -= fq;
+			jy -= fq;
+			m6 -= fq;
+			m9 += fq;
+			m10 += fq;
+			m11 += fq;
+			m12 += fq;
+			m13 += fq;
+			m16 -= fq;
+			m17 += fq;
+
+			// q=9
+			fq = dist[10*Np+n];
+			rho += fq;
+			m1 += 8.0*fq;
+			m2 += fq;
+			jx += fq;
+			m4 += fq;
+			jy -= fq;
+			m6 -= fq;
+			m9 += fq;
+			m10 += fq;
+			m11 += fq;
+			m12 += fq;
+			m13 -= fq;
+			m16 += fq;
+			m17 += fq;
+
+			// q = 10
+			fq = dist[9*Np+n];
+			rho += fq;
+			m1 += 8.0*fq;
+			m2 += fq;
+			jx -= fq;
+			m4 -= fq;
+			jy += fq;
+			m6 += fq;
+			m9 += fq;
+			m10 += fq;
+			m11 += fq;
+			m12 += fq;
+			m13 -= fq;
+			m16 -= fq;
+			m17 -= fq;
+
+			// q=11
+			fq = dist[12*Np+n];
+			rho += fq;
+			m1 += 8.0*fq;
+			m2 += fq;
+			jx += fq;
+			m4 += fq;
+			jz += fq;
+			m8 += fq;
+			m9 += fq;
+			m10 += fq;
+			m11 -= fq;
+			m12 -= fq;
+			m15 = fq;
+			m16 -= fq;
+			m18 = fq;
+
+			// q=12
+			fq = dist[11*Np+n];
+			rho += fq;
+			m1 += 8.0*fq;
+			m2 += fq;
+			jx -= fq;
+			m4 -= fq;
+			jz -= fq;
+			m8 -= fq;
+			m9 += fq;
+			m10 += fq;
+			m11 -= fq;
+			m12 -= fq;
+			m15 += fq;
+			m16 += fq;
+			m18 -= fq;
+
+			// q=13
+			fq = dist[14*Np+n];
+			rho += fq;
+			m1 += 8.0*fq;
+			m2 += fq;
+			jx += fq;
+			m4 += fq;
+			jz -= fq;
+			m8 -= fq;
+			m9 += fq;
+			m10 += fq;
+			m11 -= fq;
+			m12 -= fq;
+			m15 -= fq;
+			m16 -= fq;
+			m18 -= fq;
+
+			// q=14
+			fq = dist[13*Np+n];
+			rho += fq;
+			m1 += 8.0*fq;
+			m2 += fq;
+			jx -= fq;
+			m4 -= fq;
+			jz += fq;
+			m8 += fq;
+			m9 += fq;
+			m10 += fq;
+			m11 -= fq;
+			m12 -= fq;
+			m15 -= fq;
+			m16 += fq;
+			m18 += fq;
+
+			// q=15
+			fq = dist[16*Np+n];
+			rho += fq;
+			m1 += 8.0*fq;
+			m2 += fq;
+			jy += fq;
+			m6 += fq;
+			jz += fq;
+			m8 += fq;
+			m9 -= 2.0*fq;
+			m10 -= 2.0*fq;
+			m14 = fq;
+			m17 += fq;
+			m18 -= fq;
+
+			// q=16
+			fq = dist[15*Np+n];
+			rho += fq;
+			m1 += 8.0*fq;
+			m2 += fq;
+			jy -= fq;
+			m6 -= fq;
+			jz -= fq;
+			m8 -= fq;
+			m9 -= 2.0*fq;
+			m10 -= 2.0*fq;
+			m14 += fq;
+			m17 -= fq;
+			m18 += fq;
+
+			// q=17
+			fq = dist[18*Np+n];
+			rho += fq;
+			m1 += 8.0*fq;
+			m2 += fq;
+			jy += fq;
+			m6 += fq;
+			jz -= fq;
+			m8 -= fq;
+			m9 -= 2.0*fq;
+			m10 -= 2.0*fq;
+			m14 -= fq;
+			m17 += fq;
+			m18 += fq;
+
+			// q=18
+			fq = dist[17*Np+n];
+			rho += fq;
+			m1 += 8.0*fq;
+			m2 += fq;
+			jy -= fq;
+			m6 -= fq;
+			jz += fq;
+			m8 += fq;
+			m9 -= 2.0*fq;
+			m10 -= 2.0*fq;
+			m14 -= fq;
+			m17 -= fq;
+			m18 -= fq;
+
+            // Compute greyscale related parameters
+            c0 = 0.5*(1.0+porosity*0.5*mu_eff/perm);
+            if (porosity==1.0) c0 = 0.5;//i.e. apparent pore nodes
+            //GeoFun = 1.75/sqrt(150.0*porosity*porosity*porosity);
+            c1 = porosity*0.5*GeoFun/sqrt(perm);
+            if (porosity==1.0) c1 = 0.0;//i.e. apparent pore nodes
+
+            vx = jx/rho0+0.5*(porosity*Gx);
+            vy = jy/rho0+0.5*(porosity*Gy);
+            vz = jz/rho0+0.5*(porosity*Gz);
+            v_mag=sqrt(vx*vx+vy*vy+vz*vz);
+            ux = vx/(c0+sqrt(c0*c0+c1*v_mag));
+            uy = vy/(c0+sqrt(c0*c0+c1*v_mag));
+            uz = vz/(c0+sqrt(c0*c0+c1*v_mag));
+            u_mag=sqrt(ux*ux+uy*uy+uz*uz);
+
+            //Update the total force to include linear (Darcy) and nonlinear (Forchheimer) drags due to the porous medium
+            Fx = rho0*(-porosity*mu_eff/perm*ux - porosity*GeoFun/sqrt(perm)*u_mag*ux + porosity*Gx);
+            Fy = rho0*(-porosity*mu_eff/perm*uy - porosity*GeoFun/sqrt(perm)*u_mag*uy + porosity*Gy);
+            Fz = rho0*(-porosity*mu_eff/perm*uz - porosity*GeoFun/sqrt(perm)*u_mag*uz + porosity*Gz);
+            if (porosity==1.0){
+                Fx=rho0*(Gx);
+                Fy=rho0*(Gy);
+                Fz=rho0*(Gz);
+            }
+
+			// write the velocity 
+			Velocity[n] = ux;
+			Velocity[Np+n] = uy;
+			Velocity[2*Np+n] = uz;
+
+			//........................................................................
+			//..............carry out relaxation process..............................
+			//..........Toelke, Fruediger et. al. 2006................................
+            //---------------- NO higher-order force -------------------------------//
+			if (C == 0.0)	nx = ny = nz = 0.0;
+			m1 = m1 + rlx_setA*((19*(ux*ux+uy*uy+uz*uz)*rho0/porosity - 11*rho) -19*alpha*C - m1);
+			m2 = m2 + rlx_setA*((3*rho - 5.5*(ux*ux+uy*uy+uz*uz)*rho0/porosity)- m2);
+            jx = jx + Fx;
+			m4 = m4 + rlx_setB*((-0.6666666666666666*ux*rho0)- m4)
+                    + (1-0.5*rlx_setB)*(-0.6666666666666666*Fx);
+            jy = jy + Fy;
+			m6 = m6 + rlx_setB*((-0.6666666666666666*uy*rho0)- m6)
+                    + (1-0.5*rlx_setB)*(-0.6666666666666666*Fy);
+            jz = jz + Fz;
+			m8 = m8 + rlx_setB*((-0.6666666666666666*uz*rho0)- m8)
+                    + (1-0.5*rlx_setB)*(-0.6666666666666666*Fz);
+			m9 = m9 + rlx_setA*(((2*ux*ux-uy*uy-uz*uz)*rho0/porosity) + 0.5*alpha*C*(2*nx*nx-ny*ny-nz*nz) - m9);
+			m10 = m10 + rlx_setA*( - m10);
+            //m10 = m10 + rlx_setA*(-0.5*rho0*((2*ux*ux-uy*uy-uz*uz)/porosity)- m10);
+			m11 = m11 + rlx_setA*(((uy*uy-uz*uz)*rho0/porosity) + 0.5*alpha*C*(ny*ny-nz*nz)- m11);
+			m12 = m12 + rlx_setA*( - m12);
+            //m12 = m12 + rlx_setA*(-0.5*(rho0*(uy*uy-uz*uz)/porosity)- m12);
+			m13 = m13 + rlx_setA*( (ux*uy*rho0/porosity) + 0.5*alpha*C*nx*ny - m13);
+			m14 = m14 + rlx_setA*( (uy*uz*rho0/porosity) + 0.5*alpha*C*ny*nz - m14);
+			m15 = m15 + rlx_setA*( (ux*uz*rho0/porosity) + 0.5*alpha*C*nx*nz - m15);
+			m16 = m16 + rlx_setB*( - m16);
+			m17 = m17 + rlx_setB*( - m17);
+			m18 = m18 + rlx_setB*( - m18);
+            //----------------------------------------------------------------------//
+
+            //----------------With higher-order force ------------------------------//
+			//if (C == 0.0)	nx = ny = nz = 0.0;
+			//m1 = m1 + rlx_setA*((19*(ux*ux+uy*uy+uz*uz)*rho0/porosity - 11*rho) -19*alpha*C - m1)
+            //        + (1-0.5*rlx_setA)*38*(Fx*ux+Fy*uy+Fz*uz)/porosity;
+			//m2 = m2 + rlx_setA*((3*rho - 5.5*(ux*ux+uy*uy+uz*uz)*rho0/porosity)- m2)
+            //        + (1-0.5*rlx_setA)*11*(-Fx*ux-Fy*uy-Fz*uz)/porosity;
+            //jx = jx + Fx;
+			//m4 = m4 + rlx_setB*((-0.6666666666666666*ux*rho0)- m4)
+            //        + (1-0.5*rlx_setB)*(-0.6666666666666666*Fx);
+            //jy = jy + Fy;
+			//m6 = m6 + rlx_setB*((-0.6666666666666666*uy*rho0)- m6)
+            //        + (1-0.5*rlx_setB)*(-0.6666666666666666*Fy);
+            //jz = jz + Fz;
+			//m8 = m8 + rlx_setB*((-0.6666666666666666*uz*rho0)- m8)
+            //        + (1-0.5*rlx_setB)*(-0.6666666666666666*Fz);
+			//m9 = m9 + rlx_setA*(((2*ux*ux-uy*uy-uz*uz)*rho0/porosity) + 0.5*alpha*C*(2*nx*nx-ny*ny-nz*nz) - m9)
+            //        + (1-0.5*rlx_setA)*(4*Fx*ux-2*Fy*uy-2*Fz*uz)/porosity;
+			////m10 = m10 + rlx_setA*( - m10);
+            //m10 = m10 + rlx_setA*(-0.5*rho0*((2*ux*ux-uy*uy-uz*uz)/porosity)- m10)
+            //          + (1-0.5*rlx_setA)*(-2*Fx*ux+Fy*uy+Fz*uz)/porosity;
+			//m11 = m11 + rlx_setA*(((uy*uy-uz*uz)*rho0/porosity) + 0.5*alpha*C*(ny*ny-nz*nz)- m11)
+            //          + (1-0.5*rlx_setA)*(2*Fy*uy-2*Fz*uz)/porosity;
+			////m12 = m12 + rlx_setA*( - m12);
+            //m12 = m12 + rlx_setA*(-0.5*(rho0*(uy*uy-uz*uz)/porosity)- m12)
+            //          + (1-0.5*rlx_setA)*(-Fy*uy+Fz*uz)/porosity;
+			//m13 = m13 + rlx_setA*( (ux*uy*rho0/porosity) + 0.5*alpha*C*nx*ny - m13);
+            //          + (1-0.5*rlx_setA)*(Fy*ux+Fx*uy)/porosity;
+			//m14 = m14 + rlx_setA*( (uy*uz*rho0/porosity) + 0.5*alpha*C*ny*nz - m14);
+            //          + (1-0.5*rlx_setA)*(Fz*uy+Fy*uz)/porosity;
+			//m15 = m15 + rlx_setA*( (ux*uz*rho0/porosity) + 0.5*alpha*C*nx*nz - m15);
+            //          + (1-0.5*rlx_setA)*(Fz*ux+Fx*uz)/porosity;
+			//m16 = m16 + rlx_setB*( - m16);
+			//m17 = m17 + rlx_setB*( - m17);
+			//m18 = m18 + rlx_setB*( - m18);
+            //----------------------------------------------------------------------//
+
+			//.................inverse transformation......................................................
+			// q=0
+			fq = mrt_V1*rho-mrt_V2*m1+mrt_V3*m2;
+			dist[n] = fq;
+
+			// q = 1
+			fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(jx-m4)+mrt_V6*(m9-m10);
+			dist[1*Np+n] = fq;
+
+			// q=2
+			fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(m4-jx)+mrt_V6*(m9-m10);
+			dist[2*Np+n] = fq;
+
+			// q = 3
+			fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(jy-m6)+mrt_V7*(m10-m9)+mrt_V8*(m11-m12);
+			dist[3*Np+n] = fq;
+
+			// q = 4
+			fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(m6-jy)+mrt_V7*(m10-m9)+mrt_V8*(m11-m12);
+			dist[4*Np+n] = fq;
+
+			// q = 5
+			fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(jz-m8)+mrt_V7*(m10-m9)+mrt_V8*(m12-m11);
+			dist[5*Np+n] = fq;
+
+			// q = 6
+			fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(m8-jz)+mrt_V7*(m10-m9)+mrt_V8*(m12-m11);
+			dist[6*Np+n] = fq;
+
+			// q = 7
+			fq = mrt_V1*rho+mrt_V9*m1+mrt_V10*m2+0.1*(jx+jy)+0.025*(m4+m6)+
+					mrt_V7*m9+mrt_V11*m10+mrt_V8*m11+mrt_V12*m12+0.25*m13+0.125*(m16-m17);
+			dist[7*Np+n] = fq;
+
+
+			// q = 8
+			fq = mrt_V1*rho+mrt_V9*m1+mrt_V10*m2-0.1*(jx+jy)-0.025*(m4+m6) +mrt_V7*m9+mrt_V11*m10+mrt_V8*m11
+					+mrt_V12*m12+0.25*m13+0.125*(m17-m16);
+			dist[8*Np+n] = fq;
+
+			// q = 9
+			fq = mrt_V1*rho+mrt_V9*m1+mrt_V10*m2+0.1*(jx-jy)+0.025*(m4-m6)+
+					mrt_V7*m9+mrt_V11*m10+mrt_V8*m11+mrt_V12*m12-0.25*m13+0.125*(m16+m17);
+			dist[9*Np+n] = fq;
+
+			// q = 10
+			fq = mrt_V1*rho+mrt_V9*m1+mrt_V10*m2+0.1*(jy-jx)+0.025*(m6-m4)+
+					mrt_V7*m9+mrt_V11*m10+mrt_V8*m11+mrt_V12*m12-0.25*m13-0.125*(m16+m17);
+			dist[10*Np+n] = fq;
+
+
+			// q = 11
+			fq = mrt_V1*rho+mrt_V9*m1
+					+mrt_V10*m2+0.1*(jx+jz)+0.025*(m4+m8)
+					+mrt_V7*m9+mrt_V11*m10-mrt_V8*m11
+					-mrt_V12*m12+0.25*m15+0.125*(m18-m16);
+			dist[11*Np+n] = fq;
+
+			// q = 12
+			fq = mrt_V1*rho+mrt_V9*m1+mrt_V10*m2-0.1*(jx+jz)-0.025*(m4+m8)+
+					mrt_V7*m9+mrt_V11*m10-mrt_V8*m11-mrt_V12*m12+0.25*m15+0.125*(m16-m18);
+			dist[12*Np+n] = fq;
+
+			// q = 13
+			fq = mrt_V1*rho+mrt_V9*m1
+					+mrt_V10*m2+0.1*(jx-jz)+0.025*(m4-m8)
+					+mrt_V7*m9+mrt_V11*m10-mrt_V8*m11
+					-mrt_V12*m12-0.25*m15-0.125*(m16+m18);
+			dist[13*Np+n] = fq;
+
+			// q= 14
+			fq = mrt_V1*rho+mrt_V9*m1
+					+mrt_V10*m2+0.1*(jz-jx)+0.025*(m8-m4)
+					+mrt_V7*m9+mrt_V11*m10-mrt_V8*m11
+					-mrt_V12*m12-0.25*m15+0.125*(m16+m18);
+
+			dist[14*Np+n] = fq;
+
+			// q = 15
+			fq = mrt_V1*rho+mrt_V9*m1
+					+mrt_V10*m2+0.1*(jy+jz)+0.025*(m6+m8)
+					-mrt_V6*m9-mrt_V7*m10+0.25*m14+0.125*(m17-m18);
+			dist[15*Np+n] = fq;
+
+			// q = 16
+			fq =  mrt_V1*rho+mrt_V9*m1
+					+mrt_V10*m2-0.1*(jy+jz)-0.025*(m6+m8)
+					-mrt_V6*m9-mrt_V7*m10+0.25*m14+0.125*(m18-m17);
+			dist[16*Np+n] = fq;
+
+
+			// q = 17
+			fq = mrt_V1*rho+mrt_V9*m1
+					+mrt_V10*m2+0.1*(jy-jz)+0.025*(m6-m8)
+					-mrt_V6*m9-mrt_V7*m10-0.25*m14+0.125*(m17+m18);
+			dist[17*Np+n] = fq;
+
+			// q = 18
+			fq = mrt_V1*rho+mrt_V9*m1
+					+mrt_V10*m2+0.1*(jz-jy)+0.025*(m8-m6)
+					-mrt_V6*m9-mrt_V7*m10-0.25*m14-0.125*(m17+m18);
+			dist[18*Np+n] = fq;
+			//........................................................................
+
+			// Instantiate mass transport distributions
+			// Stationary value - distribution 0
+			nAB = 1.0/(nA+nB);
+			Aq[n] = 0.3333333333333333*nA;
+			Bq[n] = 0.3333333333333333*nB;
+
+			//...............................................
+			// q = 0,2,4
+			// Cq = {1,0,0}, {0,1,0}, {0,0,1}
+			delta = beta*nA*nB*nAB*0.1111111111111111*nx;
+			if (!(nA*nB*nAB>0)) delta=0;
+			a1 = nA*(0.1111111111111111*(1+4.5*ux))+delta;
+			b1 = nB*(0.1111111111111111*(1+4.5*ux))-delta;
+			a2 = nA*(0.1111111111111111*(1-4.5*ux))-delta;
+			b2 = nB*(0.1111111111111111*(1-4.5*ux))+delta;
+
+			Aq[1*Np+n] = a1;
+			Bq[1*Np+n] = b1;
+			Aq[2*Np+n] = a2;
+			Bq[2*Np+n] = b2;
+
+			//...............................................
+			// q = 2
+			// Cq = {0,1,0}
+			delta = beta*nA*nB*nAB*0.1111111111111111*ny;
+			if (!(nA*nB*nAB>0)) delta=0;
+			a1 = nA*(0.1111111111111111*(1+4.5*uy))+delta;
+			b1 = nB*(0.1111111111111111*(1+4.5*uy))-delta;
+			a2 = nA*(0.1111111111111111*(1-4.5*uy))-delta;
+			b2 = nB*(0.1111111111111111*(1-4.5*uy))+delta;
+
+			Aq[3*Np+n] = a1;
+			Bq[3*Np+n] = b1;
+			Aq[4*Np+n] = a2;
+			Bq[4*Np+n] = b2;
+			//...............................................
+			// q = 4
+			// Cq = {0,0,1}
+			delta = beta*nA*nB*nAB*0.1111111111111111*nz;
+			if (!(nA*nB*nAB>0)) delta=0;
+			a1 = nA*(0.1111111111111111*(1+4.5*uz))+delta;
+			b1 = nB*(0.1111111111111111*(1+4.5*uz))-delta;
+			a2 = nA*(0.1111111111111111*(1-4.5*uz))-delta;
+			b2 = nB*(0.1111111111111111*(1-4.5*uz))+delta;
+
+			Aq[5*Np+n] = a1;
+			Bq[5*Np+n] = b1;
+			Aq[6*Np+n] = a2;
+			Bq[6*Np+n] = b2;
+			//...............................................
+
+		}
+	}
+}
+
+////Model-2&3
+//__global__ void dvc_ScaLBL_D3Q19_AAodd_GreyscaleColor(int *neighborList, int *Map, double *dist, double *Aq, double *Bq, double *Den,
+//		 double *Phi, double *GreySolidGrad, double *Poros,double *Perm, double *Velocity, 
+//         double rhoA, double rhoB, double tauA, double tauB,double tauA_eff,double tauB_eff,double alpha, double beta,
+//		 double Gx, double Gy, double Gz, int strideY, int strideZ, int start, int finish, int Np){
+//
+//	int n,nn,ijk,nread;
+//	int nr1,nr2,nr3,nr4,nr5,nr6;
+//	int nr7,nr8,nr9,nr10;
+//	int nr11,nr12,nr13,nr14;
+//	//int nr15,nr16,nr17,nr18;
+//	double fq;
+//	// conserved momemnts
+//	double rho,jx,jy,jz;
+//	double vx,vy,vz,v_mag;
+//    double ux,uy,uz,u_mag;
+//	// non-conserved moments
+//	double m1,m2,m4,m6,m8,m9,m10,m11,m12,m13,m14,m15,m16,m17,m18;
+//	double m3,m5,m7;
+//	double t1,t2,t4,t6,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18;
+//	double t3,t5,t7;
+//	double nA,nB; // number density
+//	double a1,b1,a2,b2,nAB,delta;
+//	double C,nx,ny,nz; //color gradient magnitude and direction
+//	double phi,tau,rho0,rlx_setA,rlx_setB;
+//
+//    double GeoFun=0.0;//geometric function from Guo's PRE 66, 036304 (2002)
+//    double porosity;
+//    double perm;//voxel permeability
+//    double c0, c1; //Guo's model parameters
+//    double tau_eff;
+//    double mu_eff;//kinematic viscosity
+//    double nx_phase,ny_phase,nz_phase,C_phase;
+//    double Fx,Fy,Fz;
+//
+//	const double mrt_V1=0.05263157894736842;
+//	const double mrt_V2=0.012531328320802;
+//	const double mrt_V3=0.04761904761904762;
+//	const double mrt_V4=0.004594820384294068;
+//	const double mrt_V5=0.01587301587301587;
+//	const double mrt_V6=0.0555555555555555555555555;
+//	const double mrt_V7=0.02777777777777778;
+//	const double mrt_V8=0.08333333333333333;
+//	const double mrt_V9=0.003341687552213868;
+//	const double mrt_V10=0.003968253968253968;
+//	const double mrt_V11=0.01388888888888889;
+//	const double mrt_V12=0.04166666666666666;
+//
+//	int S = Np/NBLOCKS/NTHREADS + 1;
+//	for (int s=0; s<S; s++){
+//		//........Get 1-D index for this thread....................
+//		n =  S*blockIdx.x*blockDim.x + s*blockDim.x + threadIdx.x + start;
+//		if (n<finish) {
+//			// read the component number densities
+//			nA = Den[n];
+//			nB = Den[Np + n];
+//            porosity = Poros[n];
+//            perm = Perm[n];
+//
+//			// compute phase indicator field
+//			phi=(nA-nB)/(nA+nB);
+//
+//			// local density
+//			rho0=rhoA + 0.5*(1.0-phi)*(rhoB-rhoA);
+//			// local relaxation time
+//			tau=tauA + 0.5*(1.0-phi)*(tauB-tauA);
+//			tau_eff=tauA_eff + 0.5*(1.0-phi)*(tauB_eff-tauA_eff);
+//			rlx_setA = 1.f/tau;
+//			rlx_setB = 8.f*(2.f-rlx_setA)/(8.f-rlx_setA);
+//            mu_eff = (tau_eff-0.5)/3.0;//kinematic viscosity
+//			
+//			// Get the 1D index based on regular data layout
+//			ijk = Map[n];
+//			//					COMPUTE THE COLOR GRADIENT
+//			//........................................................................
+//			//.................Read Phase Indicator Values............................
+//			//........................................................................
+//			nn = ijk-1;							// neighbor index (get convention)
+//			m1 = Phi[nn];						// get neighbor for phi - 1
+//			t1 = m1+(1.0-porosity)*GreySolidGrad[nn];				
+//            if (fabs(t1)>1.0) t1 =((t1>0.0)-(t1<0.0))*(1.0-fabs(t1))+t1;
+//			//........................................................................
+//			nn = ijk+1;							// neighbor index (get convention)
+//			m2 = Phi[nn];						// get neighbor for phi - 2
+//			t2 = m2+(1.0-porosity)*GreySolidGrad[nn];				
+//            if (fabs(t2)>1.0) t2 =((t2>0.0)-(t2<0.0))*(1.0-fabs(t2))+t2;
+//			//........................................................................
+//			nn = ijk-strideY;							// neighbor index (get convention)
+//			m3 = Phi[nn];					// get neighbor for phi - 3
+//			t3 = m3+(1.0-porosity)*GreySolidGrad[nn];				
+//            if (fabs(t3)>1.0) t3 =((t3>0.0)-(t3<0.0))*(1.0-fabs(t3))+t3;
+//			//........................................................................
+//			nn = ijk+strideY;							// neighbor index (get convention)
+//			m4 = Phi[nn];					// get neighbor for phi - 4
+//			t4 = m4+(1.0-porosity)*GreySolidGrad[nn];				
+//            if (fabs(t4)>1.0) t4 =((t4>0.0)-(t4<0.0))*(1.0-fabs(t4))+t4;
+//			//........................................................................
+//			nn = ijk-strideZ;						// neighbor index (get convention)
+//			m5 = Phi[nn];					// get neighbor for phi - 5
+//			t5 = m5+(1.0-porosity)*GreySolidGrad[nn];				
+//            if (fabs(t5)>1.0) t5 =((t5>0.0)-(t5<0.0))*(1.0-fabs(t5))+t5;
+//			//........................................................................
+//			nn = ijk+strideZ;						// neighbor index (get convention)
+//			m6 = Phi[nn];					// get neighbor for phi - 6
+//			t6 = m6+(1.0-porosity)*GreySolidGrad[nn];				
+//            if (fabs(t6)>1.0) t6 =((t6>0.0)-(t6<0.0))*(1.0-fabs(t6))+t6;
+//			//........................................................................
+//			nn = ijk-strideY-1;						// neighbor index (get convention)
+//			m7 = Phi[nn];					// get neighbor for phi - 7
+//			t7 = m7+(1.0-porosity)*GreySolidGrad[nn];				
+//            if (fabs(t7)>1.0) t7 =((t7>0.0)-(t7<0.0))*(1.0-fabs(t7))+t7;
+//			//........................................................................
+//			nn = ijk+strideY+1;						// neighbor index (get convention)
+//			m8 = Phi[nn];					// get neighbor for phi - 8
+//			t8 = m8+(1.0-porosity)*GreySolidGrad[nn];				
+//            if (fabs(t8)>1.0) t8 =((t8>0.0)-(t8<0.0))*(1.0-fabs(t8))+t8;
+//			//........................................................................
+//			nn = ijk+strideY-1;						// neighbor index (get convention)
+//			m9 = Phi[nn];					// get neighbor for phi - 9
+//			t9 = m9+(1.0-porosity)*GreySolidGrad[nn];				
+//            if (fabs(t9)>1.0) t9 =((t9>0.0)-(t9<0.0))*(1.0-fabs(t9))+t9;
+//			//........................................................................
+//			nn = ijk-strideY+1;						// neighbor index (get convention)
+//			m10 = Phi[nn];					// get neighbor for phi - 10
+//			t10 = m10+(1.0-porosity)*GreySolidGrad[nn];				
+//            if (fabs(t10)>1.0) t10 =((t10>0.0)-(t10<0.0))*(1.0-fabs(t10))+t10;
+//			//........................................................................
+//			nn = ijk-strideZ-1;						// neighbor index (get convention)
+//			m11 = Phi[nn];					// get neighbor for phi - 11
+//			t11 = m11+(1.0-porosity)*GreySolidGrad[nn];				
+//            if (fabs(t11)>1.0) t11 =((t11>0.0)-(t11<0.0))*(1.0-fabs(t11))+t11;
+//			//........................................................................
+//			nn = ijk+strideZ+1;						// neighbor index (get convention)
+//			m12 = Phi[nn];					// get neighbor for phi - 12
+//			t12 = m12+(1.0-porosity)*GreySolidGrad[nn];				
+//            if (fabs(t12)>1.0) t12 =((t12>0.0)-(t12<0.0))*(1.0-fabs(t12))+t12;
+//			//........................................................................
+//			nn = ijk+strideZ-1;						// neighbor index (get convention)
+//			m13 = Phi[nn];					// get neighbor for phi - 13
+//			t13 = m13+(1.0-porosity)*GreySolidGrad[nn];				
+//            if (fabs(t13)>1.0) t13 =((t13>0.0)-(t13<0.0))*(1.0-fabs(t13))+t13;
+//			//........................................................................
+//			nn = ijk-strideZ+1;						// neighbor index (get convention)
+//			m14 = Phi[nn];					// get neighbor for phi - 14
+//			t14 = m14+(1.0-porosity)*GreySolidGrad[nn];				
+//            if (fabs(t14)>1.0) t14 =((t14>0.0)-(t14<0.0))*(1.0-fabs(t14))+t14;
+//			//........................................................................
+//			nn = ijk-strideZ-strideY;					// neighbor index (get convention)
+//			m15 = Phi[nn];					// get neighbor for phi - 15
+//			t15 = m15+(1.0-porosity)*GreySolidGrad[nn];				
+//            if (fabs(t15)>1.0) t15 =((t15>0.0)-(t15<0.0))*(1.0-fabs(t15))+t15;
+//			//........................................................................
