From 9fa091a49db08000dc26d5a21408b07915d7655f Mon Sep 17 00:00:00 2001
From: Rex Zhe Li <zhe.rex.li@gmail.com>
Date: Fri, 17 Jan 2020 18:46:28 -0500
Subject: [PATCH] save the work, CPU versions seem to work, but need non-unity
 porosity test

---
 common/Domain.cpp         |    2 +-
 common/ScaLBL.h           |    7 +
 cpu/Greyscale.cpp         | 1070 +++++++++++++++++++++++++++++++++++++
 models/GreyscaleModel.cpp |   20 +-
 models/GreyscaleModel.h   |    1 +
 5 files changed, 1093 insertions(+), 7 deletions(-)

diff --git a/common/Domain.cpp b/common/Domain.cpp
index 82bcaee2..48bfed15 100644
--- a/common/Domain.cpp
+++ b/common/Domain.cpp
@@ -391,7 +391,7 @@ void Domain::Decomp(std::string Filename)
 			for (int idx=0; idx<ReadValues.size(); idx++){
 				long int label=ReadValues[idx];
 				long int count=LabelCount[idx];
-				printf("Label=%d, Count=%d \n",label,count);
+				printf("Label=%ld, Count=%ld \n",label,count);
 			}
 		}
 
diff --git a/common/ScaLBL.h b/common/ScaLBL.h
index ecb1ffed..d2495e3f 100644
--- a/common/ScaLBL.h
+++ b/common/ScaLBL.h
@@ -62,6 +62,13 @@ extern "C" void ScaLBL_D3Q19_AAeven_Greyscale(double *dist, int start, int finis
 extern "C" void ScaLBL_D3Q19_AAodd_Greyscale(int *neighborList, double *dist, int start, int finish, int Np, double rlx, double Fx, double Fy, double Fz, 
                                              double *Poros,double *Perm, double *Velocity);
 
+extern "C" void ScaLBL_D3Q19_AAeven_Greyscale_IMRT(double *dist, int start, int finish, int Np, double rlx, double Fx, double Fy, double Fz,
+                                              double *Poros,double *Perm, double *Velocity,double Den);
+
+extern "C" void ScaLBL_D3Q19_AAodd_Greyscale_IMRT(int *neighborList, double *dist, int start, int finish, int Np, double rlx, double Fx, double Fy, double Fz, 
+                                             double *Poros,double *Perm, double *Velocity,double Den);
+
+
 // 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,
 		double Fy, double Fz);
diff --git a/cpu/Greyscale.cpp b/cpu/Greyscale.cpp
index 48e61a56..11a8eb5c 100644
--- a/cpu/Greyscale.cpp
+++ b/cpu/Greyscale.cpp
@@ -379,3 +379,1073 @@ extern "C" void ScaLBL_D3Q19_AAodd_Greyscale(int *neighborList, double *dist, in
 		Velocity[2*Np+n] = uz;
 	}
 }
+
+
+extern "C" void ScaLBL_D3Q19_AAeven_Greyscale_IMRT(double *dist, int start, int finish, int Np, double rlx, double Gx, double Gy, double Gz,
+                                              double *Poros,double *Perm, double *Velocity, double Den){
+	int n;
+	double vx,vy,vz,v_mag;
+    double ux,uy,uz,u_mag;
+    double pressure;//defined for this incompressible model
+	// conserved momemnts
+	double jx,jy,jz;
+	// non-conserved moments
+	double m1,m2,m4,m6,m8,m9,m10,m11,m12,m13,m14,m15,m16,m17,m18;
+	double m3,m5,m7;
+    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 = (1.0/rlx-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];
+		m1  = -30.0*fq;
+		m2  = 12.0*fq;
+
+		// q=1
+		fq = dist[2*Np+n];
+        pressure = 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];
+		pressure += 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];
+		pressure += 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];
+		pressure += 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];
+		pressure += 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];
+		pressure += 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];
+		pressure += 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];
+		pressure += 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];
+		pressure += 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];
+		pressure += 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];
+		pressure += 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];
+		pressure += 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];
+		pressure += 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];
+		pressure += 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];
+		pressure += 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];
+		pressure += 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];
+		pressure += 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];
+		pressure += 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/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/Den+0.5*porosity*Gx;
+		vy = jy/Den+0.5*porosity*Gy;
+		vz = jz/Den+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 = Den*(-porosity*mu/perm*ux - porosity*GeoFun/sqrt(perm)*u_mag*ux + porosity*Gx);
+        Fy = Den*(-porosity*mu/perm*uy - porosity*GeoFun/sqrt(perm)*u_mag*uy + porosity*Gy);
+        Fz = Den*(-porosity*mu/perm*uz - porosity*GeoFun/sqrt(perm)*u_mag*uz + porosity*Gz);
+        if (porosity==1.0){
+            Fx=Den*Gx;
+            Fy=Den*Gy;
+            Fz=Den*Gz;
+        }
+
+        //Calculate pressure for Incompressible-MRT model
+        pressure=0.5/porosity*(pressure-0.5*Den*u_mag*u_mag/porosity);
+
+		//..............carry out relaxation process...............................................
