diff --git a/cpu/Greyscale.cpp b/cpu/Greyscale.cpp
index 95cf516b..f2be769e 100644
--- a/cpu/Greyscale.cpp
+++ b/cpu/Greyscale.cpp
@@ -391,7 +391,6 @@ extern "C" void ScaLBL_D3Q19_AAeven_Greyscale_IMRT(double *dist, int start, int
 	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)
@@ -851,7 +850,6 @@ extern "C" void ScaLBL_D3Q19_AAodd_Greyscale_IMRT(int *neighborList, double *dis
 	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)
diff --git a/gpu/Greyscale.cu b/gpu/Greyscale.cu
index fdb0a462..5b8273fe 100644
--- a/gpu/Greyscale.cu
+++ b/gpu/Greyscale.cu
@@ -396,14 +396,17 @@ __global__ void dvc_ScaLBL_D3Q19_AAodd_Greyscale(int *neighborList, double *dist
 
 __global__ void dvc_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 rho,jx,jy,jz;
+	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
@@ -413,6 +416,20 @@ __global__ void dvc_ScaLBL_D3Q19_AAeven_Greyscale_IMRT(double *dist, int start,
     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....................
@@ -420,447 +437,935 @@ __global__ void dvc_ScaLBL_D3Q19_AAeven_Greyscale_IMRT(double *dist, int start,
 
 		if ( n<finish ){
 
-		// q=0
-		fq = dist[n];
-		rho = fq;
-		m1  = -30.0*fq;
-		m2  = 12.0*fq;
+            //........................................................................
+            //					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];
-		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=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];
-		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];
+            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];
-		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=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];
-		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];
+            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];
-		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=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];
-		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];
+            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];
-		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=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];
-		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];
+            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];
-		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];
+            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];
-		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];
+            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];
-		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=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];
-		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];
+            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];
-		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];
+            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];
-		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];
+            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];
-		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=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];
-		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];
+            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];
-		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];
+            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];
-		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];
+            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;
+            //---------------------------------------------------------------------//
 
-		//........................................................................
-		//..............carry out relaxation process..............................
-		//..........Toelke, Fruediger et. al. 2006................................
-		if (C == 0.0)	nx = ny = nz = 0.0;
-		m1 = m1 + rlx_setA*((19*(jx*jx+jy*jy+jz*jz)/rho0 - 11*rho) -19*alpha*C - m1);
-		m2 = m2 + rlx_setA*((3*rho - 5.5*(jx*jx+jy*jy+jz*jz)/rho0)- 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)/rho0) + 0.5*alpha*C*(2*nx*nx-ny*ny-nz*nz) - m9);
-		m10 = m10 + rlx_setA*( - m10);
-		m11 = m11 + rlx_setA*(((jy*jy-jz*jz)/rho0) + 0.5*alpha*C*(ny*ny-nz*nz)- m11);
-		m12 = m12 + rlx_setA*( - m12);
-		m13 = m13 + rlx_setA*( (jx*jy/rho0) + 0.5*alpha*C*nx*ny - m13);
-		m14 = m14 + rlx_setA*( (jy*jz/rho0) + 0.5*alpha*C*ny*nz - m14);
-		m15 = m15 + rlx_setA*( (jx*jz/rho0) + 0.5*alpha*C*nx*nz - m15);
-		m16 = m16 + rlx_setB*( - m16);
-		m17 = m17 + rlx_setB*( - m17);
-		m18 = m18 + rlx_setB*( - m18);
+            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;
+            }
 
-		// q=0
-		f0 = dist[n];
-		f1 = dist[2*Np+n];
-		f2 = dist[1*Np+n];
-		f3 = dist[4*Np+n];
-		f4 = dist[3*Np+n];
-		f5 = dist[6*Np+n];
-		f6 = dist[5*Np+n];
-		f7 = dist[8*Np+n];
-		f8 = dist[7*Np+n];
-		f9 = dist[10*Np+n];
-		f10 = dist[9*Np+n];
-		f11 = dist[12*Np+n];
-		f12 = dist[11*Np+n];
-		f13 = dist[14*Np+n];
-		f14 = dist[13*Np+n];
-		f15 = dist[16*Np+n];
-		f16 = dist[15*Np+n];
-		f17 = dist[18*Np+n];
-		f18 = dist[17*Np+n];
+            //Calculate pressure for Incompressible-MRT model
+            pressure=0.5/porosity*(pressure-0.5*Den*u_mag*u_mag/porosity);
 