+//			nn = ijk+strideZ+strideY;					// neighbor index (get convention)
+//			m16 = Phi[nn];					// get neighbor for phi - 16
+//			t16 = m16+(1.0-porosity)*GreySolidGrad[nn];				
+//            if (fabs(t16)>1.0) t16 =((t16>0.0)-(t16<0.0))*(1.0-fabs(t16))+t16;
+//			//........................................................................
+//			nn = ijk+strideZ-strideY;					// neighbor index (get convention)
+//			m17 = Phi[nn];					// get neighbor for phi - 17
+//			t17 = m17+(1.0-porosity)*GreySolidGrad[nn];				
+//            if (fabs(t17)>1.0) t17 =((t17>0.0)-(t17<0.0))*(1.0-fabs(t17))+t17;
+//			//........................................................................
+//			nn = ijk-strideZ+strideY;					// neighbor index (get convention)
+//			m18 = Phi[nn];					// get neighbor for phi - 18
+//			t18 = m18+(1.0-porosity)*GreySolidGrad[nn];				
+//            if (fabs(t18)>1.0) t18 =((t18>0.0)-(t18<0.0))*(1.0-fabs(t18))+t18;
+//			//............Compute the Color Gradient...................................
+//			nx_phase = -(m1-m2+0.5*(m7-m8+m9-m10+m11-m12+m13-m14));
+//			ny_phase = -(m3-m4+0.5*(m7-m8-m9+m10+m15-m16+m17-m18));
+//			nz_phase = -(m5-m6+0.5*(m11-m12-m13+m14+m15-m16-m17+m18));
+//			C_phase = sqrt(nx_phase*nx_phase+ny_phase*ny_phase+nz_phase*nz_phase);
+//            //correct the normal color gradient by considering the effect of grey solid
+//			nx = -(t1-t2+0.5*(t7-t8+t9-t10+t11-t12+t13-t14));
+//			ny = -(t3-t4+0.5*(t7-t8-t9+t10+t15-t16+t17-t18));
+//			nz = -(t5-t6+0.5*(t11-t12-t13+t14+t15-t16-t17+t18));
+//
+//            if (C_phase==0.0){//i.e. if in a bulk phase, there is no need for grey-solid correction
+//                nx = nx_phase; 
+//                ny = ny_phase;
+//                nz = nz_phase;
+//            }
+//
+//			//...........Normalize the Color Gradient.................................
+//			C = sqrt(nx*nx+ny*ny+nz*nz);
+//			double ColorMag = C;
+//			if (C==0.0) ColorMag=1.0;
+//			nx = nx/ColorMag;
+//			ny = ny/ColorMag;
+//			nz = nz/ColorMag;		
+//
+//			// q=0
+//			fq = dist[n];
+//			rho = fq;
+//			m1  = -30.0*fq;
+//			m2  = 12.0*fq;
+//
+//			// q=1
+//			//nread = neighborList[n]; // neighbor 2 
+//			//fq = dist[nread]; // reading the f1 data into register fq		
+//			nr1 = neighborList[n]; 
+//			fq = dist[nr1]; // reading the f1 data into register fq
+//			rho += fq;
+//			m1 -= 11.0*fq;
+//			m2 -= 4.0*fq;
+//			jx = fq;
+//			m4 = -4.0*fq;
+//			m9 = 2.0*fq;
+//			m10 = -4.0*fq;
+//
+//			// f2 = dist[10*Np+n];
+//			//nread = neighborList[n+Np]; // neighbor 1 ( < 10Np => even part of dist)
+//			//fq = dist[nread];  // reading the f2 data into register fq
+//			nr2 = neighborList[n+Np]; // neighbor 1 ( < 10Np => even part of dist)
+//			fq = dist[nr2];  // reading the f2 data into register fq
+//			rho += fq;
+//			m1 -= 11.0*(fq);
+//			m2 -= 4.0*(fq);
+//			jx -= fq;
+//			m4 += 4.0*(fq);
+//			m9 += 2.0*(fq);
+//			m10 -= 4.0*(fq);
+//
+//			// q=3
+//			//nread = neighborList[n+2*Np]; // neighbor 4
+//			//fq = dist[nread];
+//			nr3 = neighborList[n+2*Np]; // neighbor 4
+//			fq = dist[nr3];
+//			rho += fq;
+//			m1 -= 11.0*fq;
+//			m2 -= 4.0*fq;
+//			jy = fq;
+//			m6 = -4.0*fq;
+//			m9 -= fq;
+//			m10 += 2.0*fq;
+//			m11 = fq;
+//			m12 = -2.0*fq;
+//
+//			// q = 4
+//			//nread = neighborList[n+3*Np]; // neighbor 3
+//			//fq = dist[nread];
+//			nr4 = neighborList[n+3*Np]; // neighbor 3
+//			fq = dist[nr4];
+//			rho+= fq;
+//			m1 -= 11.0*fq;
+//			m2 -= 4.0*fq;
+//			jy -= fq;
+//			m6 += 4.0*fq;
+//			m9 -= fq;
+//			m10 += 2.0*fq;
+//			m11 += fq;
+//			m12 -= 2.0*fq;
+//
+//			// q=5
+//			//nread = neighborList[n+4*Np];
+//			//fq = dist[nread];
+//			nr5 = neighborList[n+4*Np];
+//			fq = dist[nr5];
+//			rho += fq;
+//			m1 -= 11.0*fq;
+//			m2 -= 4.0*fq;
+//			jz = fq;
+//			m8 = -4.0*fq;
+//			m9 -= fq;
+//			m10 += 2.0*fq;
+//			m11 -= fq;
+//			m12 += 2.0*fq;
+//
+//
+//			// q = 6
+//			//nread = neighborList[n+5*Np];
+//			//fq = dist[nread];
+//			nr6 = neighborList[n+5*Np];
+//			fq = dist[nr6];
+//			rho+= fq;
+//			m1 -= 11.0*fq;
+//			m2 -= 4.0*fq;
+//			jz -= fq;
+//			m8 += 4.0*fq;
+//			m9 -= fq;
+//			m10 += 2.0*fq;
+//			m11 -= fq;
+//			m12 += 2.0*fq;
+//
+//			// q=7
+//			//nread = neighborList[n+6*Np];
+//			//fq = dist[nread];
+//			nr7 = neighborList[n+6*Np];
+//			fq = dist[nr7];
+//			rho += fq;
+//			m1 += 8.0*fq;
+//			m2 += fq;
+//			jx += fq;
+//			m4 += fq;
+//			jy += fq;
+//			m6 += fq;
+//			m9  += fq;
+//			m10 += fq;
+//			m11 += fq;
+//			m12 += fq;
+//			m13 = fq;
+//			m16 = fq;
+//			m17 = -fq;
+//
+//			// q = 8
+//			//nread = neighborList[n+7*Np];
+//			//fq = dist[nread];
+//			nr8 = neighborList[n+7*Np];
+//			fq = dist[nr8];
+//			rho += fq;
+//			m1 += 8.0*fq;
+//			m2 += fq;
+//			jx -= fq;
+//			m4 -= fq;
+//			jy -= fq;
+//			m6 -= fq;
+//			m9 += fq;
+//			m10 += fq;
+//			m11 += fq;
+//			m12 += fq;
+//			m13 += fq;
+//			m16 -= fq;
+//			m17 += fq;
+//
+//			// q=9
+//			//nread = neighborList[n+8*Np];
+//			//fq = dist[nread];
+//			nr9 = neighborList[n+8*Np];
+//			fq = dist[nr9];
+//			rho += fq;
+//			m1 += 8.0*fq;
+//			m2 += fq;
+//			jx += fq;
+//			m4 += fq;
+//			jy -= fq;
+//			m6 -= fq;
+//			m9 += fq;
+//			m10 += fq;
+//			m11 += fq;
+//			m12 += fq;
+//			m13 -= fq;
+//			m16 += fq;
+//			m17 += fq;
+//
+//			// q = 10
+//			//nread = neighborList[n+9*Np];
+//			//fq = dist[nread];
+//			nr10 = neighborList[n+9*Np];
+//			fq = dist[nr10];
+//			rho += fq;
+//			m1 += 8.0*fq;
+//			m2 += fq;
+//			jx -= fq;
+//			m4 -= fq;
+//			jy += fq;
+//			m6 += fq;
+//			m9 += fq;
+//			m10 += fq;
+//			m11 += fq;
+//			m12 += fq;
+//			m13 -= fq;
+//			m16 -= fq;
+//			m17 -= fq;
+//
+//			// q=11
+//			//nread = neighborList[n+10*Np];
+//			//fq = dist[nread];
+//			nr11 = neighborList[n+10*Np];
+//			fq = dist[nr11];
+//			rho += fq;
+//			m1 += 8.0*fq;
+//			m2 += fq;
+//			jx += fq;
+//			m4 += fq;
+//			jz += fq;
+//			m8 += fq;
+//			m9 += fq;
+//			m10 += fq;
+//			m11 -= fq;
+//			m12 -= fq;
+//			m15 = fq;
+//			m16 -= fq;
+//			m18 = fq;
+//
+//			// q=12
+//			//nread = neighborList[n+11*Np];
+//			//fq = dist[nread];
+//			nr12 = neighborList[n+11*Np];
+//			fq = dist[nr12];
+//			rho += fq;
+//			m1 += 8.0*fq;
+//			m2 += fq;
+//			jx -= fq;
+//			m4 -= fq;
+//			jz -= fq;
+//			m8 -= fq;
+//			m9 += fq;
+//			m10 += fq;
+//			m11 -= fq;
+//			m12 -= fq;
+//			m15 += fq;
+//			m16 += fq;
+//			m18 -= fq;
+//
+//			// q=13
+//			//nread = neighborList[n+12*Np];
+//			//fq = dist[nread];
+//			nr13 = neighborList[n+12*Np];
+//			fq = dist[nr13];
+//			rho += fq;
+//			m1 += 8.0*fq;
+//			m2 += fq;
+//			jx += fq;
+//			m4 += fq;
+//			jz -= fq;
+//			m8 -= fq;
+//			m9 += fq;
+//			m10 += fq;
+//			m11 -= fq;
+//			m12 -= fq;
+//			m15 -= fq;
+//			m16 -= fq;
+//			m18 -= fq;
+//
+//			// q=14
+//			//nread = neighborList[n+13*Np];
+//			//fq = dist[nread];
+//			nr14 = neighborList[n+13*Np];
+//			fq = dist[nr14];
+//			rho += fq;
+//			m1 += 8.0*fq;
+//			m2 += fq;
+//			jx -= fq;
+//			m4 -= fq;
+//			jz += fq;
+//			m8 += fq;
+//			m9 += fq;
+//			m10 += fq;
+//			m11 -= fq;
+//			m12 -= fq;
+//			m15 -= fq;
+//			m16 += fq;
+//			m18 += fq;
+//
+//			// q=15
+//			nread = neighborList[n+14*Np];
+//			fq = dist[nread];
+//			//fq = dist[17*Np+n];
+//			rho += fq;
+//			m1 += 8.0*fq;
+//			m2 += fq;
+//			jy += fq;
+//			m6 += fq;
+//			jz += fq;
+//			m8 += fq;
+//			m9 -= 2.0*fq;
+//			m10 -= 2.0*fq;
+//			m14 = fq;
+//			m17 += fq;
+//			m18 -= fq;
+//
+//			// q=16
+//			nread = neighborList[n+15*Np];
+//			fq = dist[nread];
+//			//fq = dist[8*Np+n];
+//			rho += fq;
+//			m1 += 8.0*fq;
+//			m2 += fq;
+//			jy -= fq;
+//			m6 -= fq;
+//			jz -= fq;
+//			m8 -= fq;
+//			m9 -= 2.0*fq;
+//			m10 -= 2.0*fq;
+//			m14 += fq;
+//			m17 -= fq;
+//			m18 += fq;
+//
+//			// q=17
+//			//fq = dist[18*Np+n];
+//			nread = neighborList[n+16*Np];
+//			fq = dist[nread];
+//			rho += fq;
+//			m1 += 8.0*fq;
+//			m2 += fq;
+//			jy += fq;
+//			m6 += fq;
+//			jz -= fq;
+//			m8 -= fq;
+//			m9 -= 2.0*fq;
+//			m10 -= 2.0*fq;
+//			m14 -= fq;
+//			m17 += fq;
+//			m18 += fq;
+//
+//			// q=18
+//			nread = neighborList[n+17*Np];
+//			fq = dist[nread];
+//			//fq = dist[9*Np+n];
+//			rho += fq;
+//			m1 += 8.0*fq;
+//			m2 += fq;
+//			jy -= fq;
+//			m6 -= fq;
+//			jz += fq;
+//			m8 += fq;
+//			m9 -= 2.0*fq;
+//			m10 -= 2.0*fq;
+//			m14 -= fq;
+//			m17 -= fq;
+//			m18 -= fq;
+//			
+//            // Compute greyscale related parameters
+//            c0 = 0.5*(1.0+porosity*0.5*mu_eff/perm);
+//            if (porosity==1.0) c0 = 0.5;//i.e. apparent pore nodes
+//            //GeoFun = 1.75/sqrt(150.0*porosity*porosity*porosity);
+//            c1 = porosity*0.5*GeoFun/sqrt(perm);
+//            if (porosity==1.0) c1 = 0.0;//i.e. apparent pore nodes
+//
+//            vx = jx/rho0+0.5*(porosity*Gx);
+//            vy = jy/rho0+0.5*(porosity*Gy);
+//            vz = jz/rho0+0.5*(porosity*Gz);
+//            v_mag=sqrt(vx*vx+vy*vy+vz*vz);
+//            ux = vx/(c0+sqrt(c0*c0+c1*v_mag));
+//            uy = vy/(c0+sqrt(c0*c0+c1*v_mag));
+//            uz = vz/(c0+sqrt(c0*c0+c1*v_mag));
+//            u_mag=sqrt(ux*ux+uy*uy+uz*uz);
+//
+//            //Update the total force to include linear (Darcy) and nonlinear (Forchheimer) drags due to the porous medium
+//            Fx = rho0*(-porosity*mu_eff/perm*ux - porosity*GeoFun/sqrt(perm)*u_mag*ux + porosity*Gx);
+//            Fy = rho0*(-porosity*mu_eff/perm*uy - porosity*GeoFun/sqrt(perm)*u_mag*uy + porosity*Gy);
+//            Fz = rho0*(-porosity*mu_eff/perm*uz - porosity*GeoFun/sqrt(perm)*u_mag*uz + porosity*Gz);
+//            if (porosity==1.0){
+//                Fx=rho0*(Gx);
+//                Fy=rho0*(Gy);
+//                Fz=rho0*(Gz);
+//            }
+//
+//			// write the velocity 
+//			Velocity[n] = ux;
+//			Velocity[Np+n] = uy;
+//			Velocity[2*Np+n] = uz;
+//
+//			//........................................................................
+//			//..............carry out relaxation process..............................
+//			//..........Toelke, Fruediger et. al. 2006................................
+//			if (C == 0.0)	nx = ny = nz = 0.0;
+//			m1 = m1 + rlx_setA*((19*(ux*ux+uy*uy+uz*uz)*rho0/porosity - 11*rho) -19*alpha*C - m1);
+//			m2 = m2 + rlx_setA*((3*rho - 5.5*(ux*ux+uy*uy+uz*uz)*rho0/porosity)- m2);
+//            jx = jx + Fx;
+//			m4 = m4 + rlx_setB*((-0.6666666666666666*ux*rho0)- m4)
+//                    + (1-0.5*rlx_setB)*(-0.6666666666666666*Fx);
+//            jy = jy + Fy;
+//			m6 = m6 + rlx_setB*((-0.6666666666666666*uy*rho0)- m6)
+//                    + (1-0.5*rlx_setB)*(-0.6666666666666666*Fy);
+//            jz = jz + Fz;
+//			m8 = m8 + rlx_setB*((-0.6666666666666666*uz*rho0)- m8)
+//                    + (1-0.5*rlx_setB)*(-0.6666666666666666*Fz);
+//			m9 = m9 + rlx_setA*(((2*ux*ux-uy*uy-uz*uz)*rho0/porosity) + 0.5*alpha*C*(2*nx*nx-ny*ny-nz*nz) - m9);
+//			m10 = m10 + rlx_setA*( - m10);
+//            //m10 = m10 + rlx_setA*(-0.5*rho0*((2*ux*ux-uy*uy-uz*uz)/porosity)- m10);
+//			m11 = m11 + rlx_setA*(((uy*uy-uz*uz)*rho0/porosity) + 0.5*alpha*C*(ny*ny-nz*nz)- m11);
+//			m12 = m12 + rlx_setA*( - m12);
+//            //m12 = m12 + rlx_setA*(-0.5*(rho0*(uy*uy-uz*uz)/porosity)- m12);
+//			m13 = m13 + rlx_setA*( (ux*uy*rho0/porosity) + 0.5*alpha*C*nx*ny - m13);
+//			m14 = m14 + rlx_setA*( (uy*uz*rho0/porosity) + 0.5*alpha*C*ny*nz - m14);
+//			m15 = m15 + rlx_setA*( (ux*uz*rho0/porosity) + 0.5*alpha*C*nx*nz - m15);
+//			m16 = m16 + rlx_setB*( - m16);
+//			m17 = m17 + rlx_setB*( - m17);
+//			m18 = m18 + rlx_setB*( - m18);
+//
+//			//.................inverse transformation......................................................
+//			// q=0
+//			fq = mrt_V1*rho-mrt_V2*m1+mrt_V3*m2;
+//			dist[n] = fq;
+//
+//			// q = 1
+//			fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(jx-m4)+mrt_V6*(m9-m10);
+//			//nread = neighborList[n+Np];
+//			dist[nr2] = fq;
+//
+//			// q=2
+//			fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(m4-jx)+mrt_V6*(m9-m10);
+//			//nread = neighborList[n];
+//			dist[nr1] = fq;
+//
+//			// q = 3
+//			fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(jy-m6)+mrt_V7*(m10-m9)+mrt_V8*(m11-m12);
+//			//nread = neighborList[n+3*Np];
+//			dist[nr4] = fq;
+//
+//			// q = 4
+//			fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(m6-jy)+mrt_V7*(m10-m9)+mrt_V8*(m11-m12);
+//			//nread = neighborList[n+2*Np];
+//			dist[nr3] = fq;
+//
+//			// q = 5
+//			fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(jz-m8)+mrt_V7*(m10-m9)+mrt_V8*(m12-m11);
+//			//nread = neighborList[n+5*Np];
+//			dist[nr6] = fq;
+//
+//			// q = 6
+//			fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(m8-jz)+mrt_V7*(m10-m9)+mrt_V8*(m12-m11);
+//			//nread = neighborList[n+4*Np];
+//			dist[nr5] = fq;
+//
+//			// q = 7
+//			fq = mrt_V1*rho+mrt_V9*m1+mrt_V10*m2+0.1*(jx+jy)+0.025*(m4+m6)+
+//					mrt_V7*m9+mrt_V11*m10+mrt_V8*m11+mrt_V12*m12+0.25*m13+0.125*(m16-m17);
+//			//nread = neighborList[n+7*Np];
+//			dist[nr8] = fq;
+//
+//			// q = 8
+//			fq = mrt_V1*rho+mrt_V9*m1+mrt_V10*m2-0.1*(jx+jy)-0.025*(m4+m6) +mrt_V7*m9+mrt_V11*m10+mrt_V8*m11
+//					+mrt_V12*m12+0.25*m13+0.125*(m17-m16);
+//			//nread = neighborList[n+6*Np];
+//			dist[nr7] = fq;
+//
+//			// q = 9
+//			fq = mrt_V1*rho+mrt_V9*m1+mrt_V10*m2+0.1*(jx-jy)+0.025*(m4-m6)+
+//					mrt_V7*m9+mrt_V11*m10+mrt_V8*m11+mrt_V12*m12-0.25*m13+0.125*(m16+m17);
+//			//nread = neighborList[n+9*Np];
+//			dist[nr10] = fq;
+//
+//			// q = 10
+//			fq = mrt_V1*rho+mrt_V9*m1+mrt_V10*m2+0.1*(jy-jx)+0.025*(m6-m4)+
+//					mrt_V7*m9+mrt_V11*m10+mrt_V8*m11+mrt_V12*m12-0.25*m13-0.125*(m16+m17);
+//			//nread = neighborList[n+8*Np];
+//			dist[nr9] = fq;
+//
+//			// q = 11
+//			fq = mrt_V1*rho+mrt_V9*m1
+//					+mrt_V10*m2+0.1*(jx+jz)+0.025*(m4+m8)
+//					+mrt_V7*m9+mrt_V11*m10-mrt_V8*m11
+//					-mrt_V12*m12+0.25*m15+0.125*(m18-m16);
+//			//nread = neighborList[n+11*Np];
+//			dist[nr12] = fq;
+//
+//			// q = 12
+//			fq = mrt_V1*rho+mrt_V9*m1+mrt_V10*m2-0.1*(jx+jz)-0.025*(m4+m8)+
+//					mrt_V7*m9+mrt_V11*m10-mrt_V8*m11-mrt_V12*m12+0.25*m15+0.125*(m16-m18);
+//			//nread = neighborList[n+10*Np];
+//			dist[nr11]= fq;
+//
+//			// q = 13
+//			fq = mrt_V1*rho+mrt_V9*m1
+//					+mrt_V10*m2+0.1*(jx-jz)+0.025*(m4-m8)
+//					+mrt_V7*m9+mrt_V11*m10-mrt_V8*m11
+//					-mrt_V12*m12-0.25*m15-0.125*(m16+m18);
+//			//nread = neighborList[n+13*Np];
+//			dist[nr14] = fq;
+//
+//			// q= 14
+//			fq = mrt_V1*rho+mrt_V9*m1
+//					+mrt_V10*m2+0.1*(jz-jx)+0.025*(m8-m4)
+//					+mrt_V7*m9+mrt_V11*m10-mrt_V8*m11
+//					-mrt_V12*m12-0.25*m15+0.125*(m16+m18);
+//			//nread = neighborList[n+12*Np];
+//			dist[nr13] = fq;
+//
+//
+//			// q = 15
+//			fq = mrt_V1*rho+mrt_V9*m1
+//					+mrt_V10*m2+0.1*(jy+jz)+0.025*(m6+m8)
+//					-mrt_V6*m9-mrt_V7*m10+0.25*m14+0.125*(m17-m18);
+//			nread = neighborList[n+15*Np];
+//			dist[nread] = fq;
+//
+//			// q = 16
+//			fq =  mrt_V1*rho+mrt_V9*m1
+//					+mrt_V10*m2-0.1*(jy+jz)-0.025*(m6+m8)
+//					-mrt_V6*m9-mrt_V7*m10+0.25*m14+0.125*(m18-m17);
+//			nread = neighborList[n+14*Np];
+//			dist[nread] = fq;
+//
+//
+//			// q = 17
+//			fq = mrt_V1*rho+mrt_V9*m1
+//					+mrt_V10*m2+0.1*(jy-jz)+0.025*(m6-m8)
+//					-mrt_V6*m9-mrt_V7*m10-0.25*m14+0.125*(m17+m18);
+//			nread = neighborList[n+17*Np];
+//			dist[nread] = fq;
+//
+//			// q = 18
+//			fq = mrt_V1*rho+mrt_V9*m1
+//					+mrt_V10*m2+0.1*(jz-jy)+0.025*(m8-m6)
+//					-mrt_V6*m9-mrt_V7*m10-0.25*m14-0.125*(m17+m18);
+//			nread = neighborList[n+16*Np];
+//			dist[nread] = fq;
+//			//........................................................................
+//
+//			// Instantiate mass transport distributions
+//			// Stationary value - distribution 0
+//			nAB = 1.0/(nA+nB);
+//			Aq[n] = 0.3333333333333333*nA;
+//			Bq[n] = 0.3333333333333333*nB;
+//
+//			//...............................................
+//			// q = 0,2,4
+//			// Cq = {1,0,0}, {0,1,0}, {0,0,1}
+//			delta = beta*nA*nB*nAB*0.1111111111111111*nx;
+//			if (!(nA*nB*nAB>0)) delta=0;
+//			a1 = nA*(0.1111111111111111*(1+4.5*ux))+delta;
+//			b1 = nB*(0.1111111111111111*(1+4.5*ux))-delta;
+//			a2 = nA*(0.1111111111111111*(1-4.5*ux))-delta;
+//			b2 = nB*(0.1111111111111111*(1-4.5*ux))+delta;
+//
+//			// q = 1
+//			//nread = neighborList[n+Np];
+//			Aq[nr2] = a1;
+//			Bq[nr2] = b1;
+//			// q=2
+//			//nread = neighborList[n];
+//			Aq[nr1] = a2;
+//			Bq[nr1] = b2;
+//
+//			//...............................................
+//			// Cq = {0,1,0}
+//			delta = beta*nA*nB*nAB*0.1111111111111111*ny;
+//			if (!(nA*nB*nAB>0)) delta=0;
+//			a1 = nA*(0.1111111111111111*(1+4.5*uy))+delta;
+//			b1 = nB*(0.1111111111111111*(1+4.5*uy))-delta;
+//			a2 = nA*(0.1111111111111111*(1-4.5*uy))-delta;
+//			b2 = nB*(0.1111111111111111*(1-4.5*uy))+delta;
+//
+//			// q = 3
+//			//nread = neighborList[n+3*Np];
+//			Aq[nr4] = a1;
+//			Bq[nr4] = b1;
+//			// q = 4
+//			//nread = neighborList[n+2*Np];
+//			Aq[nr3] = a2;
+//			Bq[nr3] = b2;
+//
+//			//...............................................
+//			// q = 4
+//			// Cq = {0,0,1}
+//			delta = beta*nA*nB*nAB*0.1111111111111111*nz;
+//			if (!(nA*nB*nAB>0)) delta=0;
+//			a1 = nA*(0.1111111111111111*(1+4.5*uz))+delta;
+//			b1 = nB*(0.1111111111111111*(1+4.5*uz))-delta;
+//			a2 = nA*(0.1111111111111111*(1-4.5*uz))-delta;
+//			b2 = nB*(0.1111111111111111*(1-4.5*uz))+delta;
+//
+//			// q = 5
+//			//nread = neighborList[n+5*Np];
+//			Aq[nr6] = a1;
+//			Bq[nr6] = b1;
+//			// q = 6
+//			//nread = neighborList[n+4*Np];
+//			Aq[nr5] = a2;
+//			Bq[nr5] = b2;
+//			//...............................................
+//		}
+//	}
+//}
+//
+////Model-2&3
+//__global__  void dvc_ScaLBL_D3Q19_AAeven_GreyscaleColor(int *Map, double *dist, double *Aq, double *Bq, double *Den, 
+//        double *Phi, double *GreySolidGrad, double *Poros,double *Perm, double *Velocity, 
+//        double rhoA, double rhoB, double tauA, double tauB,double tauA_eff,double tauB_eff, double alpha, double beta,
+//		double Gx, double Gy, double Gz, int strideY, int strideZ, int start, int finish, int Np){
+//	int ijk,nn,n;
+//	double fq;
+//	// conserved momemnts
+//	double rho,jx,jy,jz;
+//	double vx,vy,vz,v_mag;
+//    double ux,uy,uz,u_mag;
+//	// non-conserved moments
+//	double m1,m2,m4,m6,m8,m9,m10,m11,m12,m13,m14,m15,m16,m17,m18;
+//	double m3,m5,m7;
+//	double t1,t2,t4,t6,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18;
+//	double t3,t5,t7;
+//	double nA,nB; // number density
+//	double a1,b1,a2,b2,nAB,delta;
+//	double C,nx,ny,nz; //color gradient magnitude and direction
+//	double phi,tau,rho0,rlx_setA,rlx_setB;
+//
+//    double GeoFun=0.0;//geometric function from Guo's PRE 66, 036304 (2002)
+//    double porosity;
+//    double perm;//voxel permeability
+//    double c0, c1; //Guo's model parameters
+//    double tau_eff;
+//    double mu_eff;//kinematic viscosity
+//    double nx_phase,ny_phase,nz_phase,C_phase;
+//    double Fx,Fy,Fz;
+//
+//	const double mrt_V1=0.05263157894736842;
+//	const double mrt_V2=0.012531328320802;
+//	const double mrt_V3=0.04761904761904762;
+//	const double mrt_V4=0.004594820384294068;
+//	const double mrt_V5=0.01587301587301587;
+//	const double mrt_V6=0.0555555555555555555555555;
+//	const double mrt_V7=0.02777777777777778;
+//	const double mrt_V8=0.08333333333333333;
+//	const double mrt_V9=0.003341687552213868;
+//	const double mrt_V10=0.003968253968253968;
+//	const double mrt_V11=0.01388888888888889;
+//	const double mrt_V12=0.04166666666666666;
+//
+//	int S = Np/NBLOCKS/NTHREADS + 1;
+//	for (int s=0; s<S; s++){
+//		//........Get 1-D index for this thread....................
+//		n =  S*blockIdx.x*blockDim.x + s*blockDim.x + threadIdx.x + start;
+//		if (n<finish) {
+//
+//			// read the component number densities
+//			nA = Den[n];
+//			nB = Den[Np + n];
+//            porosity = Poros[n];
+//            perm = Perm[n];
+//
+//			// compute phase indicator field
+//			phi=(nA-nB)/(nA+nB);
+//
+//			// local density
+//			rho0=rhoA + 0.5*(1.0-phi)*(rhoB-rhoA);
+//			// local relaxation time
+//			tau=tauA + 0.5*(1.0-phi)*(tauB-tauA);
+//			tau_eff=tauA_eff + 0.5*(1.0-phi)*(tauB_eff-tauA_eff);
+//			rlx_setA = 1.f/tau;
+//			rlx_setB = 8.f*(2.f-rlx_setA)/(8.f-rlx_setA);
+//            mu_eff = (tau_eff-0.5)/3.0;//kinematic viscosity
+//
+//			// Get the 1D index based on regular data layout
+//			ijk = Map[n];
+//			//					COMPUTE THE COLOR GRADIENT
+//			//........................................................................