+//		m1 = m1 + rlx_setA*((-30*Den+19*(jx*jx+jy*jy+jz*jz)/Den/porosity + 57*pressure*porosity) - m1);
+//		m2 = m2 + rlx_setA*((12*Den - 5.5*(jx*jx+jy*jy+jz*jz)/Den/porosity-27*pressure*porosity) - m2);
+//		m4 = m4 + rlx_setB*((-0.6666666666666666*jx) - m4);
+//		m6 = m6 + rlx_setB*((-0.6666666666666666*jy) - m6);
+//		m8 = m8 + rlx_setB*((-0.6666666666666666*jz) - m8);
+//		m9 = m9 + rlx_setA*(((2*jx*jx-jy*jy-jz*jz)/Den/porosity) - m9);
+//		m10 = m10 + rlx_setA*(-0.5*((2*jx*jx-jy*jy-jz*jz)/Den/porosity)- m10);
+//		m11 = m11 + rlx_setA*(((jy*jy-jz*jz)/Den/porosity) - m11);
+//		m12 = m12 + rlx_setA*(-0.5*((jy*jy-jz*jz)/Den/porosity)- m12);
+//		m13 = m13 + rlx_setA*((jx*jy/Den/porosity) - m13);
+//		m14 = m14 + rlx_setA*((jy*jz/Den/porosity) - m14);
+//		m15 = m15 + rlx_setA*((jx*jz/Den/porosity) - m15);
+//		m16 = m16 + rlx_setB*( - m16);
+//		m17 = m17 + rlx_setB*( - m17);
+//		m18 = m18 + rlx_setB*( - m18);
+		//.......................................................................................................
+
+		//..............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);
+		m4 = m4 + rlx_setB*((-0.6666666666666666*ux*Den) - m4);
+		m6 = m6 + rlx_setB*((-0.6666666666666666*uy*Den) - m6);
+		m8 = m8 + rlx_setB*((-0.6666666666666666*uz*Den) - m8);
+		m9 = m9 + rlx_setA*((Den*(2*ux*ux-uy*uy-uz*uz)/porosity) - m9);
+		m10 = m10 + rlx_setA*(-0.5*Den*((2*ux*ux-uy*uy-uz*uz)/porosity)- m10);
+		m11 = m11 + rlx_setA*((Den*(uy*uy-uz*uz)/porosity) - m11);
+		m12 = m12 + rlx_setA*(-0.5*(Den*(uy*uy-uz*uz)/porosity)- m12);
+		m13 = m13 + rlx_setA*((Den*ux*uy/porosity) - m13);
+		m14 = m14 + rlx_setA*((Den*uy*uz/porosity) - m14);
+		m15 = m15 + rlx_setA*((Den*ux*uz/porosity) - m15);
+		m16 = m16 + rlx_setB*( - m16);
+		m17 = m17 + rlx_setB*( - m17);
+		m18 = m18 + rlx_setB*( - m18);
+		//.......................................................................................................
+
+        jx+=0.5*Fx;//There is no collision for momentum, but they must be updated subject to the body force
+        jy+=0.5*Fy;
+        jz+=0.5*Fz;
+		//.................inverse transformation......................................................