-        porosity = Poros[n];
-        perm = Perm[n];
+            //..............carry out relaxation process...............................................
+            m1 = m1 + rlx_setA*((-30*Den+19*(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)
+                    + (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)
+                    + (1-0.5*rlx_setB)*(-0.6666666666666666*Fx);
+            jy = jy + Fy;
+            m6 = m6 + rlx_setB*((-0.6666666666666666*uy*Den) - m6)
+                    + (1-0.5*rlx_setB)*(-0.6666666666666666*Fy);
+            jz = jz + Fz;
+            m8 = m8 + rlx_setB*((-0.6666666666666666*uz*Den) - m8)
+                    + (1-0.5*rlx_setB)*(-0.6666666666666666*Fz);
+            m9 = m9 + rlx_setA*((Den*(2*ux*ux-uy*uy-uz*uz)/porosity) - m9)
+                    + (1-0.5*rlx_setA)*(4*Fx*ux-2*Fy*uy-2*Fz*uz)/porosity;
+            m10 = m10 + rlx_setA*(-0.5*Den*((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*((Den*(uy*uy-uz*uz)/porosity) - m11)
+                      + (1-0.5*rlx_setA)*(2*Fy*uy-2*Fz*uz)/porosity;
+            m12 = m12 + rlx_setA*(-0.5*(Den*(uy*uy-uz*uz)/porosity)- m12)
+                      + (1-0.5*rlx_setA)*(-Fy*uy+Fz*uz)/porosity;
+            m13 = m13 + rlx_setA*((Den*ux*uy/porosity) - m13)
+                      + (1-0.5*rlx_setA)*(Fy*ux+Fx*uy)/porosity;
+            m14 = m14 + rlx_setA*((Den*uy*uz/porosity) - m14)
+                      + (1-0.5*rlx_setA)*(Fz*uy+Fy*uz)/porosity;
+            m15 = m15 + rlx_setA*((Den*ux*uz/porosity) - 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);
+            //.......................................................................................................
 
-        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
+            //.................inverse transformation......................................................
+            // q=0
+            fq = mrt_V1*Den-mrt_V2*m1+mrt_V3*m2;
+            dist[n] = fq;
 
-		rho = f0+f2+f1+f4+f3+f6+f5+f8+f7+f10+f9+f12+f11+f14+f13+f16+f15+f18+f17;
-		vx = (f1-f2+f7-f8+f9-f10+f11-f12+f13-f14)/rho+0.5*porosity*Gx;
-		vy = (f3-f4+f7-f8-f9+f10+f15-f16+f17-f18)/rho+0.5*porosity*Gy;
-		vz = (f5-f6+f11-f12-f13+f14+f15-f16-f17+f18)/rho+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);
+            // q = 1
+            fq = mrt_V1*Den-mrt_V4*m1-mrt_V5*m2+0.1*(jx-m4)+mrt_V6*(m9-m10);
+            dist[1*Np+n] = fq;
 
-        //Update the total force to include linear (Darcy) and nonlinear (Forchheimer) drags due to the porous medium
-        Fx = -porosity*mu/perm*ux - porosity*GeoFun/sqrt(perm)*u_mag*ux + porosity*Gx;
-        Fy = -porosity*mu/perm*uy - porosity*GeoFun/sqrt(perm)*u_mag*uy + porosity*Gy;
-        Fz = -porosity*mu/perm*uz - porosity*GeoFun/sqrt(perm)*u_mag*uz + porosity*Gz;
-        if (porosity==1.0){
-            Fx=Gx;
-            Fy=Gy;
-            Fz=Gz;
-        }
+            // q=2
+            fq = mrt_V1*Den-mrt_V4*m1-mrt_V5*m2+0.1*(m4-jx)+mrt_V6*(m9-m10);
+            dist[2*Np+n] = fq;
 