+//			//.................Read Phase Indicator Values............................
+//			//........................................................................
+//			nn = ijk-1;							// neighbor index (get convention)
+//			m1 = Phi[nn];						// get neighbor for phi - 1
+//			t1 = m1+(1.0-porosity)*GreySolidGrad[nn];				
+//            if (fabs(t1)>1.0) t1 =((t1>0.0)-(t1<0.0))*(1.0-fabs(t1))+t1;
+//			//........................................................................
+//			nn = ijk+1;							// neighbor index (get convention)
+//			m2 = Phi[nn];						// get neighbor for phi - 2
+//			t2 = m2+(1.0-porosity)*GreySolidGrad[nn];				
+//            if (fabs(t2)>1.0) t2 =((t2>0.0)-(t2<0.0))*(1.0-fabs(t2))+t2;
+//			//........................................................................
+//			nn = ijk-strideY;							// neighbor index (get convention)
+//			m3 = Phi[nn];					// get neighbor for phi - 3
+//			t3 = m3+(1.0-porosity)*GreySolidGrad[nn];				
+//            if (fabs(t3)>1.0) t3 =((t3>0.0)-(t3<0.0))*(1.0-fabs(t3))+t3;
+//			//........................................................................
+//			nn = ijk+strideY;							// neighbor index (get convention)
+//			m4 = Phi[nn];					// get neighbor for phi - 4
+//			t4 = m4+(1.0-porosity)*GreySolidGrad[nn];				
+//            if (fabs(t4)>1.0) t4 =((t4>0.0)-(t4<0.0))*(1.0-fabs(t4))+t4;
+//			//........................................................................
+//			nn = ijk-strideZ;						// neighbor index (get convention)
+//			m5 = Phi[nn];					// get neighbor for phi - 5
+//			t5 = m5+(1.0-porosity)*GreySolidGrad[nn];				
+//            if (fabs(t5)>1.0) t5 =((t5>0.0)-(t5<0.0))*(1.0-fabs(t5))+t5;
+//			//........................................................................
+//			nn = ijk+strideZ;						// neighbor index (get convention)
+//			m6 = Phi[nn];					// get neighbor for phi - 6
+//			t6 = m6+(1.0-porosity)*GreySolidGrad[nn];				
+//            if (fabs(t6)>1.0) t6 =((t6>0.0)-(t6<0.0))*(1.0-fabs(t6))+t6;
+//			//........................................................................
+//			nn = ijk-strideY-1;						// neighbor index (get convention)
+//			m7 = Phi[nn];					// get neighbor for phi - 7
+//			t7 = m7+(1.0-porosity)*GreySolidGrad[nn];				
+//            if (fabs(t7)>1.0) t7 =((t7>0.0)-(t7<0.0))*(1.0-fabs(t7))+t7;
+//			//........................................................................
+//			nn = ijk+strideY+1;						// neighbor index (get convention)
+//			m8 = Phi[nn];					// get neighbor for phi - 8
+//			t8 = m8+(1.0-porosity)*GreySolidGrad[nn];				
+//            if (fabs(t8)>1.0) t8 =((t8>0.0)-(t8<0.0))*(1.0-fabs(t8))+t8;
+//			//........................................................................
+//			nn = ijk+strideY-1;						// neighbor index (get convention)
+//			m9 = Phi[nn];					// get neighbor for phi - 9
+//			t9 = m9+(1.0-porosity)*GreySolidGrad[nn];				
+//            if (fabs(t9)>1.0) t9 =((t9>0.0)-(t9<0.0))*(1.0-fabs(t9))+t9;
+//			//........................................................................
+//			nn = ijk-strideY+1;						// neighbor index (get convention)
+//			m10 = Phi[nn];					// get neighbor for phi - 10
+//			t10 = m10+(1.0-porosity)*GreySolidGrad[nn];				
+//            if (fabs(t10)>1.0) t10 =((t10>0.0)-(t10<0.0))*(1.0-fabs(t10))+t10;
+//			//........................................................................
+//			nn = ijk-strideZ-1;						// neighbor index (get convention)
+//			m11 = Phi[nn];					// get neighbor for phi - 11
+//			t11 = m11+(1.0-porosity)*GreySolidGrad[nn];				
+//            if (fabs(t11)>1.0) t11 =((t11>0.0)-(t11<0.0))*(1.0-fabs(t11))+t11;
+//			//........................................................................
+//			nn = ijk+strideZ+1;						// neighbor index (get convention)
+//			m12 = Phi[nn];					// get neighbor for phi - 12
+//			t12 = m12+(1.0-porosity)*GreySolidGrad[nn];				
+//            if (fabs(t12)>1.0) t12 =((t12>0.0)-(t12<0.0))*(1.0-fabs(t12))+t12;
+//			//........................................................................
+//			nn = ijk+strideZ-1;						// neighbor index (get convention)
+//			m13 = Phi[nn];					// get neighbor for phi - 13
+//			t13 = m13+(1.0-porosity)*GreySolidGrad[nn];				
+//            if (fabs(t13)>1.0) t13 =((t13>0.0)-(t13<0.0))*(1.0-fabs(t13))+t13;
+//			//........................................................................
+//			nn = ijk-strideZ+1;						// neighbor index (get convention)
+//			m14 = Phi[nn];					// get neighbor for phi - 14
+//			t14 = m14+(1.0-porosity)*GreySolidGrad[nn];				
+//            if (fabs(t14)>1.0) t14 =((t14>0.0)-(t14<0.0))*(1.0-fabs(t14))+t14;
+//			//........................................................................
+//			nn = ijk-strideZ-strideY;					// neighbor index (get convention)
+//			m15 = Phi[nn];					// get neighbor for phi - 15
+//			t15 = m15+(1.0-porosity)*GreySolidGrad[nn];				
+//            if (fabs(t15)>1.0) t15 =((t15>0.0)-(t15<0.0))*(1.0-fabs(t15))+t15;
+//			//........................................................................
+//			nn = ijk+strideZ+strideY;					// neighbor index (get convention)
+//			m16 = Phi[nn];					// get neighbor for phi - 16
+//			t16 = m16+(1.0-porosity)*GreySolidGrad[nn];				
+//            if (fabs(t16)>1.0) t16 =((t16>0.0)-(t16<0.0))*(1.0-fabs(t16))+t16;
+//			//........................................................................
+//			nn = ijk+strideZ-strideY;					// neighbor index (get convention)
+//			m17 = Phi[nn];					// get neighbor for phi - 17
+//			t17 = m17+(1.0-porosity)*GreySolidGrad[nn];				
+//            if (fabs(t17)>1.0) t17 =((t17>0.0)-(t17<0.0))*(1.0-fabs(t17))+t17;
+//			//........................................................................
+//			nn = ijk-strideZ+strideY;					// neighbor index (get convention)
+//			m18 = Phi[nn];					// get neighbor for phi - 18
+//			t18 = m18+(1.0-porosity)*GreySolidGrad[nn];				
+//            if (fabs(t18)>1.0) t18 =((t18>0.0)-(t18<0.0))*(1.0-fabs(t18))+t18;
+//			//............Compute the Color Gradient...................................
+//			nx_phase = -(m1-m2+0.5*(m7-m8+m9-m10+m11-m12+m13-m14));
+//			ny_phase = -(m3-m4+0.5*(m7-m8-m9+m10+m15-m16+m17-m18));
+//			nz_phase = -(m5-m6+0.5*(m11-m12-m13+m14+m15-m16-m17+m18));
+//			C_phase = sqrt(nx_phase*nx_phase+ny_phase*ny_phase+nz_phase*nz_phase);
+//            //correct the normal color gradient by considering the effect of grey solid
+//			nx = -(t1-t2+0.5*(t7-t8+t9-t10+t11-t12+t13-t14));
+//			ny = -(t3-t4+0.5*(t7-t8-t9+t10+t15-t16+t17-t18));
+//			nz = -(t5-t6+0.5*(t11-t12-t13+t14+t15-t16-t17+t18));
+//
+//            if (C_phase==0.0){
+//                nx = nx_phase; 
+//                ny = ny_phase;
+//                nz = nz_phase;
+//            }
+//
+//			//...........Normalize the Color Gradient.................................
+//			C = sqrt(nx*nx+ny*ny+nz*nz);
+//			double ColorMag = C;
+//			if (C==0.0) ColorMag=1.0;
+//			nx = nx/ColorMag;
+//			ny = ny/ColorMag;
+//			nz = nz/ColorMag;		
+//
+//			// q=0
+//			fq = dist[n];
+//			rho = fq;
+//			m1  = -30.0*fq;
+//			m2  = 12.0*fq;
+//
+//			// q=1
+//			fq = dist[2*Np+n];
+//			rho += fq;
+//			m1 -= 11.0*fq;
+//			m2 -= 4.0*fq;
+//			jx = fq;
+//			m4 = -4.0*fq;
+//			m9 = 2.0*fq;
+//			m10 = -4.0*fq;
+//
+//			// f2 = dist[10*Np+n];
+//			fq = dist[1*Np+n];
+//			rho += fq;
+//			m1 -= 11.0*(fq);
+//			m2 -= 4.0*(fq);
+//			jx -= fq;
+//			m4 += 4.0*(fq);
+//			m9 += 2.0*(fq);
+//			m10 -= 4.0*(fq);
+//
+//			// q=3
+//			fq = dist[4*Np+n];
+//			rho += fq;
+//			m1 -= 11.0*fq;
+//			m2 -= 4.0*fq;
+//			jy = fq;
+//			m6 = -4.0*fq;
+//			m9 -= fq;
+//			m10 += 2.0*fq;
+//			m11 = fq;
+//			m12 = -2.0*fq;
+//
+//			// q = 4
+//			fq = dist[3*Np+n];
+//			rho+= fq;
+//			m1 -= 11.0*fq;
+//			m2 -= 4.0*fq;
+//			jy -= fq;
+//			m6 += 4.0*fq;
+//			m9 -= fq;
+//			m10 += 2.0*fq;
+//			m11 += fq;
+//			m12 -= 2.0*fq;
+//
+//			// q=5
+//			fq = dist[6*Np+n];
+//			rho += fq;
+//			m1 -= 11.0*fq;
+//			m2 -= 4.0*fq;
+//			jz = fq;
+//			m8 = -4.0*fq;
+//			m9 -= fq;
+//			m10 += 2.0*fq;
+//			m11 -= fq;
+//			m12 += 2.0*fq;
+//
+//			// q = 6
+//			fq = dist[5*Np+n];
+//			rho+= fq;
+//			m1 -= 11.0*fq;
+//			m2 -= 4.0*fq;
+//			jz -= fq;
+//			m8 += 4.0*fq;
+//			m9 -= fq;
+//			m10 += 2.0*fq;
+//			m11 -= fq;
+//			m12 += 2.0*fq;
+//
+//			// q=7
+//			fq = dist[8*Np+n];
+//			rho += fq;
+//			m1 += 8.0*fq;
+//			m2 += fq;
+//			jx += fq;
+//			m4 += fq;
+//			jy += fq;
+//			m6 += fq;
+//			m9  += fq;
+//			m10 += fq;
+//			m11 += fq;
+//			m12 += fq;
+//			m13 = fq;
+//			m16 = fq;
+//			m17 = -fq;
+//
+//			// q = 8
+//			fq = dist[7*Np+n];
+//			rho += fq;
+//			m1 += 8.0*fq;
+//			m2 += fq;
+//			jx -= fq;
+//			m4 -= fq;
+//			jy -= fq;
+//			m6 -= fq;
+//			m9 += fq;
+//			m10 += fq;
+//			m11 += fq;
+//			m12 += fq;
+//			m13 += fq;
+//			m16 -= fq;
+//			m17 += fq;
+//
+//			// q=9
+//			fq = dist[10*Np+n];
+//			rho += fq;
+//			m1 += 8.0*fq;
+//			m2 += fq;
+//			jx += fq;
+//			m4 += fq;
+//			jy -= fq;
+//			m6 -= fq;
+//			m9 += fq;
+//			m10 += fq;
+//			m11 += fq;
+//			m12 += fq;
+//			m13 -= fq;
+//			m16 += fq;
+//			m17 += fq;
+//
+//			// q = 10
+//			fq = dist[9*Np+n];
+//			rho += fq;
+//			m1 += 8.0*fq;
+//			m2 += fq;
+//			jx -= fq;
+//			m4 -= fq;
+//			jy += fq;
+//			m6 += fq;
+//			m9 += fq;
+//			m10 += fq;
+//			m11 += fq;
+//			m12 += fq;
+//			m13 -= fq;
+//			m16 -= fq;
+//			m17 -= fq;
+//
+//			// q=11
+//			fq = dist[12*Np+n];
+//			rho += fq;
+//			m1 += 8.0*fq;
+//			m2 += fq;
+//			jx += fq;
+//			m4 += fq;
+//			jz += fq;
+//			m8 += fq;
+//			m9 += fq;
+//			m10 += fq;
+//			m11 -= fq;
+//			m12 -= fq;
+//			m15 = fq;
+//			m16 -= fq;
+//			m18 = fq;
+//
+//			// q=12
+//			fq = dist[11*Np+n];
+//			rho += fq;
+//			m1 += 8.0*fq;
+//			m2 += fq;
+//			jx -= fq;
+//			m4 -= fq;
+//			jz -= fq;
+//			m8 -= fq;
+//			m9 += fq;
+//			m10 += fq;
+//			m11 -= fq;
+//			m12 -= fq;
+//			m15 += fq;
+//			m16 += fq;
+//			m18 -= fq;
+//
+//			// q=13
+//			fq = dist[14*Np+n];
+//			rho += fq;
+//			m1 += 8.0*fq;
+//			m2 += fq;
+//			jx += fq;
+//			m4 += fq;
+//			jz -= fq;
+//			m8 -= fq;
+//			m9 += fq;
+//			m10 += fq;
+//			m11 -= fq;
+//			m12 -= fq;
+//			m15 -= fq;
+//			m16 -= fq;
+//			m18 -= fq;
+//
+//			// q=14
+//			fq = dist[13*Np+n];
+//			rho += fq;
+//			m1 += 8.0*fq;
+//			m2 += fq;
+//			jx -= fq;
+//			m4 -= fq;
+//			jz += fq;
+//			m8 += fq;
+//			m9 += fq;
+//			m10 += fq;
+//			m11 -= fq;
+//			m12 -= fq;
+//			m15 -= fq;
+//			m16 += fq;
+//			m18 += fq;
+//
+//			// q=15
+//			fq = dist[16*Np+n];
+//			rho += fq;
+//			m1 += 8.0*fq;
+//			m2 += fq;
+//			jy += fq;
+//			m6 += fq;
+//			jz += fq;
+//			m8 += fq;
+//			m9 -= 2.0*fq;
+//			m10 -= 2.0*fq;
+//			m14 = fq;
+//			m17 += fq;
+//			m18 -= fq;
+//
+//			// q=16
+//			fq = dist[15*Np+n];
+//			rho += fq;
+//			m1 += 8.0*fq;
+//			m2 += fq;
+//			jy -= fq;
+//			m6 -= fq;
+//			jz -= fq;
+//			m8 -= fq;
+//			m9 -= 2.0*fq;
+//			m10 -= 2.0*fq;
+//			m14 += fq;
+//			m17 -= fq;
+//			m18 += fq;
+//
+//			// q=17
+//			fq = dist[18*Np+n];
+//			rho += fq;
+//			m1 += 8.0*fq;
+//			m2 += fq;
+//			jy += fq;
+//			m6 += fq;
+//			jz -= fq;
+//			m8 -= fq;
+//			m9 -= 2.0*fq;
+//			m10 -= 2.0*fq;
+//			m14 -= fq;
+//			m17 += fq;
+//			m18 += fq;
+//
+//			// q=18
+//			fq = dist[17*Np+n];
+//			rho += fq;
+//			m1 += 8.0*fq;
+//			m2 += fq;
+//			jy -= fq;
+//			m6 -= fq;
+//			jz += fq;
+//			m8 += fq;
+//			m9 -= 2.0*fq;
+//			m10 -= 2.0*fq;
+//			m14 -= fq;
+//			m17 -= fq;
+//			m18 -= fq;
+//
+//            // Compute greyscale related parameters
+//            c0 = 0.5*(1.0+porosity*0.5*mu_eff/perm);
+//            if (porosity==1.0) c0 = 0.5;//i.e. apparent pore nodes
+//            //GeoFun = 1.75/sqrt(150.0*porosity*porosity*porosity);
+//            c1 = porosity*0.5*GeoFun/sqrt(perm);
+//            if (porosity==1.0) c1 = 0.0;//i.e. apparent pore nodes
+//
+//            vx = jx/rho0+0.5*(porosity*Gx);
+//            vy = jy/rho0+0.5*(porosity*Gy);
+//            vz = jz/rho0+0.5*(porosity*Gz);
+//            v_mag=sqrt(vx*vx+vy*vy+vz*vz);
+//            ux = vx/(c0+sqrt(c0*c0+c1*v_mag));
+//            uy = vy/(c0+sqrt(c0*c0+c1*v_mag));
+//            uz = vz/(c0+sqrt(c0*c0+c1*v_mag));
+//            u_mag=sqrt(ux*ux+uy*uy+uz*uz);
+//
+//            //Update the total force to include linear (Darcy) and nonlinear (Forchheimer) drags due to the porous medium
+//            Fx = rho0*(-porosity*mu_eff/perm*ux - porosity*GeoFun/sqrt(perm)*u_mag*ux + porosity*Gx);
+//            Fy = rho0*(-porosity*mu_eff/perm*uy - porosity*GeoFun/sqrt(perm)*u_mag*uy + porosity*Gy);
+//            Fz = rho0*(-porosity*mu_eff/perm*uz - porosity*GeoFun/sqrt(perm)*u_mag*uz + porosity*Gz);
+//            if (porosity==1.0){
+//                Fx=rho0*(Gx);
+//                Fy=rho0*(Gy);
+//                Fz=rho0*(Gz);
+//            }
+//
+//			// write the velocity 
+//			Velocity[n] = ux;
+//			Velocity[Np+n] = uy;
+//			Velocity[2*Np+n] = uz;
+//
+//			//........................................................................
+//			//..............carry out relaxation process..............................
+//			//..........Toelke, Fruediger et. al. 2006................................
+//			if (C == 0.0)	nx = ny = nz = 0.0;
+//			m1 = m1 + rlx_setA*((19*(ux*ux+uy*uy+uz*uz)*rho0/porosity - 11*rho) -19*alpha*C - m1);
+//			m2 = m2 + rlx_setA*((3*rho - 5.5*(ux*ux+uy*uy+uz*uz)*rho0/porosity)- m2);
+//            jx = jx + Fx;
+//			m4 = m4 + rlx_setB*((-0.6666666666666666*ux*rho0)- m4)
+//                    + (1-0.5*rlx_setB)*(-0.6666666666666666*Fx);
+//            jy = jy + Fy;
+//			m6 = m6 + rlx_setB*((-0.6666666666666666*uy*rho0)- m6)
+//                    + (1-0.5*rlx_setB)*(-0.6666666666666666*Fy);
+//            jz = jz + Fz;
+//			m8 = m8 + rlx_setB*((-0.6666666666666666*uz*rho0)- m8)
+//                    + (1-0.5*rlx_setB)*(-0.6666666666666666*Fz);
+//			m9 = m9 + rlx_setA*(((2*ux*ux-uy*uy-uz*uz)*rho0/porosity) + 0.5*alpha*C*(2*nx*nx-ny*ny-nz*nz) - m9);
+//			m10 = m10 + rlx_setA*( - m10);
+//            //m10 = m10 + rlx_setA*(-0.5*rho0*((2*ux*ux-uy*uy-uz*uz)/porosity)- m10);
+//			m11 = m11 + rlx_setA*(((uy*uy-uz*uz)*rho0/porosity) + 0.5*alpha*C*(ny*ny-nz*nz)- m11);
+//			m12 = m12 + rlx_setA*( - m12);
+//            //m12 = m12 + rlx_setA*(-0.5*(rho0*(uy*uy-uz*uz)/porosity)- m12);
+//			m13 = m13 + rlx_setA*( (ux*uy*rho0/porosity) + 0.5*alpha*C*nx*ny - m13);
+//			m14 = m14 + rlx_setA*( (uy*uz*rho0/porosity) + 0.5*alpha*C*ny*nz - m14);
+//			m15 = m15 + rlx_setA*( (ux*uz*rho0/porosity) + 0.5*alpha*C*nx*nz - m15);
+//			m16 = m16 + rlx_setB*( - m16);
+//			m17 = m17 + rlx_setB*( - m17);
+//			m18 = m18 + rlx_setB*( - m18);
+//
+//			//.................inverse transformation......................................................
+//			// q=0
+//			fq = mrt_V1*rho-mrt_V2*m1+mrt_V3*m2;
+//			dist[n] = fq;
+//
+//			// q = 1
+//			fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(jx-m4)+mrt_V6*(m9-m10);
+//			dist[1*Np+n] = fq;
+//
+//			// q=2
+//			fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(m4-jx)+mrt_V6*(m9-m10);
+//			dist[2*Np+n] = fq;
+//
+//			// q = 3
+//			fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(jy-m6)+mrt_V7*(m10-m9)+mrt_V8*(m11-m12);
+//			dist[3*Np+n] = fq;
+//
+//			// q = 4
+//			fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(m6-jy)+mrt_V7*(m10-m9)+mrt_V8*(m11-m12);
+//			dist[4*Np+n] = fq;
+//
+//			// q = 5
+//			fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(jz-m8)+mrt_V7*(m10-m9)+mrt_V8*(m12-m11);
+//			dist[5*Np+n] = fq;
+//
+//			// q = 6
+//			fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(m8-jz)+mrt_V7*(m10-m9)+mrt_V8*(m12-m11);
+//			dist[6*Np+n] = fq;
+//
+//			// q = 7
+//			fq = mrt_V1*rho+mrt_V9*m1+mrt_V10*m2+0.1*(jx+jy)+0.025*(m4+m6)+
+//					mrt_V7*m9+mrt_V11*m10+mrt_V8*m11+mrt_V12*m12+0.25*m13+0.125*(m16-m17);
+//			dist[7*Np+n] = fq;
+//
+//
+//			// q = 8
+//			fq = mrt_V1*rho+mrt_V9*m1+mrt_V10*m2-0.1*(jx+jy)-0.025*(m4+m6) +mrt_V7*m9+mrt_V11*m10+mrt_V8*m11
+//					+mrt_V12*m12+0.25*m13+0.125*(m17-m16);
+//			dist[8*Np+n] = fq;
+//
+//			// q = 9
+//			fq = mrt_V1*rho+mrt_V9*m1+mrt_V10*m2+0.1*(jx-jy)+0.025*(m4-m6)+
+//					mrt_V7*m9+mrt_V11*m10+mrt_V8*m11+mrt_V12*m12-0.25*m13+0.125*(m16+m17);
+//			dist[9*Np+n] = fq;
+//
+//			// q = 10
+//			fq = mrt_V1*rho+mrt_V9*m1+mrt_V10*m2+0.1*(jy-jx)+0.025*(m6-m4)+
+//					mrt_V7*m9+mrt_V11*m10+mrt_V8*m11+mrt_V12*m12-0.25*m13-0.125*(m16+m17);
+//			dist[10*Np+n] = fq;
+//
+//
+//			// q = 11
+//			fq = mrt_V1*rho+mrt_V9*m1
+//					+mrt_V10*m2+0.1*(jx+jz)+0.025*(m4+m8)
+//					+mrt_V7*m9+mrt_V11*m10-mrt_V8*m11
+//					-mrt_V12*m12+0.25*m15+0.125*(m18-m16);
+//			dist[11*Np+n] = fq;
+//
+//			// q = 12
+//			fq = mrt_V1*rho+mrt_V9*m1+mrt_V10*m2-0.1*(jx+jz)-0.025*(m4+m8)+
+//					mrt_V7*m9+mrt_V11*m10-mrt_V8*m11-mrt_V12*m12+0.25*m15+0.125*(m16-m18);
+//			dist[12*Np+n] = fq;
+//
+//			// q = 13
+//			fq = mrt_V1*rho+mrt_V9*m1
+//					+mrt_V10*m2+0.1*(jx-jz)+0.025*(m4-m8)
+//					+mrt_V7*m9+mrt_V11*m10-mrt_V8*m11
+//					-mrt_V12*m12-0.25*m15-0.125*(m16+m18);
+//			dist[13*Np+n] = fq;
+//
+//			// q= 14
+//			fq = mrt_V1*rho+mrt_V9*m1
+//					+mrt_V10*m2+0.1*(jz-jx)+0.025*(m8-m4)
+//					+mrt_V7*m9+mrt_V11*m10-mrt_V8*m11
+//					-mrt_V12*m12-0.25*m15+0.125*(m16+m18);
+//
+//			dist[14*Np+n] = fq;
+//
+//			// q = 15
+//			fq = mrt_V1*rho+mrt_V9*m1
+//					+mrt_V10*m2+0.1*(jy+jz)+0.025*(m6+m8)
+//					-mrt_V6*m9-mrt_V7*m10+0.25*m14+0.125*(m17-m18);
+//			dist[15*Np+n] = fq;
+//
+//			// q = 16
+//			fq =  mrt_V1*rho+mrt_V9*m1
+//					+mrt_V10*m2-0.1*(jy+jz)-0.025*(m6+m8)
+//					-mrt_V6*m9-mrt_V7*m10+0.25*m14+0.125*(m18-m17);
+//			dist[16*Np+n] = fq;
+//
+//
+//			// q = 17
+//			fq = mrt_V1*rho+mrt_V9*m1
+//					+mrt_V10*m2+0.1*(jy-jz)+0.025*(m6-m8)
+//					-mrt_V6*m9-mrt_V7*m10-0.25*m14+0.125*(m17+m18);
+//			dist[17*Np+n] = fq;
+//
+//			// q = 18
+//			fq = mrt_V1*rho+mrt_V9*m1
+//					+mrt_V10*m2+0.1*(jz-jy)+0.025*(m8-m6)
+//					-mrt_V6*m9-mrt_V7*m10-0.25*m14-0.125*(m17+m18);
+//			dist[18*Np+n] = fq;
+//			//........................................................................
+//
+//			// Instantiate mass transport distributions
+//			// Stationary value - distribution 0
+//			nAB = 1.0/(nA+nB);
+//			Aq[n] = 0.3333333333333333*nA;
+//			Bq[n] = 0.3333333333333333*nB;
+//
+//			//...............................................
+//			// q = 0,2,4
+//			// Cq = {1,0,0}, {0,1,0}, {0,0,1}
+//			delta = beta*nA*nB*nAB*0.1111111111111111*nx;
+//			if (!(nA*nB*nAB>0)) delta=0;
+//			a1 = nA*(0.1111111111111111*(1+4.5*ux))+delta;
+//			b1 = nB*(0.1111111111111111*(1+4.5*ux))-delta;
+//			a2 = nA*(0.1111111111111111*(1-4.5*ux))-delta;
+//			b2 = nB*(0.1111111111111111*(1-4.5*ux))+delta;
+//
+//			Aq[1*Np+n] = a1;
+//			Bq[1*Np+n] = b1;
+//			Aq[2*Np+n] = a2;
+//			Bq[2*Np+n] = b2;
+//
+//			//...............................................
+//			// q = 2
+//			// Cq = {0,1,0}
+//			delta = beta*nA*nB*nAB*0.1111111111111111*ny;
+//			if (!(nA*nB*nAB>0)) delta=0;
+//			a1 = nA*(0.1111111111111111*(1+4.5*uy))+delta;
+//			b1 = nB*(0.1111111111111111*(1+4.5*uy))-delta;
+//			a2 = nA*(0.1111111111111111*(1-4.5*uy))-delta;
+//			b2 = nB*(0.1111111111111111*(1-4.5*uy))+delta;
+//
+//			Aq[3*Np+n] = a1;
+//			Bq[3*Np+n] = b1;
+//			Aq[4*Np+n] = a2;
+//			Bq[4*Np+n] = b2;
+//			//...............................................
+//			// q = 4
+//			// Cq = {0,0,1}
+//			delta = beta*nA*nB*nAB*0.1111111111111111*nz;
+//			if (!(nA*nB*nAB>0)) delta=0;
+//			a1 = nA*(0.1111111111111111*(1+4.5*uz))+delta;
+//			b1 = nB*(0.1111111111111111*(1+4.5*uz))-delta;
+//			a2 = nA*(0.1111111111111111*(1-4.5*uz))-delta;
+//			b2 = nB*(0.1111111111111111*(1-4.5*uz))+delta;
+//
+//			Aq[5*Np+n] = a1;
+//			Bq[5*Np+n] = b1;
+//			Aq[6*Np+n] = a2;
+//			Bq[6*Np+n] = b2;
+//			//...............................................
+//
+//		}
+//	}
+//}
+
+//__global__ void dvc_ScaLBL_D3Q19_GreyscaleColor_Init(double *dist, double *Porosity, int Np)
+//{
+//	int n;
+//	int S = Np/NBLOCKS/NTHREADS + 1;
+//    double porosity;
+//	for (int s=0; s<S; s++){
+//		//........Get 1-D index for this thread....................