+		// q=0
+		//fq = mrt_V1*rho-mrt_V2*m1+mrt_V3*m2;
+		fq = mrt_V1*Den-mrt_V2*m1+mrt_V3*m2 
+                  + 0.3333333333333333*(1. - 0.5*rlx)*(Fx*(0. - (3.*ux)/porosity) + Fy*(0. - (3.*uy)/porosity) + Fz*(0. - (3.*uz)/porosity));
+		dist[n] = fq;
+
+		// q = 1
+		//fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(jx-m4)+mrt_V6*(m9-m10) + 0.16666666*Fx;
+		fq = mrt_V1*Den-mrt_V4*m1-mrt_V5*m2+0.1*(jx-m4)+mrt_V6*(m9-m10) 
+            +0.05555555555555555*(1. - 0.5*rlx)*(Fx*(3. + (6.*ux)/porosity) + Fy*(0. - (3.*uy)/porosity) + Fz*(0. - (3.*uz)/porosity));
+		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) -  0.16666666*Fx;
+		fq = mrt_V1*Den-mrt_V4*m1-mrt_V5*m2+0.1*(m4-jx)+mrt_V6*(m9-m10) 
+            +0.05555555555555555*(1. - 0.5*rlx)*(Fx*(-3. + (6.*ux)/porosity) + Fy*(0. - (3.*uy)/porosity) + Fz*(0. - (3.*uz)/porosity));
+		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) + 0.16666666*Fy;
+		fq = mrt_V1*Den-mrt_V4*m1-mrt_V5*m2+0.1*(jy-m6)+mrt_V7*(m10-m9)+mrt_V8*(m11-m12) 
+				+0.05555555555555555*(1. - 0.5*rlx)*(Fx*(0. - (3.*ux)/porosity) + Fy*(3. + (6.*uy)/porosity) + Fz*(0. - (3.*uz)/porosity));
+		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) - 0.16666666*Fy;
+		fq = mrt_V1*Den-mrt_V4*m1-mrt_V5*m2+0.1*(m6-jy)+mrt_V7*(m10-m9)+mrt_V8*(m11-m12) 
+				+0.05555555555555555*(1. - 0.5*rlx)*(Fx*(0. - (3.*ux)/porosity) + Fy*(-3. + (6.*uy)/porosity) + Fz*(0. - (3.*uz)/porosity));
+		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) + 0.16666666*Fz;
+		fq = mrt_V1*Den-mrt_V4*m1-mrt_V5*m2+0.1*(jz-m8)+mrt_V7*(m10-m9)+mrt_V8*(m12-m11) 
+				+0.05555555555555555*(1. - 0.5*rlx)*(Fx*(0. - (3.*ux)/porosity) + Fy*(0. - (3.*uy)/porosity) + Fz*(3. + (6.*uz)/porosity));
+		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) - 0.16666666*Fz;
+		fq = mrt_V1*Den-mrt_V4*m1-mrt_V5*m2+0.1*(m8-jz)+mrt_V7*(m10-m9)+mrt_V8*(m12-m11)
+				+0.05555555555555555*(1. - 0.5*rlx)*(Fx*(0. - (3.*ux)/porosity) + Fy*(0. - (3.*uy)/porosity) + Fz*(-3. + (6.*uz)/porosity));
+		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) + 0.08333333333*(Fx+Fy);
+		fq = mrt_V1*Den+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)
+				+0.027777777777777776*(1. - 0.5*rlx)*(Fx*(3. - (3.*ux)/porosity + (9.*(ux + uy))/porosity) + Fy*(3. - (3.*uy)/porosity + (9.*(ux + uy))/porosity) + 
+  Fz*(0. - (3.*uz)/porosity));
+		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) - 0.08333333333*(Fx+Fy);
+		fq = mrt_V1*Den+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)
+				+0.027777777777777776*(1. - 0.5*rlx)*(Fx*(-3. - (3.*ux)/porosity - (9.*(-ux - uy))/porosity) + Fy*(-3. - (9.*(-ux - uy))/porosity - (3.*uy)/porosity) + 
+  Fz*(0. - (3.*uz)/porosity));
+		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) + 0.08333333333*(Fx-Fy);
+		fq = mrt_V1*Den+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)
+				+0.027777777777777776*(1. - 0.5*rlx)*(Fx*(3. - (3.*ux)/porosity + (9.*(ux - uy))/porosity) + Fy*(-3. - (9.*(ux - uy))/porosity - (3.*uy)/porosity) + 
+  Fz*(0. - (3.*uz)/porosity));
+		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)- 0.08333333333*(Fx-Fy);
+		fq = mrt_V1*Den+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)
+				+0.027777777777777776*(1. - 0.5*rlx)*(Fx*(-3. - (3.*ux)/porosity - (9.*(-ux + uy))/porosity) + Fy*(3. - (3.*uy)/porosity + (9.*(-ux + uy))/porosity) + 
+  Fz*(0. - (3.*uz)/porosity));
+		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) + 0.08333333333*(Fx+Fz);
+		fq = mrt_V1*Den+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)
+				+0.027777777777777776*(1. - 0.5*rlx)*(Fy*(0. - (3.*uy)/porosity) + Fx*(3. - (3.*ux)/porosity + (9.*(ux + uz))/porosity) + 
+  Fz*(3. - (3.*uz)/porosity + (9.*(ux + uz))/porosity));
+		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) - 0.08333333333*(Fx+Fz);
+		fq = mrt_V1*Den+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)
+				+0.027777777777777776*(1. - 0.5*rlx)*(Fy*(0. - (3.*uy)/porosity) + Fx*(-3. - (3.*ux)/porosity - (9.*(-ux - uz))/porosity) + 
+  Fz*(-3. - (9.*(-ux - uz))/porosity - (3.*uz)/porosity));
+		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) + 0.08333333333*(Fx-Fz);
+		fq = mrt_V1*Den+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)
+				+0.027777777777777776*(1. - 0.5*rlx)*(Fy*(0. - (3.*uy)/porosity) + Fx*(3. - (3.*ux)/porosity + (9.*(ux - uz))/porosity) + 
+  Fz*(-3. - (9.*(ux - uz))/porosity - (3.*uz)/porosity));
+		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) - 0.08333333333*(Fx-Fz);
+		fq = mrt_V1*Den+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)
+				+0.027777777777777776*(1. - 0.5*rlx)*(Fy*(0. - (3.*uy)/porosity) + Fx*(-3. - (3.*ux)/porosity - (9.*(-ux + uz))/porosity) + 
+  Fz*(3. - (3.*uz)/porosity + (9.*(-ux + uz))/porosity));