-		// q=0
-		dist[n] = f0*(1.0-rlx)+ rlx*0.3333333333333333*rho*(1. - (1.5*(ux*ux + uy*uy + uz*uz))/porosity)
-                  + 0.3333333333333333*rho*(1. - 0.5*rlx)*(Fx*(0. - (3.*ux)/porosity) + Fy*(0. - (3.*uy)/porosity) + Fz*(0. - (3.*uz)/porosity));
+            // q = 3
+            fq = mrt_V1*Den-mrt_V4*m1-mrt_V5*m2+0.1*(jy-m6)+mrt_V7*(m10-m9)+mrt_V8*(m11-m12);
+            dist[3*Np+n] = fq;
 
-		// q = 1
-		dist[1*Np+n] = f1*(1.0-rlx) + rlx*0.05555555555555555*rho*(1 + 3.*ux + (4.5*ux*ux)/porosity - (1.5*(ux*ux + uy*uy + uz*uz))/porosity)
-            +0.05555555555555555*rho*(1. - 0.5*rlx)*(Fx*(3. + (6.*ux)/porosity) + Fy*(0. - (3.*uy)/porosity) + Fz*(0. - (3.*uz)/porosity));
+            // q = 4
+            fq = mrt_V1*Den-mrt_V4*m1-mrt_V5*m2+0.1*(m6-jy)+mrt_V7*(m10-m9)+mrt_V8*(m11-m12);
+            dist[4*Np+n] = fq;
 
-		// q=2
-		dist[2*Np+n] = f2*(1.0-rlx) + rlx*0.05555555555555555*rho*(1 - 3.*ux + (4.5*ux*ux)/porosity - (1.5*(ux*ux + uy*uy + uz*uz))/porosity)
-            +0.05555555555555555*rho*(1. - 0.5*rlx)*(Fx*(-3. + (6.*ux)/porosity) + Fy*(0. - (3.*uy)/porosity) + Fz*(0. - (3.*uz)/porosity));
+            // q = 5
+            fq = mrt_V1*Den-mrt_V4*m1-mrt_V5*m2+0.1*(jz-m8)+mrt_V7*(m10-m9)+mrt_V8*(m12-m11);
+            dist[5*Np+n] = fq;
 
-		// q = 3
-		dist[3*Np+n] = f3*(1.0-rlx) + rlx*0.05555555555555555*rho*(1 + 3.*uy + (4.5*uy*uy)/porosity - (1.5*(ux*ux + uy*uy + uz*uz))/porosity)
-				+0.05555555555555555*rho*(1. - 0.5*rlx)*(Fx*(0. - (3.*ux)/porosity) + Fy*(3. + (6.*uy)/porosity) + Fz*(0. - (3.*uz)/porosity));
+            // q = 6
+            fq = mrt_V1*Den-mrt_V4*m1-mrt_V5*m2+0.1*(m8-jz)+mrt_V7*(m10-m9)+mrt_V8*(m12-m11);
+            dist[6*Np+n] = fq;
 
-		// q = 4
-		dist[4*Np+n] = f4*(1.0-rlx) + rlx*0.05555555555555555*rho*(1 - 3.*uy + (4.5*uy*uy)/porosity - (1.5*(ux*ux + uy*uy + uz*uz))/porosity)
-				+0.05555555555555555*rho*(1. - 0.5*rlx)*(Fx*(0. - (3.*ux)/porosity) + Fy*(-3. + (6.*uy)/porosity) + Fz*(0. - (3.*uz)/porosity));
+            // q = 7
+            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);
+            dist[7*Np+n] = fq;
 
-		// q = 5
-		dist[5*Np+n] = f5*(1.0-rlx) + rlx*0.05555555555555555*rho*(1 + 3.*uz + (4.5*uz*uz)/porosity - (1.5*(ux*ux + uy*uy + uz*uz))/porosity)
-				+0.05555555555555555*rho*(1. - 0.5*rlx)*(Fx*(0. - (3.*ux)/porosity) + Fy*(0. - (3.*uy)/porosity) + Fz*(3. + (6.*uz)/porosity));
+            // q = 8
+            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);
+            dist[8*Np+n] = fq;
 