+//		n = S*blockIdx.x*blockDim.x + s*blockDim.x + threadIdx.x;
+//		if (n<Np ){
+//            porosity = Porosity[n];
+//            if (porosity==0.0) porosity=1.f;
+//			dist[n] = 0.3333333333333333/porosity;
+//			dist[Np+n] = 0.055555555555555555/porosity;		//double(100*n)+1.f;
+//			dist[2*Np+n] = 0.055555555555555555/porosity;	//double(100*n)+2.f;
+//			dist[3*Np+n] = 0.055555555555555555/porosity;	//double(100*n)+3.f;
+//			dist[4*Np+n] = 0.055555555555555555/porosity;	//double(100*n)+4.f;
+//			dist[5*Np+n] = 0.055555555555555555/porosity;	//double(100*n)+5.f;
+//			dist[6*Np+n] = 0.055555555555555555/porosity;	//double(100*n)+6.f;
+//			dist[7*Np+n] = 0.0277777777777778/porosity;   //double(100*n)+7.f;
+//			dist[8*Np+n] = 0.0277777777777778/porosity;   //double(100*n)+8.f;
+//			dist[9*Np+n] = 0.0277777777777778/porosity;   //double(100*n)+9.f;
+//			dist[10*Np+n] = 0.0277777777777778/porosity;  //double(100*n)+10.f;
+//			dist[11*Np+n] = 0.0277777777777778/porosity;  //double(100*n)+11.f;
+//			dist[12*Np+n] = 0.0277777777777778/porosity;  //double(100*n)+12.f;
+//			dist[13*Np+n] = 0.0277777777777778/porosity;  //double(100*n)+13.f;
+//			dist[14*Np+n] = 0.0277777777777778/porosity;  //double(100*n)+14.f;
+//			dist[15*Np+n] = 0.0277777777777778/porosity;  //double(100*n)+15.f;
+//			dist[16*Np+n] = 0.0277777777777778/porosity;  //double(100*n)+16.f;
+//			dist[17*Np+n] = 0.0277777777777778/porosity;  //double(100*n)+17.f;
+//			dist[18*Np+n] = 0.0277777777777778/porosity;  //double(100*n)+18.f;
+//		}
+//	}
+//}
+
+
+//extern "C" void ScaLBL_D3Q19_GreyscaleColor_Init(double *dist, double *Porosity, int Np){
+//	dvc_ScaLBL_D3Q19_GreyscaleColor_Init<<<NBLOCKS,NTHREADS >>>(dist,Porosity,Np);
+//	cudaError_t err = cudaGetLastError();
+//	if (cudaSuccess != err){
+//		printf("CUDA error in ScaLBL_D3Q19_GreyscaleColor_Init: %s \n",cudaGetErrorString(err));
+//	}
+//}
+
+//Model-1 & 4
+extern "C" void ScaLBL_D3Q19_AAeven_GreyscaleColor(int *Map, double *dist, double *Aq, double *Bq, double *Den, 
+        double *Phi,double *GreySolidGrad, double *Poros,double *Perm,double *Vel, 
+        double rhoA, double rhoB, double tauA, double tauB,double tauA_eff,double tauB_eff, double alpha, double beta,
+		double Fx, double Fy, double Fz, int strideY, int strideZ, int start, int finish, int Np){
+
+	//cudaProfilerStart();
+	//cudaFuncSetCacheConfig(dvc_ScaLBL_D3Q19_AAeven_GreyscaleColor, cudaFuncCachePreferL1);
+
+	dvc_ScaLBL_D3Q19_AAeven_GreyscaleColor<<<NBLOCKS,NTHREADS >>>(Map, dist, Aq, Bq, Den, Phi, GreySolidGrad, Poros, Perm, Vel, 
+            rhoA, rhoB, tauA, tauB, tauA_eff, tauB_eff, alpha, beta, Fx, Fy, Fz, strideY, strideZ, start, finish, Np);
+	cudaError_t err = cudaGetLastError();
+	if (cudaSuccess != err){
+		printf("CUDA error in ScaLBL_D3Q19_AAeven_GreyscaleColor: %s \n",cudaGetErrorString(err));
+	}
+	//cudaProfilerStop();
+
+}
+
+//Model-1 & 4
+extern "C" void ScaLBL_D3Q19_AAodd_GreyscaleColor(int *d_neighborList, int *Map, double *dist, double *Aq, double *Bq, double *Den, 
+		double *Phi, double *GreySolidGrad, double *Poros,double *Perm,double *Vel, 
+        double rhoA, double rhoB, double tauA, double tauB, double tauA_eff,double tauB_eff, double alpha, double beta,
+		double Fx, double Fy, double Fz, int strideY, int strideZ, int start, int finish, int Np){
+
+	//cudaProfilerStart();
+	//cudaFuncSetCacheConfig(dvc_ScaLBL_D3Q19_AAodd_GreyscaleColor, cudaFuncCachePreferL1);
+	
+	dvc_ScaLBL_D3Q19_AAodd_GreyscaleColor<<<NBLOCKS,NTHREADS >>>(d_neighborList, Map, dist, Aq, Bq, Den, Phi,  GreySolidGrad, Poros, Perm,Vel, 
+			rhoA, rhoB, tauA, tauB, tauA_eff, tauB_eff,alpha, beta, Fx, Fy, Fz, strideY, strideZ, start, finish, Np);
+
+	cudaError_t err = cudaGetLastError();
+	if (cudaSuccess != err){
+		printf("CUDA error in ScaLBL_D3Q19_AAodd_GreyscaleColor: %s \n",cudaGetErrorString(err));
+	}
+	//cudaProfilerStop();
+}
+
+////Model-2&3
+//extern "C" void ScaLBL_D3Q19_AAeven_GreyscaleColor(int *Map, double *dist, double *Aq, double *Bq, double *Den, 
+//        double *Phi,double *GreySolidGrad, double *Poros,double *Perm,double *Vel, 
+//        double rhoA, double rhoB, double tauA, double tauB,double tauA_eff,double tauB_eff, double alpha, double beta,
+//		double Fx, double Fy, double Fz, int strideY, int strideZ, int start, int finish, int Np){
+//
+//	//cudaProfilerStart();
+//	//cudaFuncSetCacheConfig(dvc_ScaLBL_D3Q19_AAeven_GreyscaleColor, cudaFuncCachePreferL1);
+//
+//	dvc_ScaLBL_D3Q19_AAeven_GreyscaleColor<<<NBLOCKS,NTHREADS >>>(Map, dist, Aq, Bq, Den, Phi, GreySolidGrad, Poros, Perm, Vel, 
+//            rhoA, rhoB, tauA, tauB, tauA_eff, tauB_eff, alpha, beta, Fx, Fy, Fz, strideY, strideZ, start, finish, Np);
+//	cudaError_t err = cudaGetLastError();
+//	if (cudaSuccess != err){
+//		printf("CUDA error in ScaLBL_D3Q19_AAeven_GreyscaleColor: %s \n",cudaGetErrorString(err));
+//	}
+//	//cudaProfilerStop();
+//
+//}
+//
+////Model-2&3
+//extern "C" void ScaLBL_D3Q19_AAodd_GreyscaleColor(int *d_neighborList, int *Map, double *dist, double *Aq, double *Bq, double *Den, 
+//		double *Phi, double *GreySolidGrad, double *Poros,double *Perm,double *Vel, 
+//        double rhoA, double rhoB, double tauA, double tauB, double tauA_eff,double tauB_eff, double alpha, double beta,
+//		double Fx, double Fy, double Fz, int strideY, int strideZ, int start, int finish, int Np){
+//
+//	//cudaProfilerStart();
+//	//cudaFuncSetCacheConfig(dvc_ScaLBL_D3Q19_AAodd_GreyscaleColor, cudaFuncCachePreferL1);
+//	
+//	dvc_ScaLBL_D3Q19_AAodd_GreyscaleColor<<<NBLOCKS,NTHREADS >>>(d_neighborList, Map, dist, Aq, Bq, Den, Phi,  GreySolidGrad, Poros, Perm,Vel, 
+//			rhoA, rhoB, tauA, tauB, tauA_eff, tauB_eff,alpha, beta, Fx, Fy, Fz, strideY, strideZ, start, finish, Np);
+//
+//	cudaError_t err = cudaGetLastError();
+//	if (cudaSuccess != err){
+//		printf("CUDA error in ScaLBL_D3Q19_AAodd_GreyscaleColor: %s \n",cudaGetErrorString(err));
+//	}
+//	//cudaProfilerStop();
+//}
diff --git a/models/GreyscaleColorModel.cpp b/models/GreyscaleColorModel.cpp
new file mode 100644
index 00000000..d97c844d
--- /dev/null
+++ b/models/GreyscaleColorModel.cpp
@@ -0,0 +1,2343 @@
+/*
+Two-fluid greyscale color lattice boltzmann model
+ */
+#include "models/GreyscaleColorModel.h"
+#include "analysis/distance.h"
+#include "analysis/morphology.h"
+#include "common/Communication.h"
+#include "common/ReadMicroCT.h"
+#include <stdlib.h>
+#include <time.h>
+
+ScaLBL_GreyscaleColorModel::ScaLBL_GreyscaleColorModel(int RANK, int NP, MPI_Comm COMM):
+rank(RANK), nprocs(NP), Restart(0),timestep(0),timestepMax(0),tauA(0),tauB(0),tauA_eff(0),tauB_eff(0),rhoA(0),rhoB(0),alpha(0),beta(0),
+Fx(0),Fy(0),Fz(0),flux(0),din(0),dout(0),inletA(0),inletB(0),outletA(0),outletB(0),GreyPorosity(0),
+Nx(0),Ny(0),Nz(0),N(0),Np(0),nprocx(0),nprocy(0),nprocz(0),BoundaryCondition(0),greyMode(0),Lx(0),Ly(0),Lz(0),comm(COMM)
+{
+	REVERSE_FLOW_DIRECTION = false;
+}
+ScaLBL_GreyscaleColorModel::~ScaLBL_GreyscaleColorModel(){
+
+}
+
+/*void ScaLBL_GreyscaleColorModel::WriteCheckpoint(const char *FILENAME, const double *cPhi, const double *cfq, int Np)
+{
+    int q,n;
+    double value;
+    ofstream File(FILENAME,ios::binary);
+    for (n=0; n<Np; n++){
+        // Write the two density values
+        value = cPhi[n];
+        File.write((char*) &value, sizeof(value));
+        // Write the even distributions
+        for (q=0; q<19; q++){
+            value = cfq[q*Np+n];
+            File.write((char*) &value, sizeof(value));
+        }
+    }
+    File.close();
+
+}
+
+void ScaLBL_GreyscaleColorModel::ReadCheckpoint(char *FILENAME, double *cPhi, double *cfq, int Np)
+{
+    int q=0, n=0;
+    double value=0;
+    ifstream File(FILENAME,ios::binary);
+    for (n=0; n<Np; n++){
+        File.read((char*) &value, sizeof(value));
+        cPhi[n] = value;
+        // Read the distributions
+        for (q=0; q<19; q++){
+            File.read((char*) &value, sizeof(value));
+            cfq[q*Np+n] = value;
+        }
+    }
+    File.close();
+}
+ */
+void ScaLBL_GreyscaleColorModel::ReadParams(string filename){
+	// read the input database 
+	db = std::make_shared<Database>( filename );
+	domain_db = db->getDatabase( "Domain" );
+	greyscaleColor_db =  db->getDatabase( "Color" );
+	analysis_db = db->getDatabase( "Analysis" );
+	vis_db = db->getDatabase( "Visualization" );
+
+	// set defaults
+	timestepMax = 100000;
+	tauA = tauB = 1.0;
+	rhoA = rhoB = 1.0;
+	Fx = Fy = Fz = 0.0;
+	alpha=1e-3;
+	beta=0.95;
+	Restart=false;
+	din=dout=1.0;
+	flux=0.0;
+    greyMode=false;
+	
+	// Color Model parameters
+	if (greyscaleColor_db->keyExists( "timestepMax" )){
+		timestepMax = greyscaleColor_db->getScalar<int>( "timestepMax" );
+	}
+	if (greyscaleColor_db->keyExists( "tauA" )){
+		tauA = greyscaleColor_db->getScalar<double>( "tauA" );
+	}
+	if (greyscaleColor_db->keyExists( "tauB" )){
+		tauB = greyscaleColor_db->getScalar<double>( "tauB" );
+	}
+	tauA_eff = greyscaleColor_db->getWithDefault<double>( "tauA_eff", tauA );
+	tauB_eff = greyscaleColor_db->getWithDefault<double>( "tauB_eff", tauB );
+	if (greyscaleColor_db->keyExists( "rhoA" )){
+		rhoA = greyscaleColor_db->getScalar<double>( "rhoA" );
+	}
+	if (greyscaleColor_db->keyExists( "rhoB" )){
+		rhoB = greyscaleColor_db->getScalar<double>( "rhoB" );
+	}
+	if (greyscaleColor_db->keyExists( "F" )){
+		Fx = greyscaleColor_db->getVector<double>( "F" )[0];
+		Fy = greyscaleColor_db->getVector<double>( "F" )[1];
+		Fz = greyscaleColor_db->getVector<double>( "F" )[2];
+	}
+	if (greyscaleColor_db->keyExists( "alpha" )){
+		alpha = greyscaleColor_db->getScalar<double>( "alpha" );
+	}
+	if (greyscaleColor_db->keyExists( "beta" )){
+		beta = greyscaleColor_db->getScalar<double>( "beta" );
+	}
+	if (greyscaleColor_db->keyExists( "Restart" )){
+		Restart = greyscaleColor_db->getScalar<bool>( "Restart" );
+	}
+	if (greyscaleColor_db->keyExists( "din" )){
+		din = greyscaleColor_db->getScalar<double>( "din" );
+	}
+	if (greyscaleColor_db->keyExists( "dout" )){
+		dout = greyscaleColor_db->getScalar<double>( "dout" );
+	}
+	if (greyscaleColor_db->keyExists( "flux" )){
+		flux = greyscaleColor_db->getScalar<double>( "flux" );
+	}
+    if (greyscaleColor_db->keyExists("GreySolidLabels")&&
+        greyscaleColor_db->keyExists("GreySolidAffinity")&&
+        greyscaleColor_db->keyExists("PorosityList")&&
+        greyscaleColor_db->keyExists("PermeabilityList")){
+        greyMode = true;
+    }
+	inletA=1.f;
+	inletB=0.f;
+	outletA=0.f;
+	outletB=1.f;
+	//if (BoundaryCondition==4) flux *= rhoA; // mass flux must adjust for density (see formulation for details)
+
+	BoundaryCondition = 0;
+	if (domain_db->keyExists( "BC" )){
+		BoundaryCondition = domain_db->getScalar<int>( "BC" );
+	}
+	
+	// Override user-specified boundary condition for specific protocols
+	auto protocol = greyscaleColor_db->getWithDefault<std::string>( "protocol", "none" );
+	if (protocol == "seed water"){
+		if (BoundaryCondition != 0 && BoundaryCondition != 5){
+			BoundaryCondition = 0;
+			if (rank==0) printf("WARNING: protocol (seed water) supports only full periodic boundary condition \n");
+		}
+		domain_db->putScalar<int>( "BC", BoundaryCondition );
+	}
+	else if (protocol == "open connected oil"){
+		if (BoundaryCondition != 0 && BoundaryCondition != 5){
+			BoundaryCondition = 0;
+			if (rank==0) printf("WARNING: protocol (open connected oil) supports only full periodic boundary condition \n");
+		}
+		domain_db->putScalar<int>( "BC", BoundaryCondition );
+	}
+	else if (protocol == "shell aggregation"){
+		if (BoundaryCondition != 0 && BoundaryCondition != 5){
+			BoundaryCondition = 0;
+			if (rank==0) printf("WARNING: protocol (shell aggregation) supports only full periodic boundary condition \n");
+		}
+		domain_db->putScalar<int>( "BC", BoundaryCondition );
+	}  
+}
+
+void ScaLBL_GreyscaleColorModel::SetDomain(){
+	Dm  = std::shared_ptr<Domain>(new Domain(domain_db,comm));      // full domain for analysis
+	Mask  = std::shared_ptr<Domain>(new Domain(domain_db,comm));    // mask domain removes immobile phases
+	// domain parameters
+	Nx = Dm->Nx;
+	Ny = Dm->Ny;
+	Nz = Dm->Nz;
+	Lx = Dm->Lx;
+	Ly = Dm->Ly;
+	Lz = Dm->Lz;
+	N = Nx*Ny*Nz;
+	id = new signed char [N];
+	for (int i=0; i<Nx*Ny*Nz; i++) Dm->id[i] = 1;               // initialize this way
+	//Averages = std::shared_ptr<TwoPhase> ( new TwoPhase(Dm) ); // TwoPhase analysis object
+	Averages = std::shared_ptr<SubPhase> ( new SubPhase(Dm) ); // TwoPhase analysis object
+	MPI_Barrier(comm);
+	Dm->CommInit();
+	MPI_Barrier(comm);
+	// Read domain parameters
+	rank = Dm->rank();	
+	nprocx = Dm->nprocx();
+	nprocy = Dm->nprocy();
+	nprocz = Dm->nprocz();
+}
+
+void ScaLBL_GreyscaleColorModel::ReadInput(){
+	
+	sprintf(LocalRankString,"%05d",rank);
+	sprintf(LocalRankFilename,"%s%s","ID.",LocalRankString);
+	sprintf(LocalRestartFile,"%s%s","Restart.",LocalRankString);
+	
+	if (greyscaleColor_db->keyExists( "image_sequence" )){
+		auto ImageList = greyscaleColor_db->getVector<std::string>( "image_sequence");
+		int IMAGE_INDEX = greyscaleColor_db->getWithDefault<int>( "image_index", 0 );
+		std::string first_image = ImageList[IMAGE_INDEX];
+		Mask->Decomp(first_image);
+		IMAGE_INDEX++;
+	}
+	else if (domain_db->keyExists( "GridFile" )){
+        // Read the local domain data
+	    auto input_id = readMicroCT( *domain_db, MPI_COMM_WORLD );
+        // Fill the halo (assuming GCW of 1)
+        array<int,3> size0 = { (int) input_id.size(0), (int) input_id.size(1), (int) input_id.size(2) };
+        ArraySize size1 = { (size_t) Mask->Nx, (size_t) Mask->Ny, (size_t) Mask->Nz };
+        ASSERT( (int) size1[0] == size0[0]+2 && (int) size1[1] == size0[1]+2 && (int) size1[2] == size0[2]+2 );
+        fillHalo<signed char> fill( MPI_COMM_WORLD, Mask->rank_info, size0, { 1, 1, 1 }, 0, 1 );
+        Array<signed char> id_view;
+        id_view.viewRaw( size1, Mask->id );
+        fill.copy( input_id, id_view );
+        fill.fill( id_view );
+	}
+	else if (domain_db->keyExists( "Filename" )){
+		auto Filename = domain_db->getScalar<std::string>( "Filename" );
+		Mask->Decomp(Filename);
+	}
+	else{
+		Mask->ReadIDs();
+	}
+	for (int i=0; i<Nx*Ny*Nz; i++) id[i] = Mask->id[i];  // save what was read
+	
+	// Generate the signed distance map
+	// Initialize the domain and communication
+	Array<char> id_solid(Nx,Ny,Nz);
+	// Solve for the position of the solid phase
+	for (int k=0;k<Nz;k++){
+		for (int j=0;j<Ny;j++){
+			for (int i=0;i<Nx;i++){
+				int n = k*Nx*Ny+j*Nx+i;
+				// Initialize the solid phase
+				signed char label = Mask->id[n];
+				if (label > 0)		id_solid(i,j,k) = 1;
+				else	     		id_solid(i,j,k) = 0;
+			}
+		}
+	}
+	// Initialize the signed distance function
+	for (int k=0;k<Nz;k++){
+		for (int j=0;j<Ny;j++){
+			for (int i=0;i<Nx;i++){
+				// Initialize distance to +/- 1
+				Averages->SDs(i,j,k) = 2.0*double(id_solid(i,j,k))-1.0;
+			}
+		}
+	}
+//	MeanFilter(Averages->SDs);
+	if (rank==0) printf("Initialized solid phase -- Converting to Signed Distance function \n");
+	CalcDist(Averages->SDs,id_solid,*Mask);
+	
+	if (rank == 0) cout << "Domain set." << endl;
+	
+	Averages->SetParams(rhoA,rhoB,tauA,tauB,Fx,Fy,Fz,alpha,beta);
+}
+
+void ScaLBL_GreyscaleColorModel::AssignComponentLabels()
+{
+    // Initialize impermeability solid nodes and grey nodes
+    // Key input parameters:
+    // 1. ComponentLabels
+    //    labels for various impermeable minerals and grey nodes
+    // 2. ComponentAffinity
+    //    for impermeable minerals, this is same as the wettability phase field in the normal color model
+    //    for grey nodes, this is effectively the initial phase field values
+    // **Convention for ComponentLabels:
+    //   (1) zero and negative integers are for impermeability minerals
+    //   (2) positive integers > 2 are for grey nodes
+    //   (3) label = 1 and 2 are always conserved for open node of non-wetting and wetting phase, respectively.
+	double *phase;
+	phase = new double[N];
+
+	size_t NLABELS=0;
+	signed char VALUE=0;
+	double AFFINITY=0.f;
+
+	auto LabelList = greyscaleColor_db->getVector<int>( "ComponentLabels" );
+	auto AffinityList = greyscaleColor_db->getVector<double>( "ComponentAffinity" );
+
+	NLABELS=LabelList.size();
+	if (NLABELS != AffinityList.size()){
+		ERROR("Error: ComponentLabels and ComponentAffinity must be the same length! \n");
+	}
+
+	double label_count[NLABELS];
+	double label_count_global[NLABELS];
+	// Assign the labels
+
+	for (size_t idx=0; idx<NLABELS; idx++) label_count[idx]=0;
+
+	for (int k=0;k<Nz;k++){
+		for (int j=0;j<Ny;j++){
+			for (int i=0;i<Nx;i++){
+				int n = k*Nx*Ny+j*Nx+i;
+				VALUE=id[n];
+				// Assign the affinity from the paired list
+				for (unsigned int idx=0; idx < NLABELS; idx++){
+				      //printf("idx=%i, value=%i, %i, \n",idx, VALUE,LabelList[idx]);
+					if (VALUE == LabelList[idx]){
+						AFFINITY=AffinityList[idx];
+						label_count[idx] += 1.0;
+						idx = NLABELS;
+						//Mask->id[n] = 0; // set mask to zero since this is an immobile component
+					}
+				}
+				// fluid labels are reserved
+				if (VALUE == 1) AFFINITY=1.0;
+				else if (VALUE == 2) AFFINITY=-1.0;
+				phase[n] = AFFINITY;
+			}
+		}
+	}
+
+	// Set Dm to match Mask
+	for (int i=0; i<Nx*Ny*Nz; i++) Dm->id[i] = Mask->id[i]; 
+	
+	for (size_t idx=0; idx<NLABELS; idx++)
+		label_count_global[idx] = sumReduce( Dm->Comm, label_count[idx]);
+
+	if (rank==0){
+		printf("Number of component labels: %lu \n",NLABELS);
+		for (unsigned int idx=0; idx<NLABELS; idx++){
+			VALUE=LabelList[idx];
+			AFFINITY=AffinityList[idx];
+			double volume_fraction  = double(label_count_global[idx])/double((Nx-2)*(Ny-2)*(Nz-2)*nprocs);
+			printf("   label=%d, affinity=%f, volume fraction==%f\n",VALUE,AFFINITY,volume_fraction); 
+		}
+	}
+
+	ScaLBL_CopyToDevice(Phi, phase, N*sizeof(double));
+	ScaLBL_DeviceBarrier();
+	MPI_Barrier(ScaLBL_Comm->MPI_COMM_SCALBL);
+    delete [] phase;
+}
+
+void ScaLBL_GreyscaleColorModel::AssignGreySolidLabels()//Model-4
+{
+    // ONLY initialize grey nodes
+    // Key input parameters:
+    // 1. GreySolidLabels
+    //    labels for grey nodes
+    // 2. GreySolidAffinity
+    //    affinity ranges [-1,1]
+    //    oil-wet > 0
+    //    water-wet < 0
+    //    neutral = 0 
+    double *SolidPotential_host = new double [Nx*Ny*Nz];
+	double *GreySolidGrad_host  = new double [3*Np];
+
+	size_t NLABELS=0;
+	signed char VALUE=0;
+	double AFFINITY=0.f;
+
+	auto LabelList = greyscaleColor_db->getVector<int>( "GreySolidLabels" );
+	auto AffinityList = greyscaleColor_db->getVector<double>( "GreySolidAffinity" );
+
+	NLABELS=LabelList.size();
+	if (NLABELS != AffinityList.size()){
+		ERROR("Error: GreySolidLabels and GreySolidAffinity must be the same length! \n");
+	}
+
+	for (int k=0;k<Nz;k++){
+		for (int j=0;j<Ny;j++){
+			for (int i=0;i<Nx;i++){
+				int n = k*Nx*Ny+j*Nx+i;
+				VALUE=id[n];
+	            AFFINITY=0.f;//all nodes except the specified grey nodes have grey-solid affinity = 0.0
+				// Assign the affinity from the paired list
+				for (unsigned int idx=0; idx < NLABELS; idx++){
+				      //printf("idx=%i, value=%i, %i, \n",idx, VALUE,LabelList[idx]);
+					if (VALUE == LabelList[idx]){
+						AFFINITY=AffinityList[idx];
+						idx = NLABELS;
+						//Mask->id[n] = 0; // set mask to zero since this is an immobile component
+					}
+				}
+				SolidPotential_host[n] = AFFINITY;
+			}
+		}
+	}
+
+    // Calculate grey-solid color-gradient
+	double *Dst;
+	Dst = new double [3*3*3];
+	for (int kk=0; kk<3; kk++){
+		for (int jj=0; jj<3; jj++){
+			for (int ii=0; ii<3; ii++){
+				int index = kk*9+jj*3+ii;
+				Dst[index] = sqrt(double(ii-1)*double(ii-1) + double(jj-1)*double(jj-1)+ double(kk-1)*double(kk-1));
+			}
+		}
+	}
+	double w_face = 1.f;
+	double w_edge = 0.5;
+	double w_corner = 0.f;
+	//local 
+	Dst[13] = 0.f;
+	//faces
+	Dst[4] = w_face;
+	Dst[10] = w_face;
+	Dst[12] = w_face;
+	Dst[14] = w_face;
+	Dst[16] = w_face;
+	Dst[22] = w_face;
+	// corners
+	Dst[0] = w_corner;
+	Dst[2] = w_corner;
+	Dst[6] = w_corner;
+	Dst[8] = w_corner;
+	Dst[18] = w_corner;
+	Dst[20] = w_corner;
+	Dst[24] = w_corner;
+	Dst[26] = w_corner;
+	// edges
+	Dst[1] = w_edge;
+	Dst[3] = w_edge;
+	Dst[5] = w_edge;
+	Dst[7] = w_edge;
+	Dst[9] = w_edge;
+	Dst[11] = w_edge;
+	Dst[15] = w_edge;
+	Dst[17] = w_edge;
+	Dst[19] = w_edge;
+	Dst[21] = w_edge;
+	Dst[23] = w_edge;
+	Dst[25] = w_edge;
+
+	for (int k=1; k<Nz-1; k++){
+		for (int j=1; j<Ny-1; j++){
+			for (int i=1; i<Nx-1; i++){
+				int idx=Map(i,j,k);
+				if (!(idx < 0)){
+					double phi_x = 0.f;
+					double phi_y = 0.f;
+					double phi_z = 0.f;
+					for (int kk=0; kk<3; kk++){
+						for (int jj=0; jj<3; jj++){
+							for (int ii=0; ii<3; ii++){
+
+								int index = kk*9+jj*3+ii;
+								double weight= Dst[index];
+
+								int idi=i+ii-1;
+								int idj=j+jj-1;
+								int idk=k+kk-1;
+
+								if (idi < 0) idi=0;
+								if (idj < 0) idj=0;
+								if (idk < 0) idk=0;
+								if (!(idi < Nx)) idi=Nx-1;
+								if (!(idj < Ny)) idj=Ny-1;
+								if (!(idk < Nz)) idk=Nz-1;
+
+								int nn = idk*Nx*Ny + idj*Nx + idi;
+								double vec_x = double(ii-1);
+								double vec_y = double(jj-1);
+								double vec_z = double(kk-1);
+								double GWNS=SolidPotential_host[nn];
+								phi_x += GWNS*weight*vec_x;
+								phi_y += GWNS*weight*vec_y;
+								phi_z += GWNS*weight*vec_z;
+							}
+						}
+					}
+                    if (Averages->SDs(i,j,k)<2.0){
+                        GreySolidGrad_host[idx+0*Np] = phi_x;
+                        GreySolidGrad_host[idx+1*Np] = phi_y;
+                        GreySolidGrad_host[idx+2*Np] = phi_z;
+                    }
+                    else{
+                        GreySolidGrad_host[idx+0*Np] = 0.0;
+                        GreySolidGrad_host[idx+1*Np] = 0.0;
+                        GreySolidGrad_host[idx+2*Np] = 0.0;
+                    }
+				}
+			}
+		}
+	}
+
+
+	if (rank==0){
+		printf("Number of Grey-solid labels: %lu \n",NLABELS);
+		for (unsigned int idx=0; idx<NLABELS; idx++){
+			VALUE=LabelList[idx];
+			AFFINITY=AffinityList[idx];
+			printf("   grey-solid label=%d, grey-solid affinity=%f\n",VALUE,AFFINITY); 
+		}
+	}
+    
+    
+	ScaLBL_CopyToDevice(GreySolidGrad, GreySolidGrad_host, 3*Np*sizeof(double));
+	ScaLBL_DeviceBarrier();
+    delete [] SolidPotential_host;
+    delete [] GreySolidGrad_host;
+    delete [] Dst;
+}
+////----------------------------------------------------------------------------------------------------------//
+
+void ScaLBL_GreyscaleColorModel::AssignGreyPoroPermLabels()
+{
+
+	double *Porosity, *Permeability;
+	Porosity = new double[Np];
+	Permeability  = new double[Np];
+
+	size_t NLABELS=0;
+	signed char VALUE=0;
+	double POROSITY=1.f;//default: label 1 or 2, i.e. open nodes and porosity=1.0
+	double PERMEABILITY=1.f;
+
+	auto LabelList = greyscaleColor_db->getVector<int>( "GreySolidLabels" );
+	auto PorosityList = greyscaleColor_db->getVector<double>( "PorosityList" );
+	auto PermeabilityList = greyscaleColor_db->getVector<double>( "PermeabilityList" );
+
+	NLABELS=LabelList.size();
+	if (LabelList.size() != PorosityList.size()){
+		ERROR("Error: GreySolidLabels and PorosityList must be the same length! \n");
+	}
+
+	double label_count[NLABELS];
+	double label_count_global[NLABELS];
+	// Assign the labels
+
+	for (int idx=0; idx<NLABELS; idx++) label_count[idx]=0;
+
+	for (int k=0;k<Nz;k++){
+		for (int j=0;j<Ny;j++){
+			for (int i=0;i<Nx;i++){
+				int n = k*Nx*Ny+j*Nx+i;
+				VALUE=id[n];
+                POROSITY=1.f;//default: label 1 or 2, i.e. open nodes and porosity=1.0
+				// Assign the affinity from the paired list
+				for (unsigned int idx=0; idx < NLABELS; idx++){
+				      //printf("idx=%i, value=%i, %i, \n",idx, VALUE,LabelList[idx]);
+					if (VALUE == LabelList[idx]){
+						POROSITY=PorosityList[idx];
+						label_count[idx] += 1.0;
+						idx = NLABELS;
+						//Mask->id[n] = 0; // set mask to zero since this is an immobile component
+					}
+				}
+				int idx = Map(i,j,k);
+				if (!(idx < 0)){
+                    if (POROSITY<=0.0){
+                        ERROR("Error: Porosity for grey voxels must be 0.0 < Porosity <= 1.0 !\n");
+                    }
+                    else{
+					    Porosity[idx] = POROSITY;
+                    }
+                }
+			}
+		}
+	}
+
+	if (NLABELS != PermeabilityList.size()){
+		ERROR("Error: GreySolidLabels and PermeabilityList must be the same length! \n");
+	}
+	for (int k=0;k<Nz;k++){
+		for (int j=0;j<Ny;j++){
+			for (int i=0;i<Nx;i++){
+				int n = k*Nx*Ny+j*Nx+i;
+				VALUE=id[n];
+                PERMEABILITY=1.f;
+				// Assign the affinity from the paired list
+				for (unsigned int idx=0; idx < NLABELS; idx++){
+					//printf("idx=%i, value=%i, %i, \n",idx, VALUE,LabelList[idx]);
+					if (VALUE == LabelList[idx]){
+						PERMEABILITY=PermeabilityList[idx];
+						idx = NLABELS;
+						//Mask->id[n] = 0; // set mask to zero since this is an immobile component
+					}
+				}
+				int idx = Map(i,j,k);
+				if (!(idx < 0)){
+                    if (PERMEABILITY<=0.0){
+                        ERROR("Error: Permeability for grey voxel must be > 0.0 ! \n");
+                    }
+                    else{
+					    Permeability[idx] = PERMEABILITY/Dm->voxel_length/Dm->voxel_length;
+                    }
+                }
+			}
+		}
+	}
+
+
+	// Set Dm to match Mask
+	for (int i=0; i<Nx*Ny*Nz; i++) Dm->id[i] = Mask->id[i]; 
+	
+	for (int idx=0; idx<NLABELS; idx++)		label_count_global[idx]=sumReduce( Dm->Comm, label_count[idx]);
+
+    //Initialize a weighted porosity after considering grey voxels
+    GreyPorosity=0.0;
+	for (unsigned int idx=0; idx<NLABELS; idx++){
+		double volume_fraction  = double(label_count_global[idx])/double((Nx-2)*(Ny-2)*(Nz-2)*nprocs);
+        GreyPorosity+=volume_fraction*PorosityList[idx];
+    }
+
+	if (rank==0){
+        printf("Image resolution: %.5g [um/voxel]\n",Dm->voxel_length);
+		printf("Number of Grey-fluid labels: %lu \n",NLABELS);
+		for (unsigned int idx=0; idx<NLABELS; idx++){
+			VALUE=LabelList[idx];
+			POROSITY=PorosityList[idx];
+			PERMEABILITY=PermeabilityList[idx];
+			double volume_fraction  = double(label_count_global[idx])/double((Nx-2)*(Ny-2)*(Nz-2)*nprocs);
+			printf("   grey-fluid label=%d, porosity=%.3g, permeability=%.3g [um^2] (=%.3g [voxel^2]), volume fraction=%.3g\n",
+                    VALUE,POROSITY,PERMEABILITY,PERMEABILITY/Dm->voxel_length/Dm->voxel_length,volume_fraction); 
+            printf("                        effective porosity=%.3g\n",volume_fraction*POROSITY);
+		}
+        printf("The weighted porosity, considering both open and grey voxels, is %.3g\n",GreyPorosity);
+	}
+
+	ScaLBL_CopyToDevice(Porosity_dvc, Porosity, Np*sizeof(double));
+	ScaLBL_CopyToDevice(Permeability_dvc, Permeability, Np*sizeof(double));
+	ScaLBL_DeviceBarrier();
+    delete [] Porosity;
+    delete [] Permeability;
+}
+
+void ScaLBL_GreyscaleColorModel::Create(){
+	/*
+	 *  This function creates the variables needed to run a LBM 
+	 */
+	//.........................................................