+		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) + 0.08333333333*(Fy+Fz);
+		fq = mrt_V1*Den+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) 
+				+0.027777777777777776*(1. - 0.5*rlx)*(Fx*(0. - (3.*ux)/porosity) + Fy*(3. - (3.*uy)/porosity + (9.*(uy + uz))/porosity) + 
+  Fz*(3. - (3.*uz)/porosity + (9.*(uy + uz))/porosity));
+		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)- 0.08333333333*(Fy+Fz);
+		fq =  mrt_V1*Den+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)
+				+0.027777777777777776*(1. - 0.5*rlx)*(Fx*(0. - (3.*ux)/porosity) + Fy*(-3. - (3.*uy)/porosity - (9.*(-uy - uz))/porosity) + 
+  Fz*(-3. - (9.*(-uy - uz))/porosity - (3.*uz)/porosity));
+		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) + 0.08333333333*(Fy-Fz);
+		fq = mrt_V1*Den+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)
+				+0.027777777777777776*(1. - 0.5*rlx)*(Fx*(0. - (3.*ux)/porosity) + Fy*(3. - (3.*uy)/porosity + (9.*(uy - uz))/porosity) + 
+  Fz*(-3. - (9.*(uy - uz))/porosity - (3.*uz)/porosity));
+		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) - 0.08333333333*(Fy-Fz);
+		fq = mrt_V1*Den+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)
+				+0.027777777777777776*(1. - 0.5*rlx)*(Fx*(0. - (3.*ux)/porosity) + Fy*(-3. - (3.*uy)/porosity - (9.*(-uy + uz))/porosity) + 
+  Fz*(3. - (3.*uz)/porosity + (9.*(-uy + uz))/porosity));
+		dist[18*Np+n] = fq;
+		//........................................................................
+
+        //Update velocity on device
+		Velocity[0*Np+n] = ux;
+		Velocity[1*Np+n] = uy;
+		Velocity[2*Np+n] = uz;
+	}
+}
+
+extern "C" void ScaLBL_D3Q19_AAodd_Greyscale_IMRT(int *neighborList, double *dist, int start, int finish, int Np, double rlx, double Gx, double Gy, double Gz, 
+                                             double *Poros,double *Perm, double *Velocity, double Den){
+	int n, nread;
+	double vx,vy,vz,v_mag;
+    double ux,uy,uz,u_mag;
+    double pressure;//defined for this incompressible model
+	// conserved momemnts
+	double jx,jy,jz;
+	// non-conserved moments
+	double m1,m2,m4,m6,m8,m9,m10,m11,m12,m13,m14,m15,m16,m17,m18;
+	double m3,m5,m7;
+    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 = (1.0/rlx-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];
+		m1  = -30.0*fq;
+		m2  = 12.0*fq;
+
+		// q=1
+		nread = neighborList[n]; // neighbor 2 ( > 10Np => odd part of dist)
+		fq = dist[nread]; // reading the f1 data into register fq
+        pressure = fq;
+		m1 -= 11.0*fq;
+		m2 -= 4.0*fq;
+		jx = fq;
+		m4 = -4.0*fq;
+		m9 = 2.0*fq;
+		m10 = -4.0*fq;
+
+		// q=2
+		nread = neighborList[n+Np]; // neighbor 1 ( < 10Np => even part of dist)
+		fq = dist[nread];  // reading the f2 data into register fq
+		pressure += 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];
+		pressure += 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];
+		pressure += 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];
+		pressure += 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];
+		pressure += 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];
+		pressure += 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];
+		pressure += 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];
+		pressure += 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];
+		pressure += 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];
+		pressure += 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];
+		pressure += 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];
+		pressure += 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];
+		pressure += 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];
+		pressure += 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];
+		pressure += 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
+		nread = neighborList[n+16*Np];
+		fq = dist[nread];
+		pressure += 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];
+		pressure += 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/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/Den+0.5*porosity*Gx;
+		vy = jy/Den+0.5*porosity*Gy;
+		vz = jz/Den+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 = Den*(-porosity*mu/perm*ux - porosity*GeoFun/sqrt(perm)*u_mag*ux + porosity*Gx);
+        Fy = Den*(-porosity*mu/perm*uy - porosity*GeoFun/sqrt(perm)*u_mag*uy + porosity*Gy);
+        Fz = Den*(-porosity*mu/perm*uz - porosity*GeoFun/sqrt(perm)*u_mag*uz + porosity*Gz);
+        if (porosity==1.0){
+            Fx=Den*Gx;
+            Fy=Den*Gy;
+            Fz=Den*Gz;
+        }
+
+        //Calculate pressure for Incompressible-MRT model
+        pressure=0.5/porosity*(pressure-0.5*Den*u_mag*u_mag/porosity);
+
+		//..............carry out relaxation process...............................................