-		// q = 6
-		dist[6*Np+n] = f6*(1.0-rlx) + rlx*0.05555555555555555*rho*(1 - 3.*uz + (4.5*uz*uz)/porosity - (1.5*(ux*ux+ uy*uy + uz*uz))/porosity)
-				+0.05555555555555555*rho*(1. - 0.5*rlx)*(Fx*(0. - (3.*ux)/porosity) + Fy*(0. - (3.*uy)/porosity) + Fz*(-3. + (6.*uz)/porosity));
+            // q = 9
+            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);
+            dist[9*Np+n] = fq;
 
-		// q = 7
-		dist[7*Np+n] = f7*(1.0-rlx) + rlx*0.027777777777777776*rho*(1 + 3.*(ux + uy) + (4.5*(ux + uy)*(ux + uy))/porosity - (1.5*(ux*ux + uy*uy + uz*uz))/porosity)
-				+0.027777777777777776*rho*(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));
+            // q = 10
+            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);
+            dist[10*Np+n] = fq;
 
-		// q = 8
-		dist[8*Np+n] = f8*(1.0-rlx) + rlx*0.027777777777777776*rho*(1 + 3.*(-ux - uy) + (4.5*(-ux - uy)*(-ux - uy))/porosity - (1.5*(ux*ux + uy*uy + uz*uz))/porosity)
-				+0.027777777777777776*rho*(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));
+            // q = 11
+            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);
+            dist[11*Np+n] = fq;
 
-		// q = 9
-		dist[9*Np+n] = f9*(1.0-rlx) + rlx*0.027777777777777776*rho*(1 + 3.*(ux - uy) + (4.5*(ux - uy)*(ux - uy))/porosity - (1.5*(ux*ux + uy*uy + uz*uz))/porosity)
-				+0.027777777777777776*rho*(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));
+            // q = 12
+            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);
+            dist[12*Np+n] = fq;
 
-		// q = 10
-		dist[10*Np+n] = f10*(1.0-rlx) + rlx*0.027777777777777776*rho*(1 + 3.*(-ux + uy) + (4.5*(-ux + uy)*(-ux + uy))/porosity - (1.5*(ux*ux + uy*uy + uz*uz))/porosity)
-				+0.027777777777777776*rho*(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));
+            // q = 13
+            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);
+            dist[13*Np+n] = fq;
 
-		// q = 11
-		dist[11*Np+n] = f11*(1.0-rlx) + rlx*0.027777777777777776*rho*(1 + 3.*(ux + uz) + (4.5*(ux + uz)*(ux + uz))/porosity - (1.5*(ux*ux + uy*uy + uz*uz))/porosity)
-				+0.027777777777777776*rho*(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));
+            // q= 14
+            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);
+            dist[14*Np+n] = fq;
 
-		// q = 12
-		dist[12*Np+n] = f12*(1.0-rlx) + rlx*0.027777777777777776*rho*(1 + 3.*(-ux - uz) + (4.5*(-ux - uz)*(-ux - uz))/porosity - (1.5*(ux*ux + uy*uy + uz*uz))/porosity)
-				+0.027777777777777776*rho*(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));
+            // q = 15
+            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);
+            dist[15*Np+n] = fq;
 
-		// q = 13
-		dist[13*Np+n] = f13*(1.0-rlx) + rlx*0.027777777777777776*rho*(1 + 3.*(ux - uz) + (4.5*(ux - uz)*(ux - uz))/porosity - (1.5*(ux*ux + uy*uy + uz*uz))/porosity)
-				+0.027777777777777776*rho*(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));
+            // q = 16
+            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);
+            dist[16*Np+n] = fq;
 
-		// q= 14
-		dist[14*Np+n] = f14*(1.0-rlx) + rlx*0.027777777777777776*rho*(1 + 3.*(-ux + uz) + (4.5*(-ux + uz)*(-ux + uz))/porosity - (1.5*(ux*ux + uy*uy + uz*uz))/porosity)
-				+0.027777777777777776*rho*(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));
+            // q = 17
+            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);
+            dist[17*Np+n] = fq;
 
-		// q = 15
-		dist[15*Np+n] = f15*(1.0-rlx) + rlx*0.027777777777777776*rho*(1 + 3.*(uy + uz) + (4.5*(uy + uz)*(uy + uz))/porosity - (1.5*(ux*ux + uy*uy + uz*uz))/porosity)
-				+0.027777777777777776*rho*(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));
+            // q = 18
+            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);
+            dist[18*Np+n] = fq;
+            //........................................................................
 