+	// don't perform computations at the eight corners
+	//id[0] = id[Nx-1] = id[(Ny-1)*Nx] = id[(Ny-1)*Nx + Nx-1] = 0;
+	//id[(Nz-1)*Nx*Ny] = id[(Nz-1)*Nx*Ny+Nx-1] = id[(Nz-1)*Nx*Ny+(Ny-1)*Nx] = id[(Nz-1)*Nx*Ny+(Ny-1)*Nx + Nx-1] = 0;
+
+	//.........................................................
+	// Initialize communication structures in averaging domain
+	for (int i=0; i<Nx*Ny*Nz; i++) Dm->id[i] = Mask->id[i];
+	Mask->CommInit();
+	Np=Mask->PoreCount();
+	//...........................................................................
+	if (rank==0)    printf ("Create ScaLBL_Communicator \n");
+	// Create a communicator for the device (will use optimized layout)
+	// ScaLBL_Communicator ScaLBL_Comm(Mask); // original
+	ScaLBL_Comm  = std::shared_ptr<ScaLBL_Communicator>(new ScaLBL_Communicator(Mask));
+	ScaLBL_Comm_Regular  = std::shared_ptr<ScaLBL_Communicator>(new ScaLBL_Communicator(Mask));
+
+	int Npad=(Np/16 + 2)*16;
+	if (rank==0)    printf ("Set up memory efficient layout, %i | %i | %i \n", Np, Npad, N);
+	Map.resize(Nx,Ny,Nz);       Map.fill(-2);
+	auto neighborList= new int[18*Npad];
+	Np = ScaLBL_Comm->MemoryOptimizedLayoutAA(Map,neighborList,Mask->id,Np);
+	MPI_Barrier(comm);
+
+	//...........................................................................
+	//                MAIN  VARIABLES ALLOCATED HERE
+	//...........................................................................
+	// LBM variables
+	if (rank==0)    printf ("Allocating distributions \n");
+	//......................device distributions.................................
+	dist_mem_size = Np*sizeof(double);
+	neighborSize=18*(Np*sizeof(int));
+	//...........................................................................
+	ScaLBL_AllocateDeviceMemory((void **) &NeighborList, neighborSize);
+	ScaLBL_AllocateDeviceMemory((void **) &dvcMap, sizeof(int)*Np);
+	ScaLBL_AllocateDeviceMemory((void **) &fq, 19*dist_mem_size);
+	ScaLBL_AllocateDeviceMemory((void **) &Aq, 7*dist_mem_size);
+	ScaLBL_AllocateDeviceMemory((void **) &Bq, 7*dist_mem_size);
+	ScaLBL_AllocateDeviceMemory((void **) &Den, 2*dist_mem_size);
+	ScaLBL_AllocateDeviceMemory((void **) &Phi, sizeof(double)*Nx*Ny*Nz);		
+	ScaLBL_AllocateDeviceMemory((void **) &Pressure, sizeof(double)*Np);
+	ScaLBL_AllocateDeviceMemory((void **) &Velocity, 3*sizeof(double)*Np);
+    if (greyMode==true){
+        //ScaLBL_AllocateDeviceMemory((void **) &GreySolidPhi, sizeof(double)*Nx*Ny*Nz);		
+        ScaLBL_AllocateDeviceMemory((void **) &GreySolidGrad, 3*sizeof(double)*Np);		
+        ScaLBL_AllocateDeviceMemory((void **) &Porosity_dvc, sizeof(double)*Np);
+        ScaLBL_AllocateDeviceMemory((void **) &Permeability_dvc, sizeof(double)*Np);
+    }
+	//ScaLBL_AllocateDeviceMemory((void **) &ColorGrad, 3*sizeof(double)*Np);
+	//...........................................................................
+	// Update GPU data structures
+	if (rank==0)	printf ("Setting up device map and neighbor list \n");
+	fflush(stdout);
+	int *TmpMap;
+	TmpMap=new int[Np];
+	for (int k=1; k<Nz-1; k++){
+		for (int j=1; j<Ny-1; j++){
+			for (int i=1; i<Nx-1; i++){
+				int idx=Map(i,j,k);
+				if (!(idx < 0))
+					TmpMap[idx] = k*Nx*Ny+j*Nx+i;
+			}
+		}
+	}
+	// check that TmpMap is valid
+	for (int idx=0; idx<ScaLBL_Comm->LastExterior(); idx++){
+		auto n = TmpMap[idx];
+		if (n > Nx*Ny*Nz){
+			printf("Bad value! idx=%i \n", n);
+			TmpMap[idx] = Nx*Ny*Nz-1;
+		}
+	}
+	for (int idx=ScaLBL_Comm->FirstInterior(); idx<ScaLBL_Comm->LastInterior(); idx++){
+		auto n = TmpMap[idx];
+		if ( n > Nx*Ny*Nz ){
+			printf("Bad value! idx=%i \n",n);
+			TmpMap[idx] = Nx*Ny*Nz-1;
+		}
+	}
+	ScaLBL_CopyToDevice(dvcMap, TmpMap, sizeof(int)*Np);
+	ScaLBL_DeviceBarrier();
+	delete [] TmpMap;
+	
+	// copy the neighbor list 
+	ScaLBL_CopyToDevice(NeighborList, neighborList, neighborSize);
+
+	// initialize phi based on PhaseLabel (include solid component labels)
+	AssignComponentLabels();//do open/black/grey nodes initialization
+    if (greyMode==true){
+        AssignGreySolidLabels();
+        AssignGreyPoroPermLabels(); 
+    }
+}        
+
+void ScaLBL_GreyscaleColorModel::Initialize(){
+	
+	if (rank==0)	printf ("Initializing distributions \n");
+	ScaLBL_D3Q19_Init(fq, Np);
+    //ScaLBL_D3Q19_GreyscaleColor_Init(fq, Porosity_dvc, Np);
+	/*
+	 * This function initializes model
+	 */
+	if (Restart == true){
+		if (rank==0){
+			printf("Reading restart file! \n");
+		}
+
+		// Read in the restart file to CPU buffers
+		int *TmpMap;
+		TmpMap = new int[Np];
+		
+		double *cPhi, *cDist, *cDen;
+		cPhi = new double[N];
+		cDen = new double[2*Np];
+		cDist = new double[19*Np];
+		ScaLBL_CopyToHost(TmpMap, dvcMap, Np*sizeof(int));
+        ScaLBL_CopyToHost(cPhi, Phi, N*sizeof(double));
+    	
+		ifstream File(LocalRestartFile,ios::binary);
+		int idx;
+		double value,va,vb;
+		for (int n=0; n<Np; n++){
+			File.read((char*) &va, sizeof(va));
+			File.read((char*) &vb, sizeof(vb));
+			cDen[n]    = va;
+			cDen[Np+n] = vb;
+		}
+		for (int n=0; n<Np; n++){
+			// Read the distributions
+			for (int q=0; q<19; q++){
+				File.read((char*) &value, sizeof(value));
+				cDist[q*Np+n] = value;
+			}
+		}
+		File.close();
+		
+		for (int n=0; n<ScaLBL_Comm->LastExterior(); n++){
+			va = cDen[n];
+			vb = cDen[Np + n];
+			value = (va-vb)/(va+vb);
+			idx = TmpMap[n];
+			if (!(idx < 0) && idx<N)
+				cPhi[idx] = value;
+		}
+		for (int n=ScaLBL_Comm->FirstInterior(); n<ScaLBL_Comm->LastInterior(); n++){
+		  va = cDen[n];
+		  vb = cDen[Np + n];
+		  	value = (va-vb)/(va+vb);
+		  	idx = TmpMap[n];
+		  	if (!(idx < 0) && idx<N)
+		  		cPhi[idx] = value;
+		}
+		
+		// Copy the restart data to the GPU
+		ScaLBL_CopyToDevice(Den,cDen,2*Np*sizeof(double));
+		ScaLBL_CopyToDevice(fq,cDist,19*Np*sizeof(double));
+		ScaLBL_CopyToDevice(Phi,cPhi,N*sizeof(double));
+		ScaLBL_DeviceBarrier();
+
+		MPI_Barrier(comm);
+	}
+
+	if (rank==0)	printf ("Initializing phase field \n");
+	ScaLBL_PhaseField_Init(dvcMap, Phi, Den, Aq, Bq, 0, ScaLBL_Comm->LastExterior(), Np);
+	ScaLBL_PhaseField_Init(dvcMap, Phi, Den, Aq, Bq, ScaLBL_Comm->FirstInterior(), ScaLBL_Comm->LastInterior(), Np);
+
+	// establish reservoirs for external bC
+	if (BoundaryCondition == 1 || BoundaryCondition == 2 ||  BoundaryCondition == 3 || BoundaryCondition == 4 ){
+		if (Dm->kproc()==0){
+			ScaLBL_SetSlice_z(Phi,1.0,Nx,Ny,Nz,0);
+			ScaLBL_SetSlice_z(Phi,1.0,Nx,Ny,Nz,1);
+			ScaLBL_SetSlice_z(Phi,1.0,Nx,Ny,Nz,2);
+		}
+		if (Dm->kproc() == nprocz-1){
+			ScaLBL_SetSlice_z(Phi,-1.0,Nx,Ny,Nz,Nz-1);
+			ScaLBL_SetSlice_z(Phi,-1.0,Nx,Ny,Nz,Nz-2);
+			ScaLBL_SetSlice_z(Phi,-1.0,Nx,Ny,Nz,Nz-3);
+		}
+	}
+	ScaLBL_CopyToHost(Averages->Phi.data(),Phi,N*sizeof(double));
+}
+
+void ScaLBL_GreyscaleColorModel::Run(){
+	int nprocs=nprocx*nprocy*nprocz;
+	const RankInfoStruct rank_info(rank,nprocx,nprocy,nprocz);
+	
+	int IMAGE_INDEX = 0;
+	int IMAGE_COUNT = 0;
+	std::vector<std::string> ImageList;
+	bool SET_CAPILLARY_NUMBER = false;
+	bool RESCALE_FORCE = false;
+	bool MORPH_ADAPT = false;
+	bool USE_MORPH = false;
+	bool USE_SEED = false;
+	bool USE_DIRECT = false;
+	bool USE_MORPHOPEN_OIL = false;
+	int MAX_MORPH_TIMESTEPS = 50000; // maximum number of LBM timesteps to spend in morphological adaptation routine
+	int MIN_STEADY_TIMESTEPS = 100000;
+	int MAX_STEADY_TIMESTEPS = 200000;
+	int RESCALE_FORCE_AFTER_TIMESTEP = 0;
+	int RAMP_TIMESTEPS = 0;//50000;		 // number of timesteps to run initially (to get a reasonable velocity field before other pieces kick in)
+	int CURRENT_MORPH_TIMESTEPS=0;   // counter for number of timesteps spent in  morphological adaptation routine (reset each time)
+	int CURRENT_STEADY_TIMESTEPS=0;   // counter for number of timesteps spent in  morphological adaptation routine (reset each time)
+	int morph_interval = 100000;
+	int analysis_interval = 1000; 	// number of timesteps in between in situ analysis 
+	int morph_timesteps = 0;
+	double morph_delta = 0.0;
+	double seed_water = 0.0;
+	double capillary_number = 0.0;
+	double tolerance = 0.01;
+	double Ca_previous = 0.f;
+	double initial_volume = 0.0;
+	double delta_volume = 0.0;
+	double delta_volume_target = 0.0;
+	
+	/* history for morphological algoirthm */
+	double KRA_MORPH_FACTOR=0.5;
+	double volA_prev = 0.0; 
+	double log_krA_prev = 1.0;
+	double log_krA_target = 1.0;
+	double log_krA = 1.0;
+	double slope_krA_volume = 0.0;
+	if (greyscaleColor_db->keyExists( "vol_A_previous" )){
+		volA_prev  = greyscaleColor_db->getScalar<double>( "vol_A_previous" );
+	}
+	if (greyscaleColor_db->keyExists( "log_krA_previous" )){
+		log_krA_prev  = greyscaleColor_db->getScalar<double>( "log_krA_previous" );
+	}
+	if (greyscaleColor_db->keyExists( "krA_morph_factor" )){
+		KRA_MORPH_FACTOR  = greyscaleColor_db->getScalar<double>( "krA_morph_factor" );
+	}
+	
+	/* defaults for simulation protocols */
+	auto protocol = greyscaleColor_db->getWithDefault<std::string>( "protocol", "none" );
+	if (protocol == "image sequence"){
+		// Get the list of images
+		USE_DIRECT = true;
+		ImageList = greyscaleColor_db->getVector<std::string>( "image_sequence");
+		IMAGE_INDEX = greyscaleColor_db->getWithDefault<int>( "image_index", 0 );
+		IMAGE_COUNT = ImageList.size();
+		morph_interval = 10000;
+		USE_MORPH = true;
+	}
+	else if (protocol == "seed water"){
+		morph_delta = -0.05;
+		seed_water = 0.01;
+		USE_SEED = true;
+		USE_MORPH = true;
+	}
+	else if (protocol == "open connected oil"){
+		morph_delta = -0.05;
+		USE_MORPH = true;
+		USE_MORPHOPEN_OIL = true;
+	}
+	else if (protocol == "shell aggregation"){
+		morph_delta = -0.05;
+		USE_MORPH = true;
+	}  
+	if (greyscaleColor_db->keyExists( "capillary_number" )){
+		capillary_number = greyscaleColor_db->getScalar<double>( "capillary_number" );
+		SET_CAPILLARY_NUMBER=true;
+	}
+	if (greyscaleColor_db->keyExists( "rescale_force_after_timestep" )){
+		RESCALE_FORCE_AFTER_TIMESTEP = greyscaleColor_db->getScalar<int>( "rescale_force_after_timestep" );
+		RESCALE_FORCE = true;
+	}
+	if (greyscaleColor_db->keyExists( "timestep" )){
+		timestep = greyscaleColor_db->getScalar<int>( "timestep" );
+	}
+	if (BoundaryCondition != 0 && BoundaryCondition != 5 && SET_CAPILLARY_NUMBER==true){
+		if (rank == 0) printf("WARINING: capillary number target only supported for BC = 0 or 5 \n");
+		SET_CAPILLARY_NUMBER=false;
+	}
+	if (analysis_db->keyExists( "seed_water" )){
+		seed_water = analysis_db->getScalar<double>( "seed_water" );
+		if (rank == 0) printf("Seed water in oil %f (seed_water) \n",seed_water);
+		USE_SEED = true;
+	}
+	if (analysis_db->keyExists( "morph_delta" )){
+		morph_delta = analysis_db->getScalar<double>( "morph_delta" );
+		if (rank == 0) printf("Target volume change %f (morph_delta) \n",morph_delta);
+	}
+	if (analysis_db->keyExists( "morph_interval" )){
+		morph_interval = analysis_db->getScalar<int>( "morph_interval" );
+		USE_MORPH = true;
+	}
+	if (analysis_db->keyExists( "use_morphopen_oil" )){
+		USE_MORPHOPEN_OIL = analysis_db->getScalar<bool>( "use_morphopen_oil" );
+		if (rank == 0 && USE_MORPHOPEN_OIL) printf("Volume change by morphological opening \n");
+		USE_MORPH = true;
+	}
+	if (analysis_db->keyExists( "tolerance" )){
+		tolerance = analysis_db->getScalar<double>( "tolerance" );
+	}
+	if (analysis_db->keyExists( "analysis_interval" )){
+		analysis_interval = analysis_db->getScalar<int>( "analysis_interval" );
+	}
+	if (analysis_db->keyExists( "min_steady_timesteps" )){
+		MIN_STEADY_TIMESTEPS = analysis_db->getScalar<int>( "min_steady_timesteps" );
+	}
+	if (analysis_db->keyExists( "max_steady_timesteps" )){
+		MAX_STEADY_TIMESTEPS = analysis_db->getScalar<int>( "max_steady_timesteps" );
+	}
+	if (analysis_db->keyExists( "max_morph_timesteps" )){
+		MAX_MORPH_TIMESTEPS = analysis_db->getScalar<int>( "max_morph_timesteps" );
+	}
+
+
+	if (rank==0){
+		printf("********************************************************\n");
+		if (protocol == "image sequence"){
+			printf("  using protocol = image sequence \n");
+			printf("     min_steady_timesteps = %i \n",MIN_STEADY_TIMESTEPS);
+			printf("     max_steady_timesteps = %i \n",MAX_STEADY_TIMESTEPS);
+			printf("     tolerance = %f \n",tolerance);
+			std::string first_image = ImageList[IMAGE_INDEX];
+			printf("     first image in sequence: %s ***\n", first_image.c_str());
+		}
+		else if (protocol == "seed water"){
+			printf("  using protocol =  seed water \n");
+			printf("     min_steady_timesteps = %i \n",MIN_STEADY_TIMESTEPS);
+			printf("     max_steady_timesteps = %i \n",MAX_STEADY_TIMESTEPS);
+			printf("     tolerance = %f \n",tolerance);
+			printf("     morph_delta = %f \n",morph_delta);
+			printf("     seed_water = %f \n",seed_water);
+		}
+		else if (protocol == "open connected oil"){
+			printf("  using protocol = open connected oil \n");
+			printf("     min_steady_timesteps = %i \n",MIN_STEADY_TIMESTEPS);
+			printf("     max_steady_timesteps = %i \n",MAX_STEADY_TIMESTEPS);
+			printf("     tolerance = %f \n",tolerance);
+			printf("     morph_delta = %f \n",morph_delta);
+		}
+		else if (protocol == "shell aggregation"){
+			printf("  using protocol = shell aggregation \n"); 
+			printf("     min_steady_timesteps = %i \n",MIN_STEADY_TIMESTEPS);
+			printf("     max_steady_timesteps = %i \n",MAX_STEADY_TIMESTEPS);
+			printf("     tolerance = %f \n",tolerance);
+			printf("     morph_delta = %f \n",morph_delta);
+		}  
+		printf("No. of timesteps: %i \n", timestepMax);
+		fflush(stdout);
+	}
+
+	//.......create and start timer............
+	double starttime,stoptime,cputime;
+	ScaLBL_DeviceBarrier();
+	MPI_Barrier(comm);
+	starttime = MPI_Wtime();
+	//.........................................