+//		m1 = m1 + rlx_setA*((-30*Den+19*(jx*jx+jy*jy+jz*jz)/Den/porosity + 57*pressure*porosity) - m1);
+//		m2 = m2 + rlx_setA*((12*Den - 5.5*(jx*jx+jy*jy+jz*jz)/Den/porosity-27*pressure*porosity) - m2);
+//		m4 = m4 + rlx_setB*((-0.6666666666666666*jx) - m4);
+//		m6 = m6 + rlx_setB*((-0.6666666666666666*jy) - m6);
+//		m8 = m8 + rlx_setB*((-0.6666666666666666*jz) - m8);
+//		m9 = m9 + rlx_setA*(((2*jx*jx-jy*jy-jz*jz)/Den/porosity) - m9);
+//		m10 = m10 + rlx_setA*(-0.5*((2*jx*jx-jy*jy-jz*jz)/Den/porosity)- m10);
+//		m11 = m11 + rlx_setA*(((jy*jy-jz*jz)/Den/porosity) - m11);
+//		m12 = m12 + rlx_setA*(-0.5*((jy*jy-jz*jz)/Den/porosity)- m12);
+//		m13 = m13 + rlx_setA*((jx*jy/Den/porosity) - m13);
+//		m14 = m14 + rlx_setA*((jy*jz/Den/porosity) - m14);
+//		m15 = m15 + rlx_setA*((jx*jz/Den/porosity) - m15);
+//		m16 = m16 + rlx_setB*( - m16);
+//		m17 = m17 + rlx_setB*( - m17);
+//		m18 = m18 + rlx_setB*( - m18);
+		//.......................................................................................................
+        
+		//..............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);
+		m4 = m4 + rlx_setB*((-0.6666666666666666*ux*Den) - m4);
+		m6 = m6 + rlx_setB*((-0.6666666666666666*uy*Den) - m6);
+		m8 = m8 + rlx_setB*((-0.6666666666666666*uz*Den) - m8);
+		m9 = m9 + rlx_setA*((Den*(2*ux*ux-uy*uy-uz*uz)/porosity) - m9);
+		m10 = m10 + rlx_setA*(-0.5*Den*((2*ux*ux-uy*uy-uz*uz)/porosity)- m10);
+		m11 = m11 + rlx_setA*((Den*(uy*uy-uz*uz)/porosity) - m11);
+		m12 = m12 + rlx_setA*(-0.5*(Den*(uy*uy-uz*uz)/porosity)- m12);
+		m13 = m13 + rlx_setA*((Den*ux*uy/porosity) - m13);
+		m14 = m14 + rlx_setA*((Den*uy*uz/porosity) - m14);
+		m15 = m15 + rlx_setA*((Den*ux*uz/porosity) - m15);
+		m16 = m16 + rlx_setB*( - m16);
+		m17 = m17 + rlx_setB*( - m17);
+		m18 = m18 + rlx_setB*( - m18);
+		//.......................................................................................................
+        
+        jx+=0.5*Fx;//There is no collision for momentum, but they must be updated subject to the body force
+        jy+=0.5*Fy;
+        jz+=0.5*Fz;
+		//.................inverse transformation......................................................