-		// q = 16
-		dist[16*Np+n] = f16*(1.0-rlx) + rlx*0.027777777777777776*rho*(1 + 3.*(-uy - uz) + (4.5*(-uy - uz)*(-uy - uz))/porosity - (1.5*(ux*ux + uy*uy + uz*uz))/porosity)
-				+0.027777777777777776*rho*(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));
-
-		// q = 17
-		dist[17*Np+n] = f17*(1.0-rlx) + rlx*0.027777777777777776*rho*(1 + 3.*(uy - uz) + (4.5*(uy - uz)*(uy - uz))/porosity - (1.5*(ux*ux + uy*uy + uz*uz))/porosity)
-				+0.027777777777777776*rho*(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));
-
-		// q = 18
-		dist[18*Np+n] = f18*(1.0-rlx) + rlx*0.027777777777777776*rho*(1 + 3.*(-uy + uz) + (4.5*(-uy + uz)*(-uy + uz))/porosity - (1.5*(ux*ux + uy*uy + uz*uz))/porosity)
-				+0.027777777777777776*rho*(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));
-
-        //Update velocity on device
-		Velocity[0*Np+n] = ux;
-		Velocity[1*Np+n] = uy;
-		Velocity[2*Np+n] = uz;
+            //Update velocity on device
+            Velocity[0*Np+n] = ux;
+            Velocity[1*Np+n] = uy;
+            Velocity[2*Np+n] = uz;
 
 		}
 	}
 }
 
 
+__global__ void dvc_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 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;
+
+	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];
+            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*(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)
+                    + (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)
+                    + (1-0.5*rlx_setB)*(-0.6666666666666666*Fx);
+            jy = jy + Fy;
+            m6 = m6 + rlx_setB*((-0.6666666666666666*uy*Den) - m6)
+                    + (1-0.5*rlx_setB)*(-0.6666666666666666*Fy);
+            jz = jz + Fz;
+            m8 = m8 + rlx_setB*((-0.6666666666666666*uz*Den) - m8)
+                    + (1-0.5*rlx_setB)*(-0.6666666666666666*Fz);
+            m9 = m9 + rlx_setA*((Den*(2*ux*ux-uy*uy-uz*uz)/porosity) - m9)
+                    + (1-0.5*rlx_setA)*(4*Fx*ux-2*Fy*uy-2*Fz*uz)/porosity;
+            m10 = m10 + rlx_setA*(-0.5*Den*((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*((Den*(uy*uy-uz*uz)/porosity) - m11)
+                      + (1-0.5*rlx_setA)*(2*Fy*uy-2*Fz*uz)/porosity;
+            m12 = m12 + rlx_setA*(-0.5*(Den*(uy*uy-uz*uz)/porosity)- m12)
+                      + (1-0.5*rlx_setA)*(-Fy*uy+Fz*uz)/porosity;
+            m13 = m13 + rlx_setA*((Den*ux*uy/porosity) - m13)
+                      + (1-0.5*rlx_setA)*(Fy*ux+Fx*uy)/porosity;
+            m14 = m14 + rlx_setA*((Den*uy*uz/porosity) - m14)
+                      + (1-0.5*rlx_setA)*(Fz*uy+Fy*uz)/porosity;
+            m15 = m15 + rlx_setA*((Den*ux*uz/porosity) - 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*Den-mrt_V2*m1+mrt_V3*m2;
+            dist[n] = fq;
+
+            // q = 1
+            fq = mrt_V1*Den-mrt_V4*m1-mrt_V5*m2+0.1*(jx-m4)+mrt_V6*(m9-m10);
+            nread = neighborList[n+Np];
+            dist[nread] = fq;
+
+            // q=2
+            fq = mrt_V1*Den-mrt_V4*m1-mrt_V5*m2+0.1*(m4-jx)+mrt_V6*(m9-m10);
+            nread = neighborList[n];
+            dist[nread] = fq;
+
+            // q = 3
+            fq = mrt_V1*Den-mrt_V4*m1-mrt_V5*m2+0.1*(jy-m6)+mrt_V7*(m10-m9)+mrt_V8*(m11-m12);
+            nread = neighborList[n+3*Np];
+            dist[nread] = fq;
+
+            // q = 4
+            fq = mrt_V1*Den-mrt_V4*m1-mrt_V5*m2+0.1*(m6-jy)+mrt_V7*(m10-m9)+mrt_V8*(m11-m12);
+            nread = neighborList[n+2*Np];
+            dist[nread] = fq;
+
+            // q = 5
+            fq = mrt_V1*Den-mrt_V4*m1-mrt_V5*m2+0.1*(jz-m8)+mrt_V7*(m10-m9)+mrt_V8*(m12-m11);
+            nread = neighborList[n+5*Np];
+            dist[nread] = fq;
+
+            // q = 6
+            fq = mrt_V1*Den-mrt_V4*m1-mrt_V5*m2+0.1*(m8-jz)+mrt_V7*(m10-m9)+mrt_V8*(m12-m11);
+            nread = neighborList[n+4*Np];
+            dist[nread] = fq;
+
+            // q = 7
+            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);
+            nread = neighborList[n+7*Np];
+            dist[nread] = fq;
+
+            // q = 8
+            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);
+            nread = neighborList[n+6*Np];
+            dist[nread] = fq;
+
+            // q = 9
+            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);
+            nread = neighborList[n+9*Np];
+            dist[nread] = fq;
+
+            // q = 10
+            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);
+            nread = neighborList[n+8*Np];
+            dist[nread] = fq;
+
+            // q = 11
+            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);
+            nread = neighborList[n+11*Np];
+            dist[nread] = fq;
+
+            // q = 12
+            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);
+            nread = neighborList[n+10*Np];
+            dist[nread]= fq;
+
+            // q = 13
+            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);
+            nread = neighborList[n+13*Np];
+            dist[nread] = fq;
+
+            // q= 14
+            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);
+            nread = neighborList[n+12*Np];
+            dist[nread] = fq;
+
+            // q = 15
+            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);
+            nread = neighborList[n+15*Np];
+            dist[nread] = fq;
+
+            // q = 16
+            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);
+            nread = neighborList[n+14*Np];
+            dist[nread] = fq;
+
+            // q = 17
+            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);
+            nread = neighborList[n+17*Np];
+            dist[nread] = fq;
+
+            // q = 18
+            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);
+            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;
+
+		}
+	}
+}
+
 