+
+	//************ MAIN ITERATION LOOP ***************************************/
+	PROFILE_START("Loop");
+    //std::shared_ptr<Database> analysis_db;
+	bool Regular = false;
+	auto current_db = db->cloneDatabase();
+	runAnalysis analysis( current_db, rank_info, ScaLBL_Comm, Dm, Np, Regular, Map );
+	//analysis.createThreads( analysis_method, 4 );
+	while (timestep < timestepMax ) {
+		//if ( rank==0 ) { printf("Running timestep %i (%i MB)\n",timestep+1,(int)(Utilities::getMemoryUsage()/1048576)); }
+		PROFILE_START("Update");
+		// *************ODD TIMESTEP*************
+		timestep++;
+		// Compute the Phase indicator field
+		// Read for Aq, Bq happens in this routine (requires communication)
+		ScaLBL_Comm->BiSendD3Q7AA(Aq,Bq); //READ FROM NORMAL
+		ScaLBL_D3Q7_AAodd_PhaseField(NeighborList, dvcMap, Aq, Bq, Den, Phi, ScaLBL_Comm->FirstInterior(), ScaLBL_Comm->LastInterior(), Np);
+		ScaLBL_Comm->BiRecvD3Q7AA(Aq,Bq); //WRITE INTO OPPOSITE
+		ScaLBL_DeviceBarrier();
+		ScaLBL_D3Q7_AAodd_PhaseField(NeighborList, dvcMap, Aq, Bq, Den, Phi, 0, ScaLBL_Comm->LastExterior(), Np);
+
+		// Perform the collision operation
+		ScaLBL_Comm->SendD3Q19AA(fq); //READ FROM NORMAL
+		if (BoundaryCondition > 0 && BoundaryCondition < 5){
+			ScaLBL_Comm->Color_BC_z(dvcMap, Phi, Den, inletA, inletB);
+			ScaLBL_Comm->Color_BC_Z(dvcMap, Phi, Den, outletA, outletB);
+		}
+		// Halo exchange for phase field
+		ScaLBL_Comm_Regular->SendHalo(Phi);
+        if (greyMode==true){
+            //Model-1&4
+            ScaLBL_D3Q19_AAodd_GreyscaleColor(NeighborList, dvcMap, fq, Aq, Bq, Den, Phi,GreySolidGrad,Porosity_dvc,Permeability_dvc,Velocity, 
+                    rhoA, rhoB, tauA, tauB,tauA_eff, tauB_eff, 
+                    alpha, beta, Fx, Fy, Fz, Nx, Nx*Ny, ScaLBL_Comm->FirstInterior(), ScaLBL_Comm->LastInterior(), Np);
+            ////Model-2&3
+            //ScaLBL_D3Q19_AAodd_GreyscaleColor(NeighborList, dvcMap, fq, Aq, Bq, Den, Phi,GreySolidPhi,Porosity_dvc,Permeability_dvc,Velocity, 
+            //        rhoA, rhoB, tauA, tauB,tauA_eff, tauB_eff, 
+            //        alpha, beta, Fx, Fy, Fz, Nx, Nx*Ny, ScaLBL_Comm->FirstInterior(), ScaLBL_Comm->LastInterior(), Np);
+        }
+        else{
+            ScaLBL_D3Q19_AAodd_Color(NeighborList, dvcMap, fq, Aq, Bq, Den, Phi, Velocity, rhoA, rhoB, tauA, tauB,
+                    alpha, beta, Fx, Fy, Fz, Nx, Nx*Ny, ScaLBL_Comm->FirstInterior(), ScaLBL_Comm->LastInterior(), Np);
+        }
+		ScaLBL_Comm_Regular->RecvHalo(Phi);
+		ScaLBL_Comm->RecvD3Q19AA(fq); //WRITE INTO OPPOSITE
+		ScaLBL_DeviceBarrier();
+		// Set BCs
+		if (BoundaryCondition == 3){
+			ScaLBL_Comm->D3Q19_Pressure_BC_z(NeighborList, fq, din, timestep);
+			ScaLBL_Comm->D3Q19_Pressure_BC_Z(NeighborList, fq, dout, timestep);
+		}
+		if (BoundaryCondition == 4){
+			din = ScaLBL_Comm->D3Q19_Flux_BC_z(NeighborList, fq, flux, timestep);
+			ScaLBL_Comm->D3Q19_Pressure_BC_Z(NeighborList, fq, dout, timestep);
+		}
+		else if (BoundaryCondition == 5){
+			ScaLBL_Comm->D3Q19_Reflection_BC_z(fq);
+			ScaLBL_Comm->D3Q19_Reflection_BC_Z(fq);
+		}
+        if (greyMode==true){
+            //Model-1&4
+            ScaLBL_D3Q19_AAodd_GreyscaleColor(NeighborList, dvcMap, fq, Aq, Bq, Den, Phi,GreySolidGrad,Porosity_dvc,Permeability_dvc,Velocity,
+                    rhoA, rhoB, tauA, tauB,tauA_eff, tauB_eff,
+                    alpha, beta, Fx, Fy, Fz, Nx, Nx*Ny, 0, ScaLBL_Comm->LastExterior(), Np);
+            ////Model-2&3
+            //ScaLBL_D3Q19_AAodd_GreyscaleColor(NeighborList, dvcMap, fq, Aq, Bq, Den, Phi,GreySolidPhi,Porosity_dvc,Permeability_dvc,Velocity,
+            //        rhoA, rhoB, tauA, tauB,tauA_eff, tauB_eff,
+            //        alpha, beta, Fx, Fy, Fz, Nx, Nx*Ny, 0, ScaLBL_Comm->LastExterior(), Np);
+        }
+        else{
+            ScaLBL_D3Q19_AAodd_Color(NeighborList, dvcMap, fq, Aq, Bq, Den, Phi, Velocity, rhoA, rhoB, tauA, tauB,
+                    alpha, beta, Fx, Fy, Fz, Nx, Nx*Ny, 0, ScaLBL_Comm->LastExterior(), Np);
+        }
+		ScaLBL_DeviceBarrier(); 
+		MPI_Barrier(ScaLBL_Comm->MPI_COMM_SCALBL);
+
+		// *************EVEN TIMESTEP*************
+		timestep++;
+		// Compute the Phase indicator field
+		ScaLBL_Comm->BiSendD3Q7AA(Aq,Bq); //READ FROM NORMAL
+		ScaLBL_D3Q7_AAeven_PhaseField(dvcMap, Aq, Bq, Den, Phi, ScaLBL_Comm->FirstInterior(), ScaLBL_Comm->LastInterior(), Np);
+		ScaLBL_Comm->BiRecvD3Q7AA(Aq,Bq); //WRITE INTO OPPOSITE
+		ScaLBL_DeviceBarrier();
+		ScaLBL_D3Q7_AAeven_PhaseField(dvcMap, Aq, Bq, Den, Phi, 0, ScaLBL_Comm->LastExterior(), Np);
+
+		// Perform the collision operation
+		ScaLBL_Comm->SendD3Q19AA(fq); //READ FORM NORMAL
+		// Halo exchange for phase field
+		if (BoundaryCondition > 0 && BoundaryCondition < 5){
+			ScaLBL_Comm->Color_BC_z(dvcMap, Phi, Den, inletA, inletB);
+			ScaLBL_Comm->Color_BC_Z(dvcMap, Phi, Den, outletA, outletB);
+		}
+		ScaLBL_Comm_Regular->SendHalo(Phi);
+        if (greyMode==true){
+            //Model-1&4
+            ScaLBL_D3Q19_AAeven_GreyscaleColor(dvcMap, fq, Aq, Bq, Den, Phi,GreySolidGrad,Porosity_dvc,Permeability_dvc,Velocity, 
+                    rhoA, rhoB, tauA, tauB,tauA_eff, tauB_eff,
+                    alpha, beta, Fx, Fy, Fz,  Nx, Nx*Ny, ScaLBL_Comm->FirstInterior(), ScaLBL_Comm->LastInterior(), Np);
+            ////Model-2&3
+            //ScaLBL_D3Q19_AAeven_GreyscaleColor(dvcMap, fq, Aq, Bq, Den, Phi,GreySolidPhi,Porosity_dvc,Permeability_dvc,Velocity, 
+            //        rhoA, rhoB, tauA, tauB,tauA_eff, tauB_eff,
+            //        alpha, beta, Fx, Fy, Fz,  Nx, Nx*Ny, ScaLBL_Comm->FirstInterior(), ScaLBL_Comm->LastInterior(), Np);
+        }
+        else{
+            ScaLBL_D3Q19_AAeven_Color(dvcMap, fq, Aq, Bq, Den, Phi, Velocity, rhoA, rhoB, tauA, tauB,
+                    alpha, beta, Fx, Fy, Fz,  Nx, Nx*Ny, ScaLBL_Comm->FirstInterior(), ScaLBL_Comm->LastInterior(), Np);
+        }
+		ScaLBL_Comm_Regular->RecvHalo(Phi);
+		ScaLBL_Comm->RecvD3Q19AA(fq); //WRITE INTO OPPOSITE
+		ScaLBL_DeviceBarrier();
+		// Set boundary conditions
+		if (BoundaryCondition == 3){
+			ScaLBL_Comm->D3Q19_Pressure_BC_z(NeighborList, fq, din, timestep);
+			ScaLBL_Comm->D3Q19_Pressure_BC_Z(NeighborList, fq, dout, timestep);
+		}
+		else if (BoundaryCondition == 4){
+			din = ScaLBL_Comm->D3Q19_Flux_BC_z(NeighborList, fq, flux, timestep);
+			ScaLBL_Comm->D3Q19_Pressure_BC_Z(NeighborList, fq, dout, timestep);
+		}
+		else if (BoundaryCondition == 5){
+			ScaLBL_Comm->D3Q19_Reflection_BC_z(fq);
+			ScaLBL_Comm->D3Q19_Reflection_BC_Z(fq);
+		}
+        if (greyMode==true){
+            //Model-1&4
+            ScaLBL_D3Q19_AAeven_GreyscaleColor(dvcMap, fq, Aq, Bq, Den, Phi,GreySolidGrad,Porosity_dvc,Permeability_dvc,Velocity,
+                    rhoA, rhoB, tauA, tauB,tauA_eff, tauB_eff,
+                    alpha, beta, Fx, Fy, Fz, Nx, Nx*Ny, 0, ScaLBL_Comm->LastExterior(), Np);
+            ////Model-2&3
+            //ScaLBL_D3Q19_AAeven_GreyscaleColor(dvcMap, fq, Aq, Bq, Den, Phi,GreySolidPhi,Porosity_dvc,Permeability_dvc,Velocity,
+            //        rhoA, rhoB, tauA, tauB,tauA_eff, tauB_eff,
+            //        alpha, beta, Fx, Fy, Fz, Nx, Nx*Ny, 0, ScaLBL_Comm->LastExterior(), Np);
+        }
+        else{
+            ScaLBL_D3Q19_AAeven_Color(dvcMap, fq, Aq, Bq, Den, Phi, Velocity, rhoA, rhoB, tauA, tauB,
+                    alpha, beta, Fx, Fy, Fz, Nx, Nx*Ny, 0, ScaLBL_Comm->LastExterior(), Np);
+        }
+		ScaLBL_DeviceBarrier(); 
+		MPI_Barrier(ScaLBL_Comm->MPI_COMM_SCALBL);
+		//************************************************************************
+		PROFILE_STOP("Update");
+
+		if (rank==0 && timestep%analysis_interval == 0 && BoundaryCondition == 4){
+			printf("%i %f \n",timestep,din);
+		}
+		// Run the analysis
+		analysis.basic(timestep, current_db, *Averages, Phi, Pressure, Velocity, fq, Den );
+
+		// allow initial ramp-up to get closer to steady state
+		if (timestep > RAMP_TIMESTEPS && timestep%analysis_interval == 0 && USE_MORPH){
+			analysis.finish();
+			CURRENT_STEADY_TIMESTEPS += analysis_interval;
+
+			double volB = Averages->gwb.V; 
+			double volA = Averages->gnb.V; 
+			volA /= Dm->Volume;
+			volB /= Dm->Volume;;
+			//initial_volume = volA*Dm->Volume;
+			double vA_x = Averages->gnb.Px/Averages->gnb.M; 
+			double vA_y = Averages->gnb.Py/Averages->gnb.M; 
+			double vA_z = Averages->gnb.Pz/Averages->gnb.M; 
+			double vB_x = Averages->gwb.Px/Averages->gwb.M; 
+			double vB_y = Averages->gwb.Py/Averages->gwb.M; 
+			double vB_z = Averages->gwb.Pz/Averages->gwb.M;
+			double muA = rhoA*(tauA-0.5)/3.f; 
+			double muB = rhoB*(tauB-0.5)/3.f;				
+			double force_mag = sqrt(Fx*Fx+Fy*Fy+Fz*Fz);
+			double dir_x = Fx/force_mag;
+			double dir_y = Fy/force_mag;
+			double dir_z = Fz/force_mag;
+			if (force_mag == 0.0){
+				// default to z direction
+				dir_x = 0.0;
+				dir_y = 0.0;
+				dir_z = 1.0;
+				force_mag = 1.0;
+			}
+			double current_saturation = volB/(volA+volB);
+			double flow_rate_A = volA*(vA_x*dir_x + vA_y*dir_y + vA_z*dir_z);
+			double flow_rate_B = volB*(vB_x*dir_x + vB_y*dir_y + vB_z*dir_z);
+			double Ca = fabs(muA*flow_rate_A + muB*flow_rate_B)/(5.796*alpha);
+			
+			if ( morph_timesteps > morph_interval ){
+				
+				bool isSteady = false;
+				if ( (fabs((Ca - Ca_previous)/Ca) < tolerance &&  CURRENT_STEADY_TIMESTEPS > MIN_STEADY_TIMESTEPS))
+					isSteady = true;
+				if (CURRENT_STEADY_TIMESTEPS > MAX_STEADY_TIMESTEPS)
+					isSteady = true;
+				if (RESCALE_FORCE == true && SET_CAPILLARY_NUMBER == true && CURRENT_STEADY_TIMESTEPS > RESCALE_FORCE_AFTER_TIMESTEP){
+				  RESCALE_FORCE = false;
+				  double RESCALE_FORCE_FACTOR = capillary_number / Ca;
+				  if (RESCALE_FORCE_FACTOR > 2.0) RESCALE_FORCE_FACTOR = 2.0;
+				  if (RESCALE_FORCE_FACTOR < 0.5) RESCALE_FORCE_FACTOR = 0.5;
+				  Fx *= RESCALE_FORCE_FACTOR;
+				  Fy *= RESCALE_FORCE_FACTOR;
+				  Fz *= RESCALE_FORCE_FACTOR;
+				  force_mag = sqrt(Fx*Fx+Fy*Fy+Fz*Fz);
+				  if (force_mag > 1e-3){
+				    Fx *= 1e-3/force_mag;   // impose ceiling for stability
+				    Fy *= 1e-3/force_mag;   
+				    Fz *= 1e-3/force_mag;   
+				  }
+				  if (rank == 0) printf("    -- adjust force by factor %f \n ",capillary_number / Ca);
+				  Averages->SetParams(rhoA,rhoB,tauA,tauB,Fx,Fy,Fz,alpha,beta);
+				  greyscaleColor_db->putVector<double>("F",{Fx,Fy,Fz});
+				}
+				if ( isSteady ){
+					MORPH_ADAPT = true;
+					CURRENT_MORPH_TIMESTEPS=0;
+					delta_volume_target = Dm->Volume*volA *morph_delta; // set target volume change
+					//****** ENDPOINT ADAPTATION ********/
+					double krA_TMP= fabs(muA*flow_rate_A / force_mag);
+					double krB_TMP= fabs(muB*flow_rate_B / force_mag);
+					log_krA = log(krA_TMP);
+					if (krA_TMP < 0.0){
+						// cannot do endpoint adaptation if kr is negative
+						log_krA = log_krA_prev;
+					}
+					else if (krA_TMP < krB_TMP && morph_delta > 0.0){
+						/** morphological target based on relative permeability for A **/
+						log_krA_target = log(KRA_MORPH_FACTOR*(krA_TMP));
+						slope_krA_volume = (log_krA - log_krA_prev)/(Dm->Volume*(volA - volA_prev));
+						delta_volume_target=min(delta_volume_target,Dm->Volume*(volA+(log_krA_target - log_krA)/slope_krA_volume));
+						if (rank==0){
+							printf("    Enabling endpoint adaptation: krA = %f, krB = %f \n",krA_TMP,krB_TMP);	
+							printf("    log(kr)=%f, volume=%f, TARGET log(kr)=%f, volume change=%f \n",log_krA, volA, log_krA_target, delta_volume_target/(volA*Dm->Volume));							
+						}
+					}
+					log_krA_prev = log_krA;
+					volA_prev = volA;
+					//******************************** **/
+					/**  compute averages & write data **/
+					Averages->Full();
+					Averages->Write(timestep);
+					analysis.WriteVisData(timestep, current_db, *Averages, Phi, Pressure, Velocity, fq, Den );
+					analysis.finish();
+					
+					if (rank==0){
+						printf("** WRITE STEADY POINT *** ");
+						printf("Ca = %f, (previous = %f) \n",Ca,Ca_previous);
+						double h = Dm->voxel_length;		
+						// pressures
+						double pA = Averages->gnb.p;
+						double pB = Averages->gwb.p;
+						double pAc = Averages->gnc.p;
+						double pBc = Averages->gwc.p;
+						double pAB = (pA-pB)/(h*6.0*alpha);
+						double pAB_connected = (pAc-pBc)/(h*6.0*alpha);
+						// connected contribution
+						double Vol_nc = Averages->gnc.V/Dm->Volume;
+						double Vol_wc = Averages->gwc.V/Dm->Volume;
+						double Vol_nd = Averages->gnd.V/Dm->Volume;
+						double Vol_wd = Averages->gwd.V/Dm->Volume;
+						double Mass_n = Averages->gnc.M + Averages->gnd.M;
+						double Mass_w = Averages->gwc.M + Averages->gwd.M;
+						double vAc_x = Averages->gnc.Px/Mass_n; 
+						double vAc_y = Averages->gnc.Py/Mass_n; 
+						double vAc_z = Averages->gnc.Pz/Mass_n; 
+						double vBc_x = Averages->gwc.Px/Mass_w; 
+						double vBc_y = Averages->gwc.Py/Mass_w; 
+						double vBc_z = Averages->gwc.Pz/Mass_w;
+						// disconnected contribution
+						double vAd_x = Averages->gnd.Px/Mass_n; 
+						double vAd_y = Averages->gnd.Py/Mass_n; 
+						double vAd_z = Averages->gnd.Pz/Mass_n; 
+						double vBd_x = Averages->gwd.Px/Mass_w; 
+						double vBd_y = Averages->gwd.Py/Mass_w; 
+						double vBd_z = Averages->gwd.Pz/Mass_w;
+						
+						double flow_rate_A_connected = Vol_nc*(vAc_x*dir_x + vAc_y*dir_y + vAc_z*dir_z);
+						double flow_rate_B_connected = Vol_wc*(vBc_x*dir_x + vBc_y*dir_y + vBc_z*dir_z);
+						double flow_rate_A_disconnected = (Vol_nd)*(vAd_x*dir_x + vAd_y*dir_y + vAd_z*dir_z);
+						double flow_rate_B_disconnected = (Vol_wd)*(vBd_x*dir_x + vBd_y*dir_y + vBd_z*dir_z);
+						
+						double kAeff_connected = h*h*muA*flow_rate_A_connected/(force_mag);
+						double kBeff_connected = h*h*muB*flow_rate_B_connected/(force_mag);
+						
+						double kAeff_disconnected = h*h*muA*flow_rate_A_disconnected/(force_mag);
+						double kBeff_disconnected = h*h*muB*flow_rate_B_disconnected/(force_mag);
+
+						double kAeff = h*h*muA*(flow_rate_A)/(force_mag);
+						double kBeff = h*h*muB*(flow_rate_B)/(force_mag);
+
+						double viscous_pressure_drop = (rhoA*volA + rhoB*volB)*force_mag;
+						double Mobility = muA/muB;
+						
+						bool WriteHeader=false;
+						FILE * kr_log_file = fopen("relperm.csv","r");
+						if (kr_log_file != NULL)
+							fclose(kr_log_file);
+						else
+							WriteHeader=true;
+						kr_log_file = fopen("relperm.csv","a");
+						if (WriteHeader)
+							fprintf(kr_log_file,"timesteps sat.water eff.perm.oil eff.perm.water eff.perm.oil.connected eff.perm.water.connected eff.perm.oil.disconnected eff.perm.water.disconnected cap.pressure cap.pressure.connected pressure.drop Ca M\n");
+
+						fprintf(kr_log_file,"%i %.5g %.5g %.5g %.5g %.5g %.5g %.5g %.5g %.5g %.5g %.5g %.5g\n",CURRENT_STEADY_TIMESTEPS,current_saturation,kAeff,kBeff,kAeff_connected,kBeff_connected,kAeff_disconnected,kBeff_disconnected,pAB,pAB_connected,viscous_pressure_drop,Ca,Mobility);
+						fclose(kr_log_file);
+
+						printf("  Measured capillary number %f \n ",Ca);
+					}
+					if (SET_CAPILLARY_NUMBER ){
+						Fx *= capillary_number / Ca;
+						Fy *= capillary_number / Ca;
+						Fz *= capillary_number / Ca;
+						if (force_mag > 1e-3){
+							Fx *= 1e-3/force_mag;   // impose ceiling for stability
+							Fy *= 1e-3/force_mag;   
+							Fz *= 1e-3/force_mag;   
+						}
+						if (rank == 0) printf("    -- adjust force by factor %f \n ",capillary_number / Ca);
+						Averages->SetParams(rhoA,rhoB,tauA,tauB,Fx,Fy,Fz,alpha,beta);
+						greyscaleColor_db->putVector<double>("F",{Fx,Fy,Fz});
+					}
+					
+					CURRENT_STEADY_TIMESTEPS = 0;
+				}
+				else{
+					if (rank==0){
+						printf("** Continue to simulate steady *** \n ");
+						printf("Ca = %f, (previous = %f) \n",Ca,Ca_previous);
+					}
+				}
+				morph_timesteps=0;
+				Ca_previous = Ca;
+			}
+
+			if (MORPH_ADAPT ){
+				CURRENT_MORPH_TIMESTEPS += analysis_interval;
+				if (USE_DIRECT){
+					// Use image sequence
+					IMAGE_INDEX++;
+					MORPH_ADAPT = false;
+					if (IMAGE_INDEX < IMAGE_COUNT){
+						std::string next_image = ImageList[IMAGE_INDEX];
+						if (rank==0) printf("***Loading next image in sequence (%i) ***\n",IMAGE_INDEX);
+						greyscaleColor_db->putScalar<int>("image_index",IMAGE_INDEX);
+						ImageInit(next_image);
+					}
+					else{
+						if (rank==0) printf("Finished simulating image sequence \n");
+						timestep = timestepMax;
+					}
+				}
+				else if (USE_SEED){
+					delta_volume = volA*Dm->Volume - initial_volume;
+					CURRENT_MORPH_TIMESTEPS += analysis_interval;
+					double massChange = SeedPhaseField(seed_water);
+					if (rank==0) printf("***Seed water in oil %f, volume change %f / %f ***\n", massChange, delta_volume, delta_volume_target);
+				}
+				else if (USE_MORPHOPEN_OIL){
+					delta_volume = volA*Dm->Volume - initial_volume;
+					if (rank==0) printf("***Morphological opening of connected oil, target volume change %f ***\n", delta_volume_target);
+					MorphOpenConnected(delta_volume_target);
+				}
+				else {
+					if (rank==0) printf("***Shell aggregation, target volume change %f ***\n", delta_volume_target);
+					//double delta_volume_target = volB - (volA + volB)*TARGET_SATURATION; // change in volume to A
+					delta_volume += MorphInit(beta,delta_volume_target-delta_volume);
+				}
+
+				if ( (delta_volume - delta_volume_target)/delta_volume_target > 0.0 ){
+					MORPH_ADAPT = false;
+					CURRENT_STEADY_TIMESTEPS=0;
+					initial_volume = volA*Dm->Volume;
+					delta_volume = 0.0;
+					if (RESCALE_FORCE_AFTER_TIMESTEP > 0)
+						RESCALE_FORCE = true;
+				}
+				else if (!(USE_DIRECT) && CURRENT_MORPH_TIMESTEPS > MAX_MORPH_TIMESTEPS) {
+					MORPH_ADAPT = false;
+					CURRENT_STEADY_TIMESTEPS=0;
+					initial_volume = volA*Dm->Volume;
+					delta_volume = 0.0;
+					RESCALE_FORCE = true;
+					if (RESCALE_FORCE_AFTER_TIMESTEP > 0)
+						RESCALE_FORCE = true;
+				}
+			}
+			morph_timesteps += analysis_interval;
+		}
+		MPI_Barrier(ScaLBL_Comm->MPI_COMM_SCALBL);
+	}
+	analysis.finish();
+	PROFILE_STOP("Loop");
+	PROFILE_SAVE("lbpm_color_simulator",1);
+	//************************************************************************
+	ScaLBL_DeviceBarrier();
+	MPI_Barrier(ScaLBL_Comm->MPI_COMM_SCALBL);
+	stoptime = MPI_Wtime();
+	if (rank==0) printf("-------------------------------------------------------------------\n");
+	// Compute the walltime per timestep
+	cputime = (stoptime - starttime)/timestep;
+	// Performance obtained from each node
+	double MLUPS = double(Np)/cputime/1000000;
+
+	if (rank==0) printf("********************************************************\n");
+	if (rank==0) printf("CPU time = %f \n", cputime);
+	if (rank==0) printf("Lattice update rate (per core)= %f MLUPS \n", MLUPS);
+	MLUPS *= nprocs;
+	if (rank==0) printf("Lattice update rate (total)= %f MLUPS \n", MLUPS);
+	if (rank==0) printf("********************************************************\n");
+
+	// ************************************************************************
+}
+
+double ScaLBL_GreyscaleColorModel::ImageInit(std::string Filename){
+	
+	if (rank==0) printf("Re-initializing fluids from file: %s \n", Filename.c_str());
+	Mask->Decomp(Filename);
+	for (int i=0; i<Nx*Ny*Nz; i++) id[i] = Mask->id[i];  // save what was read
+	for (int i=0; i<Nx*Ny*Nz; i++) Dm->id[i] = Mask->id[i];  // save what was read
+
+	AssignComponentLabels();
+
+	double Count = 0.0;
+	double PoreCount = 0.0;
+	for (int k=1; k<Nz-1; k++){
+		for (int j=1; j<Ny-1; j++){
+			for (int i=1; i<Nx-1; i++){
+				if (id[Nx*Ny*k+Nx*j+i] == 2){
+					PoreCount++;
+					Count++;
+				}
+				else if (id[Nx*Ny*k+Nx*j+i] == 1){
+					PoreCount++;						
+				}
+			}
+		}
+	}
+
+	Count=sumReduce( Dm->Comm, Count);
+	PoreCount=sumReduce( Dm->Comm, PoreCount);
+	
+	if (rank==0) printf("   new saturation: %f (%f / %f) \n", Count / PoreCount, Count, PoreCount);
+	
+	ScaLBL_D3Q19_Init(fq, Np);
+	ScaLBL_PhaseField_Init(dvcMap, Phi, Den, Aq, Bq, 0, ScaLBL_Comm->LastExterior(), Np);
+	ScaLBL_PhaseField_Init(dvcMap, Phi, Den, Aq, Bq, ScaLBL_Comm->FirstInterior(), ScaLBL_Comm->LastInterior(), Np);
+	MPI_Barrier(ScaLBL_Comm->MPI_COMM_SCALBL);
+	
+	ScaLBL_CopyToHost(Averages->Phi.data(),Phi,Nx*Ny*Nz*sizeof(double));
+
+	double saturation = Count/PoreCount;
+	return saturation;
+
+}
+
+double ScaLBL_GreyscaleColorModel::MorphOpenConnected(double target_volume_change){
+	
+	int nx = Nx;
+	int ny = Ny;
+	int nz = Nz;
+	int n;
+	int N = nx*ny*nz;
+	double volume_change=0.0;
+	
+	if (target_volume_change < 0.0){
+		Array<char> id_solid(nx,ny,nz);
+		Array<int> phase_label(nx,ny,nz);
+		DoubleArray distance(Nx,Ny,Nz);
+		DoubleArray phase(nx,ny,nz);
+		signed char *id_connected;
+		id_connected = new signed char [nx*ny*nz];
+
+		ScaLBL_CopyToHost(phase.data(), Phi, N*sizeof(double));
+
+		// Extract only the connected part of NWP
+		BlobIDstruct new_index;
+		double vF=0.0; double vS=0.0;
+		ComputeGlobalBlobIDs(nx-2,ny-2,nz-2,Dm->rank_info,phase,Averages->SDs,vF,vS,phase_label,Dm->Comm);
+		MPI_Barrier(Dm->Comm);
+
+		long long count_connected=0;
+		long long count_porespace=0;
+		long long count_water=0;
+		for (int k=1; k<nz-1; k++){
+			for (int j=1; j<ny-1; j++){
+				for (int i=1; i<nx-1; i++){
+					n=k*nx*ny+j*nx+i;
+					// only apply opening to connected component 
+					if ( phase_label(i,j,k) == 0){
+						count_connected++;
+					}
+					if (id[n] > 0){
+						count_porespace++;
+					}
+					if (id[n] == 2){
+						count_water++;
+					}
+				}
+			}
+		}
+		count_connected=sumReduce( Dm->Comm, count_connected);
+		count_porespace=sumReduce( Dm->Comm, count_porespace);
+		count_water=sumReduce( Dm->Comm, count_water);
+
+		for (int k=0; k<nz; k++){
+			for (int j=0; j<ny; j++){
+				for (int i=0; i<nx; i++){
+					n=k*nx*ny+j*nx+i;
+					// only apply opening to connected component 
+					if ( phase_label(i,j,k) == 0){
+						id_solid(i,j,k) = 1;
+						id_connected[n] = 2;
+						id[n] = 2;
+						/* delete the connected component */
+						phase(i,j,k) = -1.0;
+					}
+					else{
+						id_solid(i,j,k) = 0;
+						id_connected[n] = 0;
+					}
+				}
+			}
+		}
+		CalcDist(distance,id_solid,*Dm);
+
+		signed char water=2;
+		signed char notwater=1;
+		double SW=-(target_volume_change)/count_connected;
+		MorphOpen(distance, id_connected, Dm, SW, water, notwater);
+		
+		for (int k=0; k<nz; k++){
+			for (int j=0; j<ny; j++){
+				for (int i=0; i<nx; i++){
+					n=k*nx*ny+j*nx+i;
+					// only apply opening to connected component 
+					if ( id_connected[n] == 1){
+						id_solid(i,j,k) = 0;
+					}
+					else{
+						id_solid(i,j,k) = 1;
+					}
+				}
+			}
+		}
+		CalcDist(distance,id_solid,*Dm);
+		
+		// re-initialize
+		double beta = 0.95;
+		for (int k=0; k<nz; k++){
+			for (int j=0; j<ny; j++){
+				for (int i=0; i<nx; i++){
+					n=k*nx*ny+j*nx+i;
+					double d = distance(i,j,k);
+					if (Averages->SDs(i,j,k) > 0.f){
+						if (d < 3.f){
+							phase(i,j,k) = (2.f*(exp(-2.f*beta*d))/(1.f+exp(-2.f*beta*d))-1.f);	
+						}
+					}
+				} 
+			}
+		}
+		
+		int count_morphopen=0.0;
+		for (int k=1; k<nz-1; k++){
+			for (int j=1; j<ny-1; j++){
+				for (int i=1; i<nx-1; i++){
+					n=k*nx*ny+j*nx+i;
+					// only apply opening to connected component 
+					if ( id_connected[n] == 1){
+						count_morphopen++;
+					}
+				}
+			}
+		}
+		count_morphopen=sumReduce( Dm->Comm, count_morphopen);
+		volume_change = double(count_morphopen - count_connected);
+		
+		if (rank==0)  printf("   opening of connected oil %f \n",volume_change/count_connected);
+
+		ScaLBL_CopyToDevice(Phi,phase.data(),N*sizeof(double));
+		ScaLBL_PhaseField_Init(dvcMap, Phi, Den, Aq, Bq, 0, ScaLBL_Comm->LastExterior(), Np);
+		ScaLBL_PhaseField_Init(dvcMap, Phi, Den, Aq, Bq, ScaLBL_Comm->FirstInterior(), ScaLBL_Comm->LastInterior(), Np);
+		if (BoundaryCondition == 1 || BoundaryCondition == 2 || BoundaryCondition == 3 || BoundaryCondition == 4){
+			if (Dm->kproc()==0){
+				ScaLBL_SetSlice_z(Phi,1.0,Nx,Ny,Nz,0);
+				ScaLBL_SetSlice_z(Phi,1.0,Nx,Ny,Nz,1);
+				ScaLBL_SetSlice_z(Phi,1.0,Nx,Ny,Nz,2);
+			}
+			if (Dm->kproc() == nprocz-1){
+				ScaLBL_SetSlice_z(Phi,-1.0,Nx,Ny,Nz,Nz-1);
+				ScaLBL_SetSlice_z(Phi,-1.0,Nx,Ny,Nz,Nz-2);
+				ScaLBL_SetSlice_z(Phi,-1.0,Nx,Ny,Nz,Nz-3);
+			}
+		}
+	}
+	return(volume_change);
+}
+double ScaLBL_GreyscaleColorModel::SeedPhaseField(const double seed_water_in_oil){
+  srand(time(NULL));
+  double mass_loss =0.f;
+  double count =0.f;
+  double *Aq_tmp, *Bq_tmp;
+  
+  Aq_tmp = new double [7*Np];
+  Bq_tmp = new double [7*Np];
+
+  ScaLBL_CopyToHost(Aq_tmp, Aq, 7*Np*sizeof(double));
+  ScaLBL_CopyToHost(Bq_tmp, Bq, 7*Np*sizeof(double));
+  
+ 
+   for (int n=0; n < ScaLBL_Comm->LastExterior(); n++){
+    double random_value = seed_water_in_oil*double(rand())/ RAND_MAX;
+    double dA = Aq_tmp[n] + Aq_tmp[n+Np]  + Aq_tmp[n+2*Np] + Aq_tmp[n+3*Np] + Aq_tmp[n+4*Np] + Aq_tmp[n+5*Np] + Aq_tmp[n+6*Np];
+    double dB = Bq_tmp[n] + Bq_tmp[n+Np]  + Bq_tmp[n+2*Np] + Bq_tmp[n+3*Np] + Bq_tmp[n+4*Np] + Bq_tmp[n+5*Np] + Bq_tmp[n+6*Np];
+    double phase_id = (dA - dB) / (dA + dB);
+    if (phase_id > 0.0){
+      Aq_tmp[n] -= 0.3333333333333333*random_value;
+      Aq_tmp[n+Np] -= 0.1111111111111111*random_value;
+      Aq_tmp[n+2*Np] -= 0.1111111111111111*random_value;
+      Aq_tmp[n+3*Np] -= 0.1111111111111111*random_value;
+      Aq_tmp[n+4*Np] -= 0.1111111111111111*random_value;
+      Aq_tmp[n+5*Np] -= 0.1111111111111111*random_value;
+      Aq_tmp[n+6*Np] -= 0.1111111111111111*random_value;
+      
+      Bq_tmp[n] += 0.3333333333333333*random_value;
+      Bq_tmp[n+Np] += 0.1111111111111111*random_value;
+      Bq_tmp[n+2*Np] += 0.1111111111111111*random_value;
+      Bq_tmp[n+3*Np] += 0.1111111111111111*random_value;
+      Bq_tmp[n+4*Np] += 0.1111111111111111*random_value;
+      Bq_tmp[n+5*Np] += 0.1111111111111111*random_value;
+      Bq_tmp[n+6*Np] += 0.1111111111111111*random_value;
+    }
+    mass_loss += random_value*seed_water_in_oil;
+  }
+
+  for (int n=ScaLBL_Comm->FirstInterior(); n < ScaLBL_Comm->LastInterior(); n++){
+    double random_value = seed_water_in_oil*double(rand())/ RAND_MAX;
+    double dA = Aq_tmp[n] + Aq_tmp[n+Np]  + Aq_tmp[n+2*Np] + Aq_tmp[n+3*Np] + Aq_tmp[n+4*Np] + Aq_tmp[n+5*Np] + Aq_tmp[n+6*Np];
+    double dB = Bq_tmp[n] + Bq_tmp[n+Np]  + Bq_tmp[n+2*Np] + Bq_tmp[n+3*Np] + Bq_tmp[n+4*Np] + Bq_tmp[n+5*Np] + Bq_tmp[n+6*Np];
+    double phase_id = (dA - dB) / (dA + dB);
+    if (phase_id > 0.0){
+      Aq_tmp[n] -= 0.3333333333333333*random_value;
+      Aq_tmp[n+Np] -= 0.1111111111111111*random_value;
+      Aq_tmp[n+2*Np] -= 0.1111111111111111*random_value;
+      Aq_tmp[n+3*Np] -= 0.1111111111111111*random_value;
+      Aq_tmp[n+4*Np] -= 0.1111111111111111*random_value;
+      Aq_tmp[n+5*Np] -= 0.1111111111111111*random_value;
+      Aq_tmp[n+6*Np] -= 0.1111111111111111*random_value;
+      
+      Bq_tmp[n] += 0.3333333333333333*random_value;
+      Bq_tmp[n+Np] += 0.1111111111111111*random_value;
+      Bq_tmp[n+2*Np] += 0.1111111111111111*random_value;
+      Bq_tmp[n+3*Np] += 0.1111111111111111*random_value;
+      Bq_tmp[n+4*Np] += 0.1111111111111111*random_value;
+      Bq_tmp[n+5*Np] += 0.1111111111111111*random_value;
+      Bq_tmp[n+6*Np] += 0.1111111111111111*random_value;
+    }
+    mass_loss += random_value*seed_water_in_oil;
+  }
+
+  count= sumReduce( Dm->Comm, count);
+  mass_loss= sumReduce( Dm->Comm, mass_loss);
+  if (rank == 0) printf("Remove mass %f from %f voxels \n",mass_loss,count);
+
+  // Need to initialize Aq, Bq, Den, Phi directly
+  //ScaLBL_CopyToDevice(Phi,phase.data(),7*Np*sizeof(double));
+  ScaLBL_CopyToDevice(Aq, Aq_tmp, 7*Np*sizeof(double));
+  ScaLBL_CopyToDevice(Bq, Bq_tmp, 7*Np*sizeof(double));
+
+  return(mass_loss);
+}
+
+double ScaLBL_GreyscaleColorModel::MorphInit(const double beta, const double target_delta_volume){
+	const RankInfoStruct rank_info(rank,nprocx,nprocy,nprocz);
+
+	double vF = 0.f;
+	double vS = 0.f;
+	double delta_volume;
+	double WallFactor = 0.0;
+	bool USE_CONNECTED_NWP = false;
+
+	DoubleArray phase(Nx,Ny,Nz);
+	IntArray phase_label(Nx,Ny,Nz);;
+	DoubleArray phase_distance(Nx,Ny,Nz);
+	Array<char> phase_id(Nx,Ny,Nz);
+	fillHalo<double> fillDouble(Dm->Comm,Dm->rank_info,{Nx-2,Ny-2,Nz-2},{1,1,1},0,1);
+	
+
+	// Basic algorithm to 
+	// 1. Copy phase field to CPU
+	ScaLBL_CopyToHost(phase.data(), Phi, N*sizeof(double));
+
+	double count = 0.f;
+	for (int k=1; k<Nz-1; k++){
+		for (int j=1; j<Ny-1; j++){
+			for (int i=1; i<Nx-1; i++){
+				if (phase(i,j,k) > 0.f && Averages->SDs(i,j,k) > 0.f) count+=1.f;
+			}
+		}
+	}
+	double volume_initial = sumReduce( Dm->Comm, count);
+	/*
+	sprintf(LocalRankFilename,"phi_initial.%05i.raw",rank);
+	FILE *INPUT = fopen(LocalRankFilename,"wb");
+	fwrite(phase.data(),8,N,INPUT);
+	fclose(INPUT);
+	*/
+	// 2. Identify connected components of phase field -> phase_label
+	
+	double volume_connected = 0.0;
+       	double second_biggest = 0.0;
+	if (USE_CONNECTED_NWP){
+		BlobIDstruct new_index;
+		ComputeGlobalBlobIDs(Nx-2,Ny-2,Nz-2,rank_info,phase,Averages->SDs,vF,vS,phase_label,comm);
+		MPI_Barrier(Dm->Comm);
+
+		// only operate on component "0"
+		count = 0.0;
+
+		for (int k=0; k<Nz; k++){
+			for (int j=0; j<Ny; j++){
+				for (int i=0; i<Nx; i++){
+					int label = phase_label(i,j,k);
+					if (label == 0 ){
+						phase_id(i,j,k) = 0;
+						count += 1.0;
+					}
+					else 		
+						phase_id(i,j,k) = 1;
+					if (label == 1 ){
+						second_biggest += 1.0;
+					}
+				}
+			}
+		}	
+		volume_connected = sumReduce( Dm->Comm, count);
+		second_biggest = sumReduce( Dm->Comm, second_biggest);
+	}
+	else {
+		// use the whole NWP 
+		for (int k=0; k<Nz; k++){
+			for (int j=0; j<Ny; j++){
+				for (int i=0; i<Nx; i++){
+					if (Averages->SDs(i,j,k) > 0.f){
+						if (phase(i,j,k) > 0.f ){
+							phase_id(i,j,k) = 0;
+						}
+						else {
+							phase_id(i,j,k) = 1;
+						}
+					}
+					else {
+						phase_id(i,j,k) = 1;
+					}
+				}
+			}
+		}
+	}
+
+	/*int reach_x, reach_y, reach_z;
+	for (int k=0; k<Nz; k++){
+		for (int j=0; j<Ny; j++){
+			for (int i=0; i<Nx; i++){
+			}
+		}
+	}*/
+
+	// 3. Generate a distance map to the largest object -> phase_distance
+	CalcDist(phase_distance,phase_id,*Dm);
+
+	double temp,value;
+	double factor=0.5/beta;
+	for (int k=0; k<Nz; k++){
+		for (int j=0; j<Ny; j++){
+			for (int i=0; i<Nx; i++){
+				if (phase_distance(i,j,k) < 3.f ){
+					value = phase(i,j,k);
+					if (value > 1.f)   value=1.f;
+					if (value < -1.f)  value=-1.f;
+					// temp -- distance based on analytical form McClure, Prins et al, Comp. Phys. Comm.