+		// q=0
+		//fq = mrt_V1*rho-mrt_V2*m1+mrt_V3*m2;
+		fq = mrt_V1*Den-mrt_V2*m1+mrt_V3*m2 
+                  + 0.3333333333333333*(1. - 0.5*rlx)*(Fx*(0. - (3.*ux)/porosity) + Fy*(0. - (3.*uy)/porosity) + Fz*(0. - (3.*uz)/porosity));
+		dist[n] = fq;
+
+		// q = 1
+		//fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(jx-m4)+mrt_V6*(m9-m10) + 0.16666666*Fx;
+		fq = mrt_V1*Den-mrt_V4*m1-mrt_V5*m2+0.1*(jx-m4)+mrt_V6*(m9-m10) 
+            +0.05555555555555555*(1. - 0.5*rlx)*(Fx*(3. + (6.*ux)/porosity) + Fy*(0. - (3.*uy)/porosity) + Fz*(0. - (3.*uz)/porosity));
+		nread = neighborList[n+Np];
+		dist[nread] = fq;
+
+		// q=2
+		//fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(m4-jx)+mrt_V6*(m9-m10) -  0.16666666*Fx;
+		fq = mrt_V1*Den-mrt_V4*m1-mrt_V5*m2+0.1*(m4-jx)+mrt_V6*(m9-m10) 
+            +0.05555555555555555*(1. - 0.5*rlx)*(Fx*(-3. + (6.*ux)/porosity) + Fy*(0. - (3.*uy)/porosity) + Fz*(0. - (3.*uz)/porosity));
+		nread = neighborList[n];
+		dist[nread] = 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) + 0.16666666*Fy;
+		fq = mrt_V1*Den-mrt_V4*m1-mrt_V5*m2+0.1*(jy-m6)+mrt_V7*(m10-m9)+mrt_V8*(m11-m12) 
+				+0.05555555555555555*(1. - 0.5*rlx)*(Fx*(0. - (3.*ux)/porosity) + Fy*(3. + (6.*uy)/porosity) + Fz*(0. - (3.*uz)/porosity));
+		nread = neighborList[n+3*Np];
+		dist[nread] = 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) - 0.16666666*Fy;
+		fq = mrt_V1*Den-mrt_V4*m1-mrt_V5*m2+0.1*(m6-jy)+mrt_V7*(m10-m9)+mrt_V8*(m11-m12) 
+				+0.05555555555555555*(1. - 0.5*rlx)*(Fx*(0. - (3.*ux)/porosity) + Fy*(-3. + (6.*uy)/porosity) + Fz*(0. - (3.*uz)/porosity));
+		nread = neighborList[n+2*Np];
+		dist[nread] = 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) + 0.16666666*Fz;
+		fq = mrt_V1*Den-mrt_V4*m1-mrt_V5*m2+0.1*(jz-m8)+mrt_V7*(m10-m9)+mrt_V8*(m12-m11) 
+				+0.05555555555555555*(1. - 0.5*rlx)*(Fx*(0. - (3.*ux)/porosity) + Fy*(0. - (3.*uy)/porosity) + Fz*(3. + (6.*uz)/porosity));
+		nread = neighborList[n+5*Np];
+		dist[nread] = 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) - 0.16666666*Fz;
+		fq = mrt_V1*Den-mrt_V4*m1-mrt_V5*m2+0.1*(m8-jz)+mrt_V7*(m10-m9)+mrt_V8*(m12-m11)
+				+0.05555555555555555*(1. - 0.5*rlx)*(Fx*(0. - (3.*ux)/porosity) + Fy*(0. - (3.*uy)/porosity) + Fz*(-3. + (6.*uz)/porosity));
+		nread = neighborList[n+4*Np];
+		dist[nread] = 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) + 0.08333333333*(Fx+Fy);
+		fq = mrt_V1*Den+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)
+				+0.027777777777777776*(1. - 0.5*rlx)*(Fx*(3. - (3.*ux)/porosity + (9.*(ux + uy))/porosity) + Fy*(3. - (3.*uy)/porosity + (9.*(ux + uy))/porosity) + 
+  Fz*(0. - (3.*uz)/porosity));
+		nread = neighborList[n+7*Np];
+		dist[nread] = 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) - 0.08333333333*(Fx+Fy);
+		fq = mrt_V1*Den+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)
+				+0.027777777777777776*(1. - 0.5*rlx)*(Fx*(-3. - (3.*ux)/porosity - (9.*(-ux - uy))/porosity) + Fy*(-3. - (9.*(-ux - uy))/porosity - (3.*uy)/porosity) + 
+  Fz*(0. - (3.*uz)/porosity));
+		nread = neighborList[n+6*Np];
+		dist[nread] = 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) + 0.08333333333*(Fx-Fy);
+		fq = mrt_V1*Den+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)
+				+0.027777777777777776*(1. - 0.5*rlx)*(Fx*(3. - (3.*ux)/porosity + (9.*(ux - uy))/porosity) + Fy*(-3. - (9.*(ux - uy))/porosity - (3.*uy)/porosity) + 
+  Fz*(0. - (3.*uz)/porosity));
+		nread = neighborList[n+9*Np];
+		dist[nread] = 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)- 0.08333333333*(Fx-Fy);
+		fq = mrt_V1*Den+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)