 extern "C" void ScaLBL_D3Q19_AAeven_Greyscale(double *dist, int start, int finish, int Np, double rlx, double Fx, double Fy, double Fz,double *Poros,double *Perm, double *Velocity){
 	
@@ -873,6 +1378,7 @@ 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){
+
     dvc_ScaLBL_D3Q19_AAodd_Greyscale<<<NBLOCKS,NTHREADS >>>(neighborList,dist,start,finish,Np,rlx,Fx,Fy,Fz,Poros,Perm,Velocity);
 
     cudaError_t err = cudaGetLastError();
@@ -880,3 +1386,24 @@ extern "C" void ScaLBL_D3Q19_AAodd_Greyscale(int *neighborList, double *dist, in
 		printf("CUDA error in ScaLBL_D3Q19_AAodd_Greyscale: %s \n",cudaGetErrorString(err));
 	}
 }
+
+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){
+	
+    dvc_ScaLBL_D3Q19_AAeven_Greyscale_IMRT<<<NBLOCKS,NTHREADS >>>(dist,start,finish,Np,rlx,Fx,Fy,Fz,Poros,Perm,Velocity,Den);
+
+    cudaError_t err = cudaGetLastError();
+	if (cudaSuccess != err){
+		printf("CUDA error in ScaLBL_D3Q19_AAeven_Greyscale_IMRT: %s \n",cudaGetErrorString(err));
+	}
+}
+
+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){
+
+    dvc_ScaLBL_D3Q19_AAodd_Greyscale_IMRT<<<NBLOCKS,NTHREADS >>>(neighborList,dist,start,finish,Np,rlx,Fx,Fy,Fz,Poros,Perm,Velocity,Den);
+
+    cudaError_t err = cudaGetLastError();
+	if (cudaSuccess != err){
+		printf("CUDA error in ScaLBL_D3Q19_AAodd_Greyscale_IMRT: %s \n",cudaGetErrorString(err));
+	}
+}
+