+					temp = -factor*log((1.0+value)/(1.0-value));
+					/// use this approximation close to the object
+					if (fabs(value) < 0.8 && Averages->SDs(i,j,k) > 1.f ){
+						phase_distance(i,j,k) = temp;
+					}
+					// erase the original object
+					phase(i,j,k) = -1.0;
+				}
+			}
+		}
+	}
+
+	if (USE_CONNECTED_NWP){
+	if (volume_connected - second_biggest < 2.0*fabs(target_delta_volume) && target_delta_volume < 0.0){
+		// if connected volume is less than 2% just delete the whole thing
+		if (rank==0) printf("Connected region has shrunk! \n");
+		REVERSE_FLOW_DIRECTION = true;
+	}
+	
+/*	else{*/
+		if (rank==0) printf("Pathway volume / next largest ganglion %f \n",volume_connected/second_biggest );
+	}
+		if (rank==0) printf("MorphGrow with target volume fraction change %f \n", target_delta_volume/volume_initial);
+		double target_delta_volume_incremental = target_delta_volume;
+		if (fabs(target_delta_volume) > 0.01*volume_initial)  
+			target_delta_volume_incremental = 0.01*volume_initial*target_delta_volume/fabs(target_delta_volume);
+		delta_volume = MorphGrow(Averages->SDs,phase_distance,phase_id,Averages->Dm, target_delta_volume_incremental, WallFactor);
+
+		for (int k=0; k<Nz; k++){
+			for (int j=0; j<Ny; j++){
+				for (int i=0; i<Nx; i++){
+					if (phase_distance(i,j,k) < 0.0 ) phase_id(i,j,k) = 0;
+					else 		     				  phase_id(i,j,k) = 1;
+					//if (phase_distance(i,j,k) < 0.0 ) phase(i,j,k) = 1.0;
+				}
+			}
+		}	
+
+		CalcDist(phase_distance,phase_id,*Dm); // re-calculate distance
+
+		// 5. Update phase indicator field based on new distnace
+		for (int k=0; k<Nz; k++){
+			for (int j=0; j<Ny; j++){
+				for (int i=0; i<Nx; i++){
+					double d = phase_distance(i,j,k);
+					if (Averages->SDs(i,j,k) > 0.f){
+						if (d < 3.f){
+							//phase(i,j,k) = -1.0;
+							phase(i,j,k) = (2.f*(exp(-2.f*beta*d))/(1.f+exp(-2.f*beta*d))-1.f);	
+						}
+					}
+				} 
+			}
+		}
+		fillDouble.fill(phase);
+	//}
+
+	count = 0.f;
+	for (int k=1; k<Nz-1; k++){
+		for (int j=1; j<Ny-1; j++){
+			for (int i=1; i<Nx-1; i++){
+				if (phase(i,j,k) > 0.f && Averages->SDs(i,j,k) > 0.f){
+					count+=1.f;
+				}
+			}
+		}
+	}
+	double volume_final= sumReduce( Dm->Comm, count);
+
+	delta_volume = (volume_final-volume_initial);
+	if (rank == 0)  printf("MorphInit: change fluid volume fraction by %f \n", delta_volume/volume_initial);
+	if (rank == 0)  printf("   new saturation =  %f \n", volume_final/(0.238323*double((Nx-2)*(Ny-2)*(Nz-2)*nprocs)));
+
+	// 6. copy back to the device
+	//if (rank==0)  printf("MorphInit: copy data  back to device\n");
+	ScaLBL_CopyToDevice(Phi,phase.data(),N*sizeof(double));
+	/*
+	sprintf(LocalRankFilename,"dist_final.%05i.raw",rank);
+	FILE *DIST = fopen(LocalRankFilename,"wb");
+	fwrite(phase_distance.data(),8,N,DIST);
+	fclose(DIST);
+	
+	sprintf(LocalRankFilename,"phi_final.%05i.raw",rank);
+	FILE *PHI = fopen(LocalRankFilename,"wb");
+	fwrite(phase.data(),8,N,PHI);
+	fclose(PHI);
+	*/
+	// 7. Re-initialize phase field and density
+	ScaLBL_PhaseField_Init(dvcMap, Phi, Den, Aq, Bq, 0, ScaLBL_Comm->LastExterior(), Np);
+	ScaLBL_PhaseField_Init(dvcMap, Phi, Den, Aq, Bq, ScaLBL_Comm->FirstInterior(), ScaLBL_Comm->LastInterior(), Np);
+	if (BoundaryCondition == 1 || BoundaryCondition == 2 || BoundaryCondition == 3 || BoundaryCondition == 4){
+		if (Dm->kproc()==0){
+			ScaLBL_SetSlice_z(Phi,1.0,Nx,Ny,Nz,0);
+			ScaLBL_SetSlice_z(Phi,1.0,Nx,Ny,Nz,1);
+			ScaLBL_SetSlice_z(Phi,1.0,Nx,Ny,Nz,2);
+		}
+		if (Dm->kproc() == nprocz-1){
+			ScaLBL_SetSlice_z(Phi,-1.0,Nx,Ny,Nz,Nz-1);
+			ScaLBL_SetSlice_z(Phi,-1.0,Nx,Ny,Nz,Nz-2);
+			ScaLBL_SetSlice_z(Phi,-1.0,Nx,Ny,Nz,Nz-3);
+		}
+	}
+	return delta_volume;
+}
+
+void ScaLBL_GreyscaleColorModel::WriteDebug(){
+	// Copy back final phase indicator field and convert to regular layout
+	DoubleArray PhaseField(Nx,Ny,Nz);
+	//ScaLBL_Comm->RegularLayout(Map,Phi,PhaseField);
+	ScaLBL_CopyToHost(PhaseField.data(), Phi, sizeof(double)*N);
+
+	FILE *OUTFILE;
+	sprintf(LocalRankFilename,"Phase.%05i.raw",rank);
+	OUTFILE = fopen(LocalRankFilename,"wb");
+	fwrite(PhaseField.data(),8,N,OUTFILE);
+	fclose(OUTFILE);
+
+    ScaLBL_Comm->RegularLayout(Map,&Den[0],PhaseField);
+	FILE *AFILE;
+	sprintf(LocalRankFilename,"A.%05i.raw",rank);
+	AFILE = fopen(LocalRankFilename,"wb");
+	fwrite(PhaseField.data(),8,N,AFILE);
+	fclose(AFILE);
+
+	ScaLBL_Comm->RegularLayout(Map,&Den[Np],PhaseField);
+	FILE *BFILE;
+	sprintf(LocalRankFilename,"B.%05i.raw",rank);
+	BFILE = fopen(LocalRankFilename,"wb");
+	fwrite(PhaseField.data(),8,N,BFILE);
+	fclose(BFILE);
+
+	ScaLBL_Comm->RegularLayout(Map,Pressure,PhaseField);
+	FILE *PFILE;
+	sprintf(LocalRankFilename,"Pressure.%05i.raw",rank);
+	PFILE = fopen(LocalRankFilename,"wb");
+	fwrite(PhaseField.data(),8,N,PFILE);
+	fclose(PFILE);
+
+	ScaLBL_Comm->RegularLayout(Map,&Velocity[0],PhaseField);
+	FILE *VELX_FILE;
+	sprintf(LocalRankFilename,"Velocity_X.%05i.raw",rank);
+	VELX_FILE = fopen(LocalRankFilename,"wb");
+	fwrite(PhaseField.data(),8,N,VELX_FILE);
+	fclose(VELX_FILE);
+
+	ScaLBL_Comm->RegularLayout(Map,&Velocity[Np],PhaseField);
+	FILE *VELY_FILE;
+	sprintf(LocalRankFilename,"Velocity_Y.%05i.raw",rank);
+	VELY_FILE = fopen(LocalRankFilename,"wb");
+	fwrite(PhaseField.data(),8,N,VELY_FILE);
+	fclose(VELY_FILE);
+
+	ScaLBL_Comm->RegularLayout(Map,&Velocity[2*Np],PhaseField);
+	FILE *VELZ_FILE;
+	sprintf(LocalRankFilename,"Velocity_Z.%05i.raw",rank);
+	VELZ_FILE = fopen(LocalRankFilename,"wb");
+	fwrite(PhaseField.data(),8,N,VELZ_FILE);
+	fclose(VELZ_FILE);
+
+	ScaLBL_Comm->RegularLayout(Map,&Porosity_dvc[0],PhaseField);
+	FILE *POROS_FILE;
+	sprintf(LocalRankFilename,"Porosity.%05i.raw",rank);
+	POROS_FILE = fopen(LocalRankFilename,"wb");
+	fwrite(PhaseField.data(),8,N,POROS_FILE);
+	fclose(POROS_FILE);
+
+	ScaLBL_Comm->RegularLayout(Map,&Permeability_dvc[0],PhaseField);
+	FILE *PERM_FILE;
+	sprintf(LocalRankFilename,"Permeability.%05i.raw",rank);
+	PERM_FILE = fopen(LocalRankFilename,"wb");
+	fwrite(PhaseField.data(),8,N,PERM_FILE);
+	fclose(PERM_FILE);
+
+	ScaLBL_Comm->RegularLayout(Map,&GreySolidGrad[0],PhaseField);
+	FILE *GreySG_X_FILE;
+	sprintf(LocalRankFilename,"GreySolidGrad_X.%05i.raw",rank);
+	GreySG_X_FILE = fopen(LocalRankFilename,"wb");
+	fwrite(PhaseField.data(),8,N,GreySG_X_FILE);
+	fclose(GreySG_X_FILE);
+
+	ScaLBL_Comm->RegularLayout(Map,&GreySolidGrad[Np],PhaseField);
+	FILE *GreySG_Y_FILE;
+	sprintf(LocalRankFilename,"GreySolidGrad_Y.%05i.raw",rank);
+	GreySG_Y_FILE = fopen(LocalRankFilename,"wb");
+	fwrite(PhaseField.data(),8,N,GreySG_Y_FILE);
+	fclose(GreySG_Y_FILE);
+
+	ScaLBL_Comm->RegularLayout(Map,&GreySolidGrad[2*Np],PhaseField);
+	FILE *GreySG_Z_FILE;
+	sprintf(LocalRankFilename,"GreySolidGrad_Z.%05i.raw",rank);
+	GreySG_Z_FILE = fopen(LocalRankFilename,"wb");
+	fwrite(PhaseField.data(),8,N,GreySG_Z_FILE);
+	fclose(GreySG_Z_FILE);
+
+/*	ScaLBL_Comm->RegularLayout(Map,&ColorGrad[0],PhaseField);
+	FILE *CGX_FILE;
+	sprintf(LocalRankFilename,"Gradient_X.%05i.raw",rank);
+	CGX_FILE = fopen(LocalRankFilename,"wb");
+	fwrite(PhaseField.data(),8,N,CGX_FILE);
+	fclose(CGX_FILE);
+
+	ScaLBL_Comm->RegularLayout(Map,&ColorGrad[Np],PhaseField);
+	FILE *CGY_FILE;
+	sprintf(LocalRankFilename,"Gradient_Y.%05i.raw",rank);
+	CGY_FILE = fopen(LocalRankFilename,"wb");
+	fwrite(PhaseField.data(),8,N,CGY_FILE);
+	fclose(CGY_FILE);
+
+	ScaLBL_Comm->RegularLayout(Map,&ColorGrad[2*Np],PhaseField);
+	FILE *CGZ_FILE;
+	sprintf(LocalRankFilename,"Gradient_Z.%05i.raw",rank);
+	CGZ_FILE = fopen(LocalRankFilename,"wb");
+	fwrite(PhaseField.data(),8,N,CGZ_FILE);
+	fclose(CGZ_FILE);
+*/
+}
+
+//void ScaLBL_GreyscaleColorModel::AssignGreySolidLabels()//Model-1
+//{
+//    // ONLY initialize grey nodes
+//    // Key input parameters:
+//    // 1. GreySolidLabels
+//    //    labels for grey nodes
+//    // 2. GreySolidAffinity
+//    //    affinity ranges [-1,1]
+//    //    oil-wet > 0
+//    //    water-wet < 0
+//    //    neutral = 0 
+//    double *SolidPotential_host = new double [Nx*Ny*Nz];
+//	double *GreySolidGrad_host  = new double [3*Np];
+//
+//	size_t NLABELS=0;
+//	signed char VALUE=0;
+//	double AFFINITY=0.f;
+//
+//	auto LabelList = greyscaleColor_db->getVector<int>( "GreySolidLabels" );
+//	auto AffinityList = greyscaleColor_db->getVector<double>( "GreySolidAffinity" );
+//
+//	NLABELS=LabelList.size();
+//	if (NLABELS != AffinityList.size()){
+//		ERROR("Error: GreySolidLabels and GreySolidAffinity must be the same length! \n");
+//	}
+//
+//	for (int k=0;k<Nz;k++){
+//		for (int j=0;j<Ny;j++){
+//			for (int i=0;i<Nx;i++){
+//				int n = k*Nx*Ny+j*Nx+i;
+//				VALUE=id[n];
+//	            AFFINITY=0.f;//all nodes except the specified grey nodes have grey-solid affinity = 0.0
+//				// Assign the affinity from the paired list
+//				for (unsigned int idx=0; idx < NLABELS; idx++){
+//				      //printf("idx=%i, value=%i, %i, \n",idx, VALUE,LabelList[idx]);
+//					if (VALUE == LabelList[idx]){
+//						AFFINITY=AffinityList[idx];
+//						idx = NLABELS;
+//						//Mask->id[n] = 0; // set mask to zero since this is an immobile component
+//					}
+//				}
+//				SolidPotential_host[n] = AFFINITY;
+//			}
+//		}
+//	}
+//
+//    // Calculate grey-solid color-gradient
+//	double *Dst;
+//	Dst = new double [3*3*3];
+//	for (int kk=0; kk<3; kk++){
+//		for (int jj=0; jj<3; jj++){
+//			for (int ii=0; ii<3; ii++){
+//				int index = kk*9+jj*3+ii;
+//				Dst[index] = sqrt(double(ii-1)*double(ii-1) + double(jj-1)*double(jj-1)+ double(kk-1)*double(kk-1));
+//			}
+//		}
+//	}
+//	double w_face = 1.f;
+//	double w_edge = 0.5;
+//	double w_corner = 0.f;
+//	//local 
+//	Dst[13] = 0.f;
+//	//faces
+//	Dst[4] = w_face;
+//	Dst[10] = w_face;
+//	Dst[12] = w_face;
+//	Dst[14] = w_face;
+//	Dst[16] = w_face;
+//	Dst[22] = w_face;
+//	// corners
+//	Dst[0] = w_corner;
+//	Dst[2] = w_corner;
+//	Dst[6] = w_corner;
+//	Dst[8] = w_corner;
+//	Dst[18] = w_corner;
+//	Dst[20] = w_corner;
+//	Dst[24] = w_corner;
+//	Dst[26] = w_corner;
+//	// edges
+//	Dst[1] = w_edge;
+//	Dst[3] = w_edge;
+//	Dst[5] = w_edge;
+//	Dst[7] = w_edge;
+//	Dst[9] = w_edge;
+//	Dst[11] = w_edge;
+//	Dst[15] = w_edge;
+//	Dst[17] = w_edge;
+//	Dst[19] = w_edge;
+//	Dst[21] = w_edge;
+//	Dst[23] = w_edge;
+//	Dst[25] = w_edge;
+//
+//	for (int k=1; k<Nz-1; k++){
+//		for (int j=1; j<Ny-1; j++){
+//			for (int i=1; i<Nx-1; i++){
+//				int idx=Map(i,j,k);
+//				if (!(idx < 0)){
+//					double phi_x = 0.f;
+//					double phi_y = 0.f;
+//					double phi_z = 0.f;
+//					for (int kk=0; kk<3; kk++){
+//						for (int jj=0; jj<3; jj++){
+//							for (int ii=0; ii<3; ii++){
+//
+//								int index = kk*9+jj*3+ii;
+//								double weight= Dst[index];
+//
+//								int idi=i+ii-1;
+//								int idj=j+jj-1;
+//								int idk=k+kk-1;
+//
+//								if (idi < 0) idi=0;
+//								if (idj < 0) idj=0;
+//								if (idk < 0) idk=0;
+//								if (!(idi < Nx)) idi=Nx-1;
+//								if (!(idj < Ny)) idj=Ny-1;
+//								if (!(idk < Nz)) idk=Nz-1;
+//
+//								int nn = idk*Nx*Ny + idj*Nx + idi;
+//								double vec_x = double(ii-1);
+//								double vec_y = double(jj-1);
+//								double vec_z = double(kk-1);
+//								double GWNS=SolidPotential_host[nn];
+//								phi_x += GWNS*weight*vec_x;
+//								phi_y += GWNS*weight*vec_y;
+//								phi_z += GWNS*weight*vec_z;
+//							}
+//						}
+//					}
+//					GreySolidGrad_host[idx+0*Np] = phi_x;
+//					GreySolidGrad_host[idx+1*Np] = phi_y;
+//					GreySolidGrad_host[idx+2*Np] = phi_z;
+//				}
+//			}
+//		}
+//	}
+//
+//	if (rank==0){
+//		printf("Number of Grey-solid labels: %lu \n",NLABELS);
+//		for (unsigned int idx=0; idx<NLABELS; idx++){
+//			VALUE=LabelList[idx];
+//			AFFINITY=AffinityList[idx];
+//			printf("   grey-solid label=%d, grey-solid affinity=%f\n",VALUE,AFFINITY); 
+//		}
+//	}
+//    
+//    
+//	ScaLBL_CopyToDevice(GreySolidGrad, GreySolidGrad_host, 3*Np*sizeof(double));
+//	ScaLBL_DeviceBarrier();
+//    delete [] SolidPotential_host;
+//    delete [] GreySolidGrad_host;
+//    delete [] Dst;
+//}
+////----------------------------------------------------------------------------------------------------------//
+
+
+//void ScaLBL_GreyscaleColorModel::AssignGreySolidLabels()//Model-2 & Model-3
+//{
+//    // ONLY initialize grey nodes
+//    // Key input parameters:
+//    // 1. GreySolidLabels
+//    //    labels for grey nodes
+//    // 2. GreySolidAffinity
+//    //    affinity ranges [-1,1]
+//    //    oil-wet > 0
+//    //    water-wet < 0
+//    //    neutral = 0 
+//
+//	double *GreySolidPhi_host  = new double [Nx*Ny*Nz];
+//	//initialize grey solid phase field
+//    for (int k=0;k<Nz;k++){
+//		for (int j=0;j<Ny;j++){
+//			for (int i=0;i<Nx;i++){
+//				int n = k*Nx*Ny+j*Nx+i;
+//                GreySolidPhi_host[n]=0.f;
+//            }
+//        }
+//    }
+//
+//	auto LabelList = greyscaleColor_db->getVector<int>( "GreySolidLabels" );
+//	auto AffinityList = greyscaleColor_db->getVector<double>( "GreySolidAffinity" );
+//
+//	size_t NLABELS=0;
+//	NLABELS=LabelList.size();
+//	if (NLABELS != AffinityList.size()){
+//		ERROR("Error: GreySolidLabels and GreySolidAffinity must be the same length! \n");
+//	}
+//
+//	double *Dst;
+//	Dst = new double [3*3*3];
+//	for (int kk=0; kk<3; kk++){
+//		for (int jj=0; jj<3; jj++){
+//			for (int ii=0; ii<3; ii++){
+//				int index = kk*9+jj*3+ii;
+//				Dst[index] = sqrt(double(ii-1)*double(ii-1) + double(jj-1)*double(jj-1)+ double(kk-1)*double(kk-1));
+//			}
+//		}
+//	}
+//	double w_face = 1.f;
+//	double w_edge = 1.f;
+//	double w_corner = 0.f;
+//	//local 
+//	Dst[13] = 0.f;
+//	//faces
+//	Dst[4] = w_face;
+//	Dst[10] = w_face;
+//	Dst[12] = w_face;
+//	Dst[14] = w_face;
+//	Dst[16] = w_face;
+//	Dst[22] = w_face;
+//	// corners
+//	Dst[0] = w_corner;
+//	Dst[2] = w_corner;
+//	Dst[6] = w_corner;
+//	Dst[8] = w_corner;
+//	Dst[18] = w_corner;
+//	Dst[20] = w_corner;
+//	Dst[24] = w_corner;
+//	Dst[26] = w_corner;
+//	// edges
+//	Dst[1] = w_edge;
+//	Dst[3] = w_edge;
+//	Dst[5] = w_edge;
+//	Dst[7] = w_edge;
+//	Dst[9] = w_edge;
+//	Dst[11] = w_edge;
+//	Dst[15] = w_edge;
+//	Dst[17] = w_edge;
+//	Dst[19] = w_edge;
+//	Dst[21] = w_edge;
+//	Dst[23] = w_edge;
+//	Dst[25] = w_edge;
+//
+//	for (int k=1; k<Nz-1; k++){
+//		for (int j=1; j<Ny-1; j++){
+//			for (int i=1; i<Nx-1; i++){
+//
+//                int n = k*Nx*Ny+j*Nx+i;
+//                signed char VALUE=Mask->id[n];
+//                double AFFINITY=0.f;
+//				// Assign the affinity from the paired list
+//				for (unsigned int idx=0; idx < NLABELS; idx++){
+//				      //printf("idx=%i, value=%i, %i, \n",idx, VALUE,LabelList[idx]);
+//					if (VALUE == LabelList[idx]){
+//						AFFINITY=AffinityList[idx];
+//						idx = NLABELS;
+//						//Mask->id[n] = 0; // set mask to zero since this is an immobile component
+//					}
+//				}
+//
+//                if (VALUE>2){//i.e. a grey node
+//                    double neighbor_counter = 0;
+//                    for (int kk=0; kk<3; kk++){
+//                        for (int jj=0; jj<3; jj++){
+//                            for (int ii=0; ii<3; ii++){
+//
+//                                int index = kk*9+jj*3+ii;
+//								double weight= Dst[index];
+//
+//                                int idi=i+ii-1;
+//                                int idj=j+jj-1;
+//                                int idk=k+kk-1;
+//
+//                                if (idi < 0) idi=0;
+//                                if (idj < 0) idj=0;
+//                                if (idk < 0) idk=0;
+//                                if (!(idi < Nx)) idi=Nx-1;
+//                                if (!(idj < Ny)) idj=Ny-1;
+//                                if (!(idk < Nz)) idk=Nz-1;
+//
+//                                int nn = idk*Nx*Ny + idj*Nx + idi;
+//								//if (Mask->id[nn] != VALUE){//Model-2:i.e. open nodes, impermeable solid nodes or any other type of greynodes
+//								if (Mask->id[nn] <=0){//Model-3:i.e. only impermeable solid nodes or any other type of greynodes
+//                                    neighbor_counter +=weight;
+//                                }
+//                            }
+//                        }
+//                    }
+//                    if (neighbor_counter>0){
+//                        GreySolidPhi_host[n] = AFFINITY;
+//                    }
+//                }
+//			}
+//		}
+//	}
+//
+//	if (rank==0){
+//		printf("Number of grey-solid labels: %lu \n",NLABELS);
+//		for (unsigned int idx=0; idx<NLABELS; idx++){
+//			signed char VALUE=LabelList[idx];
+//			double AFFINITY=AffinityList[idx];
+//			printf("   grey-solid label=%d, grey-solid affinity=%f\n",VALUE,AFFINITY); 
+//		}
+//	}
+//    
+//	ScaLBL_CopyToDevice(GreySolidPhi, GreySolidPhi_host, Nx*Ny*Nz*sizeof(double));
+//	ScaLBL_DeviceBarrier();
+//
+//    //debug
+//	//FILE *OUTFILE;
+//	//sprintf(LocalRankFilename,"GreySolidInit.%05i.raw",rank);
+//	//OUTFILE = fopen(LocalRankFilename,"wb");
+//	//fwrite(GreySolidPhi_host,8,N,OUTFILE);
+//	//fclose(OUTFILE);
+//
+//    delete [] GreySolidPhi_host;
+//    delete [] Dst;
+//}
+
+//--------- This is another old version of calculating greyscale-solid color-gradient modification-------//
+// **not working effectively, to be deprecated
+//void ScaLBL_GreyscaleColorModel::AssignGreySolidLabels()
+//{
+//    // ONLY initialize grey nodes
+//    // Key input parameters:
+//    // 1. GreySolidLabels
+//    //    labels for grey nodes
+//    // 2. GreySolidAffinity
+//    //    affinity ranges [-1,1]
+//    //    oil-wet > 0
+//    //    water-wet < 0
+//    //    neutral = 0 
+//
+//    //double *SolidPotential_host = new double [Nx*Ny*Nz];
+//	double *GreySolidPhi_host  = new double [Nx*Ny*Nz];
+//	signed char VALUE=0;
+//	double AFFINITY=0.f;
+//
+//	auto LabelList = greyscaleColor_db->getVector<int>( "GreySolidLabels" );
+//	auto AffinityList = greyscaleColor_db->getVector<double>( "GreySolidAffinity" );
+//
+//	size_t NLABELS=0;
+//	NLABELS=LabelList.size();
+//	if (NLABELS != AffinityList.size()){
+//		ERROR("Error: GreySolidLabels and GreySolidAffinity must be the same length! \n");
+//	}
+//
+//	for (int k=0;k<Nz;k++){
+//		for (int j=0;j<Ny;j++){
+//			for (int i=0;i<Nx;i++){
+//				int n = k*Nx*Ny+j*Nx+i;
+//				VALUE=id[n];
+//	            AFFINITY=0.f;//all nodes except the specified grey nodes have grey-solid affinity = 0.0
+//				// Assign the affinity from the paired list
+//				for (unsigned int idx=0; idx < NLABELS; idx++){
+//				      //printf("idx=%i, value=%i, %i, \n",idx, VALUE,LabelList[idx]);
+//					if (VALUE == LabelList[idx]){
+//						AFFINITY=AffinityList[idx];
+//						idx = NLABELS;
+//						//Mask->id[n] = 0; // set mask to zero since this is an immobile component
+//					}
+//				}
+//				GreySolidPhi_host[n] = AFFINITY;
+//			}
+//		}
+//	}
+//
+//	if (rank==0){
+//		printf("Number of grey-solid labels: %lu \n",NLABELS);
+//		for (unsigned int idx=0; idx<NLABELS; idx++){
+//			VALUE=LabelList[idx];
+//			AFFINITY=AffinityList[idx];
+//			printf("   grey-solid label=%d, solid-affinity=%f\n",VALUE,AFFINITY); 
+//		}
+//	}
+//    
+//	ScaLBL_CopyToDevice(GreySolidPhi, GreySolidPhi_host, Nx*Ny*Nz*sizeof(double));
+//	ScaLBL_DeviceBarrier();
+//
+//    //debug
+//	FILE *OUTFILE;
+//	sprintf(LocalRankFilename,"GreySolidInit.%05i.raw",rank);
+//	OUTFILE = fopen(LocalRankFilename,"wb");
+//	fwrite(GreySolidPhi_host,8,N,OUTFILE);
+//	fclose(OUTFILE);
+//
+//    //delete [] SolidPotential_host;
+//    delete [] GreySolidPhi_host;
+//}
+//----------------------------------------------------------------------------------------------------------//
diff --git a/models/GreyscaleColorModel.h b/models/GreyscaleColorModel.h
new file mode 100644
index 00000000..d7dde941
--- /dev/null