+				+0.027777777777777776*(1. - 0.5*rlx)*(Fx*(-3. - (3.*ux)/porosity - (9.*(-ux + uy))/porosity) + Fy*(3. - (3.*uy)/porosity + (9.*(-ux + uy))/porosity) + 
+  Fz*(0. - (3.*uz)/porosity));
+		nread = neighborList[n+8*Np];
+		dist[nread] = 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) + 0.08333333333*(Fx+Fz);
+		fq = mrt_V1*Den+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)
+				+0.027777777777777776*(1. - 0.5*rlx)*(Fy*(0. - (3.*uy)/porosity) + Fx*(3. - (3.*ux)/porosity + (9.*(ux + uz))/porosity) + 
+  Fz*(3. - (3.*uz)/porosity + (9.*(ux + uz))/porosity));
+		nread = neighborList[n+11*Np];
+		dist[nread] = 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) - 0.08333333333*(Fx+Fz);
+		fq = mrt_V1*Den+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)
+				+0.027777777777777776*(1. - 0.5*rlx)*(Fy*(0. - (3.*uy)/porosity) + Fx*(-3. - (3.*ux)/porosity - (9.*(-ux - uz))/porosity) + 
+  Fz*(-3. - (9.*(-ux - uz))/porosity - (3.*uz)/porosity));
+		nread = neighborList[n+10*Np];
+		dist[nread]= 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) + 0.08333333333*(Fx-Fz);
+		fq = mrt_V1*Den+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)
+				+0.027777777777777776*(1. - 0.5*rlx)*(Fy*(0. - (3.*uy)/porosity) + Fx*(3. - (3.*ux)/porosity + (9.*(ux - uz))/porosity) + 
+  Fz*(-3. - (9.*(ux - uz))/porosity - (3.*uz)/porosity));
+		nread = neighborList[n+13*Np];
+		dist[nread] = 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) - 0.08333333333*(Fx-Fz);
+		fq = mrt_V1*Den+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)
+				+0.027777777777777776*(1. - 0.5*rlx)*(Fy*(0. - (3.*uy)/porosity) + Fx*(-3. - (3.*ux)/porosity - (9.*(-ux + uz))/porosity) + 
+  Fz*(3. - (3.*uz)/porosity + (9.*(-ux + uz))/porosity));
+		nread = neighborList[n+12*Np];
+		dist[nread] = 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) + 0.08333333333*(Fy+Fz);
+		fq = mrt_V1*Den+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) 
+				+0.027777777777777776*(1. - 0.5*rlx)*(Fx*(0. - (3.*ux)/porosity) + Fy*(3. - (3.*uy)/porosity + (9.*(uy + uz))/porosity) + 
+  Fz*(3. - (3.*uz)/porosity + (9.*(uy + uz))/porosity));
+		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)- 0.08333333333*(Fy+Fz);
+		fq =  mrt_V1*Den+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)
+				+0.027777777777777776*(1. - 0.5*rlx)*(Fx*(0. - (3.*ux)/porosity) + Fy*(-3. - (3.*uy)/porosity - (9.*(-uy - uz))/porosity) + 
+  Fz*(-3. - (9.*(-uy - uz))/porosity - (3.*uz)/porosity));
+		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) + 0.08333333333*(Fy-Fz);
+		fq = mrt_V1*Den+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)
+				+0.027777777777777776*(1. - 0.5*rlx)*(Fx*(0. - (3.*ux)/porosity) + Fy*(3. - (3.*uy)/porosity + (9.*(uy - uz))/porosity) + 
+  Fz*(-3. - (9.*(uy - uz))/porosity - (3.*uz)/porosity));
+		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) - 0.08333333333*(Fy-Fz);
+		fq = mrt_V1*Den+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)
+				+0.027777777777777776*(1. - 0.5*rlx)*(Fx*(0. - (3.*ux)/porosity) + Fy*(-3. - (3.*uy)/porosity - (9.*(-uy + uz))/porosity) + 
+  Fz*(3. - (3.*uz)/porosity + (9.*(-uy + uz))/porosity));
+		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;
+	}
+}
+
diff --git a/models/GreyscaleModel.cpp b/models/GreyscaleModel.cpp
index 2ce6ff5e..1cdae815 100644
--- a/models/GreyscaleModel.cpp
+++ b/models/GreyscaleModel.cpp
@@ -8,7 +8,7 @@ color lattice boltzmann model
 #include <time.h>
 
 ScaLBL_GreyscaleModel::ScaLBL_GreyscaleModel(int RANK, int NP, MPI_Comm COMM):
-rank(RANK), nprocs(NP), Restart(0),timestep(0),timestepMax(0),tau(0),Fx(0),Fy(0),Fz(0),flux(0),din(0),dout(0),
+rank(RANK), nprocs(NP), Restart(0),timestep(0),timestepMax(0),tau(0),Den(0),Fx(0),Fy(0),Fz(0),flux(0),din(0),dout(0),
 Nx(0),Ny(0),Nz(0),N(0),Np(0),nprocx(0),nprocy(0),nprocz(0),BoundaryCondition(0),Lx(0),Ly(0),Lz(0),comm(COMM)
 {
 	SignDist.resize(Nx,Ny,Nz);           
@@ -30,6 +30,7 @@ void ScaLBL_GreyscaleModel::ReadParams(string filename){
 	// set defaults
 	timestepMax = 100000;
 	tau = 1.0;
+    Den = 1.0;//constant density
 	tolerance = 0.01;
 	Fx = Fy = Fz = 0.0;
 	Restart=false;
@@ -37,13 +38,16 @@ void ScaLBL_GreyscaleModel::ReadParams(string filename){
 	flux=0.0;
     dp = 10.0; //unit of 'dp': voxel
 	
-	// Color Model parameters
+	// Greyscale Model parameters
 	if (greyscale_db->keyExists( "timestepMax" )){
 		timestepMax = greyscale_db->getScalar<int>( "timestepMax" );
 	}
 	if (greyscale_db->keyExists( "tau" )){
 		tau = greyscale_db->getScalar<double>( "tau" );
 	}
+	if (greyscale_db->keyExists( "Den" )){
+		Den = greyscale_db->getScalar<double>( "Den" );
+	}
 	if (greyscale_db->keyExists( "dp" )){
 		dp = greyscale_db->getScalar<double>( "dp" );
 	}
@@ -423,15 +427,19 @@ void ScaLBL_GreyscaleModel::Run(){
 		//************************************************************************/
 		timestep++;
 		ScaLBL_Comm->SendD3Q19AA(fq); //READ FROM NORMAL
-		ScaLBL_D3Q19_AAodd_Greyscale(NeighborList, fq,  ScaLBL_Comm->FirstInterior(), ScaLBL_Comm->LastInterior(), Np, rlx, Fx, Fy, Fz,Porosity,Permeability,Velocity);
+		//ScaLBL_D3Q19_AAodd_Greyscale(NeighborList, fq,  ScaLBL_Comm->FirstInterior(), ScaLBL_Comm->LastInterior(), Np, rlx, Fx, Fy, Fz,Porosity,Permeability,Velocity);
+		ScaLBL_D3Q19_AAodd_Greyscale_IMRT(NeighborList, fq,  ScaLBL_Comm->FirstInterior(), ScaLBL_Comm->LastInterior(), Np, rlx, Fx, Fy, Fz,Porosity,Permeability,Velocity,Den);
 		ScaLBL_Comm->RecvD3Q19AA(fq); //WRITE INTO OPPOSITE
-		ScaLBL_D3Q19_AAodd_Greyscale(NeighborList, fq, 0, ScaLBL_Comm->LastExterior(), Np, rlx, Fx, Fy, Fz,Porosity,Permeability,Velocity);
+		//ScaLBL_D3Q19_AAodd_Greyscale(NeighborList, fq, 0, ScaLBL_Comm->LastExterior(), Np, rlx, Fx, Fy, Fz,Porosity,Permeability,Velocity);
+		ScaLBL_D3Q19_AAodd_Greyscale_IMRT(NeighborList, fq, 0, ScaLBL_Comm->LastExterior(), Np, rlx, Fx, Fy, Fz,Porosity,Permeability,Velocity,Den);
 		ScaLBL_DeviceBarrier(); MPI_Barrier(comm);
 		timestep++;
 		ScaLBL_Comm->SendD3Q19AA(fq); //READ FORM NORMAL
-		ScaLBL_D3Q19_AAeven_Greyscale(fq, ScaLBL_Comm->FirstInterior(), ScaLBL_Comm->LastInterior(), Np, rlx, Fx, Fy, Fz,Porosity,Permeability,Velocity);
+		//ScaLBL_D3Q19_AAeven_Greyscale(fq, ScaLBL_Comm->FirstInterior(), ScaLBL_Comm->LastInterior(), Np, rlx, Fx, Fy, Fz,Porosity,Permeability,Velocity);
+		ScaLBL_D3Q19_AAeven_Greyscale_IMRT(fq, ScaLBL_Comm->FirstInterior(), ScaLBL_Comm->LastInterior(), Np, rlx, Fx, Fy, Fz,Porosity,Permeability,Velocity,Den);
 		ScaLBL_Comm->RecvD3Q19AA(fq); //WRITE INTO OPPOSITE
-		ScaLBL_D3Q19_AAeven_Greyscale(fq, 0, ScaLBL_Comm->LastExterior(), Np, rlx, Fx, Fy, Fz,Porosity,Permeability,Velocity);
+		//ScaLBL_D3Q19_AAeven_Greyscale(fq, 0, ScaLBL_Comm->LastExterior(), Np, rlx, Fx, Fy, Fz,Porosity,Permeability,Velocity);
+		ScaLBL_D3Q19_AAeven_Greyscale_IMRT(fq, 0, ScaLBL_Comm->LastExterior(), Np, rlx, Fx, Fy, Fz,Porosity,Permeability,Velocity,Den);
 		ScaLBL_DeviceBarrier(); MPI_Barrier(comm);
 		//************************************************************************/
 		
diff --git a/models/GreyscaleModel.h b/models/GreyscaleModel.h
index 9b970a65..ac939aed 100644
--- a/models/GreyscaleModel.h
+++ b/models/GreyscaleModel.h
@@ -36,6 +36,7 @@ public:
 	int timestep,timestepMax;
 	int BoundaryCondition;
 	double tau;
+    double Den;//constant density
 	double tolerance;
 	double Fx,Fy,Fz,flux;
 	double din,dout;