+++ b/models/GreyscaleColorModel.h
@@ -0,0 +1,97 @@
+/*
+Implementation of two-fluid greyscale color lattice boltzmann model
+ */
+#include <stdio.h>
+#include <stdlib.h>
+#include <sys/stat.h>
+#include <iostream>
+#include <exception>
+#include <stdexcept>
+#include <fstream>
+
+#include "common/Communication.h"
+#include "analysis/TwoPhase.h"
+#include "analysis/runAnalysis.h"
+#include "common/MPI_Helpers.h"
+#include "ProfilerApp.h"
+#include "threadpool/thread_pool.h"
+
+class ScaLBL_GreyscaleColorModel{
+public:
+	ScaLBL_GreyscaleColorModel(int RANK, int NP, MPI_Comm COMM);
+	~ScaLBL_GreyscaleColorModel();	
+	
+	// functions in they should be run
+	void ReadParams(string filename);
+	void ReadParams(std::shared_ptr<Database> db0);
+	void SetDomain();
+	void ReadInput();
+	void Create();
+	void Initialize();
+	void Run();
+	void WriteDebug();
+	
+	bool Restart,pBC;
+	bool REVERSE_FLOW_DIRECTION;
+	int timestep,timestepMax;
+	int BoundaryCondition;
+	double tauA,tauB,rhoA,rhoB,alpha,beta;
+    double tauA_eff,tauB_eff;
+	double Fx,Fy,Fz,flux;
+	double din,dout,inletA,inletB,outletA,outletB;
+    double GreyPorosity;
+    bool greyMode;//run greyColor model if true
+	
+	int Nx,Ny,Nz,N,Np;
+	int rank,nprocx,nprocy,nprocz,nprocs;
+	double Lx,Ly,Lz;
+
+	std::shared_ptr<Domain> Dm;   // this domain is for analysis
+	std::shared_ptr<Domain> Mask; // this domain is for lbm
+	std::shared_ptr<ScaLBL_Communicator> ScaLBL_Comm;
+	std::shared_ptr<ScaLBL_Communicator> ScaLBL_Comm_Regular;
+    //std::shared_ptr<TwoPhase> Averages;
+    std::shared_ptr<SubPhase> Averages;
+    
+    // input database
+    std::shared_ptr<Database> db;
+    std::shared_ptr<Database> domain_db;
+    std::shared_ptr<Database> greyscaleColor_db;
+    std::shared_ptr<Database> analysis_db;
+    std::shared_ptr<Database> vis_db;
+
+    IntArray Map;
+    signed char *id;    
+	int *NeighborList;
+	int *dvcMap;
+	double *fq, *Aq, *Bq;
+	double *Den, *Phi;
+    //double *GreySolidPhi; //Model 2 & 3
+    double *GreySolidGrad;//Model 1 & 4
+	//double *ColorGrad;
+	double *Velocity;
+	double *Pressure;
+    double *Porosity_dvc;
+    double *Permeability_dvc;
+		
+private:
+	MPI_Comm comm;
+    
+	int dist_mem_size;
+	int neighborSize;
+	// filenames
+    char LocalRankString[8];
+    char LocalRankFilename[40];
+    char LocalRestartFile[40];
+   
+    //int rank,nprocs;
+    void LoadParams(std::shared_ptr<Database> db0);
+    void AssignComponentLabels();
+    void AssignGreySolidLabels();
+    void AssignGreyPoroPermLabels();
+    double ImageInit(std::string filename);
+    double MorphInit(const double beta, const double morph_delta);
+    double SeedPhaseField(const double seed_water_in_oil);
+    double MorphOpenConnected(double target_volume_change);
+};
+
diff --git a/models/GreyscaleModel.cpp b/models/GreyscaleModel.cpp
index 4966d618..39ee7554 100644
--- a/models/GreyscaleModel.cpp
+++ b/models/GreyscaleModel.cpp
@@ -58,7 +58,7 @@ void ScaLBL_GreyscaleModel::ReadParams(string filename){
 	din=dout=1.0;
 	flux=0.0;
     dp = 10.0; //unit of 'dp': voxel
-    CollisionType = 1; //1: IMRT; 2: BGK
+    CollisionType = 1; //1: IMRT; 2: BGK; 3: MRT
 	
 	// ---------------------- Greyscale Model parameters -----------------------//
 	if (greyscale_db->keyExists( "timestepMax" )){
@@ -98,6 +98,9 @@ void ScaLBL_GreyscaleModel::ReadParams(string filename){
 	if (collision == "BGK"){
         CollisionType=2;
 	}
+    else if (collision == "MRT"){
+        CollisionType=3;
+    }
 	// ------------------------------------------------------------------------//
     
     //------------------------ Other Domain parameters ------------------------//
@@ -213,9 +216,9 @@ void ScaLBL_GreyscaleModel::AssignComponentLabels(double *Porosity, double *Perm
 
 	for (int idx=0; idx<NLABELS; idx++) label_count[idx]=0;
 
-	for (int k=1;k<Nz-1;k++){
-		for (int j=1;j<Ny-1;j++){
-			for (int i=1;i<Nx-1;i++){
+	for (int k=0;k<Nz;k++){
+		for (int j=0;j<Ny;j++){
+			for (int i=0;i<Nx;i++){
 				int n = k*Nx*Ny+j*Nx+i;
 				VALUE=id[n];
 				// Assign the affinity from the paired list
@@ -244,9 +247,9 @@ void ScaLBL_GreyscaleModel::AssignComponentLabels(double *Porosity, double *Perm
 	if (NLABELS != PermeabilityList.size()){
 		ERROR("Error: ComponentLabels and PermeabilityList must be the same length! \n");
 	}
-	for (int k=1;k<Nz-1;k++){
-		for (int j=1;j<Ny-1;j++){
-			for (int i=1;i<Nx-1;i++){
+	for (int k=0;k<Nz;k++){
+		for (int j=0;j<Ny;j++){
+			for (int i=0;i<Nx;i++){
 				int n = k*Nx*Ny+j*Nx+i;
 				VALUE=id[n];
 				// Assign the affinity from the paired list
@@ -285,7 +288,7 @@ void ScaLBL_GreyscaleModel::AssignComponentLabels(double *Porosity, double *Perm
 
 	if (rank==0){
         printf("Image resolution: %.5g [um/voxel]\n",Dm->voxel_length);
-		printf("Component labels: %lu \n",NLABELS);
+		printf("Number of component labels: %lu \n",NLABELS);
 		for (unsigned int idx=0; idx<NLABELS; idx++){
 			VALUE=LabelList[idx];
 			POROSITY=PorosityList[idx];
@@ -337,7 +340,6 @@ void ScaLBL_GreyscaleModel::Create(){
 	neighborSize=18*(Np*sizeof(int));
 	//...........................................................................
 	ScaLBL_AllocateDeviceMemory((void **) &NeighborList, neighborSize);
-	ScaLBL_AllocateDeviceMemory((void **) &dvcMap, sizeof(int)*Np);
 	ScaLBL_AllocateDeviceMemory((void **) &fq, 19*dist_mem_size);
 	ScaLBL_AllocateDeviceMemory((void **) &Permeability, sizeof(double)*Np);		
 	ScaLBL_AllocateDeviceMemory((void **) &Porosity, sizeof(double)*Np);		
@@ -345,47 +347,19 @@ void ScaLBL_GreyscaleModel::Create(){
 	ScaLBL_AllocateDeviceMemory((void **) &Velocity, 3*sizeof(double)*Np);
 	//...........................................................................
 	// Update GPU data structures
-	if (rank==0)	printf ("Setting up device map and neighbor list \n");
+	if (rank==0)	printf ("Setting up device neighbor list \n");
 	fflush(stdout);
-	int *TmpMap;
-	TmpMap=new int[Np];
-	for (int k=1; k<Nz-1; k++){
-		for (int j=1; j<Ny-1; j++){
-			for (int i=1; i<Nx-1; i++){
-				int idx=Map(i,j,k);
-				if (!(idx < 0))
-					TmpMap[idx] = k*Nx*Ny+j*Nx+i;
-			}
-		}
-	}
-	// check that TmpMap is valid
-	for (int idx=0; idx<ScaLBL_Comm->LastExterior(); idx++){
-		int n = TmpMap[idx];
-		if (n > Nx*Ny*Nz){
-			printf("Bad value! idx=%i \n");
-			TmpMap[idx] = Nx*Ny*Nz-1;
-		}
-	}
-	for (int idx=ScaLBL_Comm->FirstInterior(); idx<ScaLBL_Comm->LastInterior(); idx++){
-		int n = TmpMap[idx];
-		if (n > Nx*Ny*Nz){
-			printf("Bad value! idx=%i \n");
-			TmpMap[idx] = Nx*Ny*Nz-1;
-		}
-	}
-	ScaLBL_CopyToDevice(dvcMap, TmpMap, sizeof(int)*Np);
-	ScaLBL_DeviceBarrier();
-	delete [] TmpMap;
-	
 	// copy the neighbor list 
 	ScaLBL_CopyToDevice(NeighborList, neighborList, neighborSize);
 	// initialize phi based on PhaseLabel (include solid component labels)
 	double *Poros, *Perm;
 	Poros = new double[Np];
-	Perm = new double[Np];
+	Perm  = new double[Np];
 	AssignComponentLabels(Poros,Perm);
 	ScaLBL_CopyToDevice(Porosity, Poros, Np*sizeof(double));
 	ScaLBL_CopyToDevice(Permeability, Perm, Np*sizeof(double));
+    delete [] Poros;
+    delete [] Perm;
 }        
 
 
@@ -402,6 +376,10 @@ void ScaLBL_GreyscaleModel::Initialize(){
 	    ScaLBL_D3Q19_Init(fq, Np);
         if (rank==0) printf("Collision model: BGK.\n");
     }
+    else if (CollisionType==3){
+	    ScaLBL_D3Q19_Init(fq, Np);
+        if (rank==0) printf("Collision model: MRT.\n");
+    }
     else{
         if (rank==0) printf("Unknown collison type! IMRT collision is used.\n"); 
 	    ScaLBL_D3Q19_GreyIMRT_Init(fq, Np, Den);
@@ -483,6 +461,9 @@ void ScaLBL_GreyscaleModel::Run(){
             case 2: 
                     ScaLBL_D3Q19_AAodd_Greyscale(NeighborList, fq,  ScaLBL_Comm->FirstInterior(), ScaLBL_Comm->LastInterior(), Np, rlx, rlx_eff, Fx, Fy, Fz,Porosity,Permeability,Velocity,Pressure_dvc);
                     break;
+            case 3: 
+                    ScaLBL_D3Q19_AAodd_Greyscale_MRT(NeighborList, fq,  ScaLBL_Comm->FirstInterior(), ScaLBL_Comm->LastInterior(), Np, rlx, rlx_eff, Fx, Fy, Fz,Porosity,Permeability,Velocity,Den,Pressure_dvc);
+                    break;
             default: 
                     ScaLBL_D3Q19_AAodd_Greyscale_IMRT(NeighborList, fq,  ScaLBL_Comm->FirstInterior(), ScaLBL_Comm->LastInterior(), Np, rlx, rlx_eff, Fx, Fy, Fz,Porosity,Permeability,Velocity,Den,Pressure_dvc);
                     break;
@@ -501,6 +482,9 @@ void ScaLBL_GreyscaleModel::Run(){
             case 2: 
 		            ScaLBL_D3Q19_AAodd_Greyscale(NeighborList, fq, 0, ScaLBL_Comm->LastExterior(), Np, rlx, rlx_eff, Fx, Fy, Fz,Porosity,Permeability,Velocity,Pressure_dvc);
                     break;
+            case 3: 
+		            ScaLBL_D3Q19_AAodd_Greyscale_MRT(NeighborList, fq, 0, ScaLBL_Comm->LastExterior(), Np, rlx, rlx_eff, Fx, Fy, Fz,Porosity,Permeability,Velocity,Den,Pressure_dvc);
+                    break;
             default: 
 		            ScaLBL_D3Q19_AAodd_Greyscale_IMRT(NeighborList, fq, 0, ScaLBL_Comm->LastExterior(), Np, rlx, rlx_eff, Fx, Fy, Fz,Porosity,Permeability,Velocity,Den,Pressure_dvc);
                     break;
@@ -517,6 +501,9 @@ void ScaLBL_GreyscaleModel::Run(){
             case 2: 
 		            ScaLBL_D3Q19_AAeven_Greyscale(fq, ScaLBL_Comm->FirstInterior(), ScaLBL_Comm->LastInterior(), Np, rlx, rlx_eff, Fx, Fy, Fz,Porosity,Permeability,Velocity,Pressure_dvc);
                     break;
+            case 3: 
+		            ScaLBL_D3Q19_AAeven_Greyscale_MRT(fq, ScaLBL_Comm->FirstInterior(), ScaLBL_Comm->LastInterior(), Np, rlx, rlx_eff, Fx, Fy, Fz,Porosity,Permeability,Velocity,Den,Pressure_dvc);
+                    break;
             default: 
 		            ScaLBL_D3Q19_AAeven_Greyscale_IMRT(fq, ScaLBL_Comm->FirstInterior(), ScaLBL_Comm->LastInterior(), Np, rlx, rlx_eff, Fx, Fy, Fz,Porosity,Permeability,Velocity,Den,Pressure_dvc);
                     break;
@@ -535,6 +522,9 @@ void ScaLBL_GreyscaleModel::Run(){
             case 2: 
 		            ScaLBL_D3Q19_AAeven_Greyscale(fq, 0, ScaLBL_Comm->LastExterior(), Np, rlx, rlx_eff, Fx, Fy, Fz,Porosity,Permeability,Velocity,Pressure_dvc);
                     break;
+            case 3: 
+		            ScaLBL_D3Q19_AAeven_Greyscale_MRT(fq, 0, ScaLBL_Comm->LastExterior(), Np, rlx, rlx_eff, Fx, Fy, Fz,Porosity,Permeability,Velocity,Den,Pressure_dvc);
+                    break;
             default: 
 		            ScaLBL_D3Q19_AAeven_Greyscale_IMRT(fq, 0, ScaLBL_Comm->LastExterior(), Np, rlx, rlx_eff, Fx, Fy, Fz,Porosity,Permeability,Velocity,Den,Pressure_dvc);
                     break;
@@ -608,11 +598,6 @@ void ScaLBL_GreyscaleModel::Run(){
 					}
 				}
 			}
-			//MPI_Allreduce(&vax_loc,&vax,1,MPI_DOUBLE,MPI_SUM,Mask->Comm);
-			//MPI_Allreduce(&vay_loc,&vay,1,MPI_DOUBLE,MPI_SUM,Mask->Comm);
-			//MPI_Allreduce(&vaz_loc,&vaz,1,MPI_DOUBLE,MPI_SUM,Mask->Comm);
-			//MPI_Allreduce(&count_loc,&count,1,MPI_DOUBLE,MPI_SUM,Mask->Comm);
-			
             vax = sumReduce( Mask->Comm, vax_loc);
             vay = sumReduce( Mask->Comm, vay_loc);
             vaz = sumReduce( Mask->Comm, vaz_loc);
diff --git a/models/GreyscaleModel.h b/models/GreyscaleModel.h
index 9ac31be4..f525eccd 100644
--- a/models/GreyscaleModel.h
+++ b/models/GreyscaleModel.h
@@ -76,7 +76,6 @@ public:
 
     signed char *id;    
 	int *NeighborList;
-	int *dvcMap;
 	double *fq;
 	double *Permeability;//grey voxel permeability
 	double *Porosity;
diff --git a/tests/CMakeLists.txt b/tests/CMakeLists.txt
index 8b14a9dc..c536a7ec 100755
--- a/tests/CMakeLists.txt
+++ b/tests/CMakeLists.txt
@@ -4,6 +4,7 @@
 ADD_LBPM_EXECUTABLE( lbpm_color_simulator )
 ADD_LBPM_EXECUTABLE( lbpm_permeability_simulator )
 ADD_LBPM_EXECUTABLE( lbpm_greyscale_simulator )
+ADD_LBPM_EXECUTABLE( lbpm_greyscaleColor_simulator )
 #ADD_LBPM_EXECUTABLE( lbpm_BGK_simulator )
 #ADD_LBPM_EXECUTABLE( lbpm_color_macro_simulator )
 ADD_LBPM_EXECUTABLE( lbpm_dfh_simulator )
@@ -70,6 +71,7 @@ ADD_LBPM_TEST_PARALLEL( TestCommD3Q19 8 )
 ADD_LBPM_TEST_1_2_4( testCommunication )
 ADD_LBPM_TEST( TestWriter )
 ADD_LBPM_TEST( TestDatabase )
+ADD_LBPM_TEST( TestSetDevice )
 ADD_LBPM_PROVISIONAL_TEST( TestMicroCTReader )
 IF ( USE_NETCDF )
     ADD_LBPM_TEST_PARALLEL( TestNetcdf 8 )
diff --git a/tests/TestSetDevice.cpp b/tests/TestSetDevice.cpp
new file mode 100644
index 00000000..51e71682
--- /dev/null
+++ b/tests/TestSetDevice.cpp
@@ -0,0 +1,37 @@
+#include <iostream>
+#include "common/MPI_Helpers.h"
+#include "common/Utilities.h"
+#include "common/ScaLBL.h"
+
+int main (int argc, char **argv)
+{
+	MPI_Init(&argc,&argv);
+    int rank = MPI_WORLD_RANK();
+    int nprocs = MPI_WORLD_SIZE();
+
+    for (int i=0; i<nprocs; i++) {
+        if ( rank==i )
+            printf("%i of %i: Hello world\n",rank,nprocs);
+        MPI_Barrier(MPI_COMM_WORLD);
+    }
+
+    // Initialize compute device
+    ScaLBL_SetDevice(rank);
+    ScaLBL_DeviceBarrier();
+    MPI_Barrier(MPI_COMM_WORLD);
+
+    // Create a memory leak for valgrind to find
+    if ( nprocs==1 ) {
+        double *x = new double[1];
+        ASSERT(x!=NULL);
+    }
+
+    // set the error code
+    // Note: the error code should be consistent across all processors
+    int error = 0;
+    
+    // Finished
+	MPI_Barrier(MPI_COMM_WORLD);
+	MPI_Finalize();
+    return error; 
+}
diff --git a/tests/lbpm_greyscaleColor_simulator.cpp b/tests/lbpm_greyscaleColor_simulator.cpp
new file mode 100644
index 00000000..fec85c0e
--- /dev/null
+++ b/tests/lbpm_greyscaleColor_simulator.cpp
@@ -0,0 +1,71 @@
+#include <stdio.h>
+#include <stdlib.h>
+#include <sys/stat.h>
+#include <iostream>
+#include <exception>
+#include <stdexcept>
+#include <fstream>
+
+#include "models/GreyscaleColorModel.h"
+#include "common/Utilities.h"
+//#define WRITE_SURFACES
+
+//*************************************************************************
+// Implementation of Greyscale Two-Fluid Color LBM using CUDA
+//*************************************************************************
+
+using namespace std;
+
+
+int main(int argc, char **argv)
+{
+
+    // Initialize MPI and error handlers
+    Utilities::startup( argc, argv );
+
+    { // Limit scope so variables that contain communicators will free before MPI_Finialize
+  
+      MPI_Comm comm;
+      MPI_Comm_dup(MPI_COMM_WORLD,&comm);
+      int rank = comm_rank(comm);
+      int nprocs = comm_size(comm);
+  
+      if (rank == 0){
+	      printf("****************************************\n");
+	      printf("Running Greyscale Two-Phase Calculation \n");
+	      printf("****************************************\n");
+      }
+      // Initialize compute device
+      ScaLBL_SetDevice(rank);
+      ScaLBL_DeviceBarrier();
+      MPI_Barrier(comm);
+  
+      PROFILE_ENABLE(1);
+      //PROFILE_ENABLE_TRACE();
+      //PROFILE_ENABLE_MEMORY();
+      PROFILE_SYNCHRONIZE();
+      PROFILE_START("Main");
+      Utilities::setErrorHandlers();
+  
+      auto filename = argv[1];
+      ScaLBL_GreyscaleColorModel GreyscaleColor(rank,nprocs,comm);
+      GreyscaleColor.ReadParams(filename);
+      GreyscaleColor.SetDomain();    
+      GreyscaleColor.ReadInput();    
+      GreyscaleColor.Create();       // creating the model will create data structure to match the pore structure and allocate variables
+      GreyscaleColor.Initialize();   // initializing the model will set initial conditions for variables
+      GreyscaleColor.Run();	       
+      GreyscaleColor.WriteDebug();
+  
+      PROFILE_STOP("Main");
+      PROFILE_SAVE("lbpm_greyscaleColor_simulator",1);
+      // ****************************************************
+  
+      MPI_Barrier(comm);
+      MPI_Comm_free(&comm);
+  
+    } // Limit scope so variables that contain communicators will free before MPI_Finialize
+
+    Utilities::shutdown();
+
+}
diff --git a/tests/lbpm_greyscale_simulator.cpp b/tests/lbpm_greyscale_simulator.cpp
index b17778ce..df8cb3cb 100644
--- a/tests/lbpm_greyscale_simulator.cpp
+++ b/tests/lbpm_greyscale_simulator.cpp
@@ -6,58 +6,67 @@
 #include <stdexcept>
 #include <fstream>
 
-#include "common/ScaLBL.h"
-#include "common/Communication.h"
-#include "common/MPI_Helpers.h"
 #include "models/GreyscaleModel.h"
+#include "common/Utilities.h"
 //#define WRITE_SURFACES
 
-/*
- * Simulator for two-phase flow in porous media
- * James E. McClure 2013-2014
- */
+//****************************************************************
+// Implementation of Greyscale Single-Fluid LBM using CUDA
+//****************************************************************
 
 using namespace std;
 
 
 int main(int argc, char **argv)
 {
-	//*****************************************
-	// ***** MPI STUFF ****************
-	//*****************************************
-	// Initialize MPI
-	int rank,nprocs;
-	MPI_Init(&argc,&argv);
-	MPI_Comm comm = MPI_COMM_WORLD;
-	MPI_Comm_rank(comm,&rank);
-	MPI_Comm_size(comm,&nprocs);
-	{
-		// parallel domain size (# of sub-domains)
 
-		if (rank == 0){
-			printf("********************************************************\n");
-			printf("Running Greyscale Single Phase Permeability Calculation \n");
-			printf("********************************************************\n");
-		}
-		// Initialize compute device
-		int device=ScaLBL_SetDevice(rank);
-		NULL_USE(device);
-		ScaLBL_DeviceBarrier();
-		MPI_Barrier(comm);
-		
-		ScaLBL_GreyscaleModel Greyscale(rank,nprocs,comm);
-		auto filename = argv[1];
-		Greyscale.ReadParams(filename);
-		Greyscale.SetDomain();    // this reads in the domain 
-		Greyscale.ReadInput();
-		Greyscale.Create();       // creating the model will create data structure to match the pore structure and allocate variables
-		Greyscale.Initialize();   // initializing the model will set initial conditions for variables
-		Greyscale.Run();	 
-		//Greyscale.VelocityField();
-		//Greyscale.WriteDebug();
-	}
-	// ****************************************************
-	MPI_Barrier(comm);
-	MPI_Finalize();
-	// ****************************************************
+    // Initialize MPI and error handlers
+    Utilities::startup( argc, argv );
+
+    { // Limit scope so variables that contain communicators will free before MPI_Finialize
+  
+      MPI_Comm comm;
+      MPI_Comm_dup(MPI_COMM_WORLD,&comm);
+      int rank = comm_rank(comm);
+      int nprocs = comm_size(comm);
+  
+      if (rank == 0){
+	      printf("********************************************************\n");
+	 	  printf("Running Greyscale Single Phase Permeability Calculation \n");
+	 	  printf("********************************************************\n");
+      }
+      // Initialize compute device
+      ScaLBL_SetDevice(rank);
+      ScaLBL_DeviceBarrier();
+      MPI_Barrier(comm);
+  
+      PROFILE_ENABLE(1);
+      //PROFILE_ENABLE_TRACE();
+      //PROFILE_ENABLE_MEMORY();
+      PROFILE_SYNCHRONIZE();
+      PROFILE_START("Main");
+      Utilities::setErrorHandlers();
+  
+      auto filename = argv[1];
+      ScaLBL_GreyscaleModel Greyscale(rank,nprocs,comm);
+      Greyscale.ReadParams(filename);
+      Greyscale.SetDomain();    
+      Greyscale.ReadInput();    
+      Greyscale.Create();       // creating the model will create data structure to match the pore structure and allocate variables
+      Greyscale.Initialize();   // initializing the model will set initial conditions for variables
+      Greyscale.Run();	       
+	  Greyscale.VelocityField();
+      //Greyscale.WriteDebug();
+  
+      PROFILE_STOP("Main");
+      PROFILE_SAVE("lbpm_greyscale_simulator",1);
+      // ****************************************************
+  
+      MPI_Barrier(comm);
+      MPI_Comm_free(&comm);
+  
+    } // Limit scope so variables that contain communicators will free before MPI_Finialize
+
+    Utilities::shutdown();
+
 }