OilfieldToolsNet/LBPM
4
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity
Files
e22de8ae7e8f6bb393df15e2482078b5be48b42b
LBPM/cpu/FreeLee.cpp
Rex Zhe Li e22de8ae7e save the work;to be built and tested
2021-01-31 19:06:07 -05:00

3385 lines
144 KiB
C++
Raw Blame History

#include <math.h>
#define STOKES
extern "C" void ScaLBL_D3Q19_FreeLeeModel_Init(double *gqbar, double *mu_phi, double *ColorGrad, double Fx, double Fy, double Fz, int Np)
{
int n;
double p = 1.0;//NOTE: take initial pressure p=1.0
for (n=0; n<Np; n++){
chem = mu_phi[n];//chemical potential
cg_x = ColorGrad[0*Np+n];
cg_y = ColorGrad[1*Np+n];
cg_z = ColorGrad[2*Np+n];
gqbar[0*Np+n] = 0.3333333333333333;
gqbar[1*Np+n] = 0.055555555555555555*(p - 0.5*(chem*cg_x+Fx)); //double(100*n)+1.f;
gqbar[2*Np+n] = 0.055555555555555555*(p - 0.5*(-chem*cg_x-Fx)); //double(100*n)+2.f;
gqbar[3*Np+n] = 0.055555555555555555*(p - 0.5*(chem*cg_y+Fy)); //double(100*n)+3.f;
gqbar[4*Np+n] = 0.055555555555555555*(p - 0.5*(-chem*cg_y-Fy)); //double(100*n)+4.f;
gqbar[5*Np+n] = 0.055555555555555555*(p - 0.5*(chem*cg_z+Fz)); //double(100*n)+5.f;
gqbar[6*Np+n] = 0.055555555555555555*(p - 0.5*(-chem*cg_z-Fz)); //double(100*n)+6.f;
gqbar[7*Np+n] = 0.0277777777777778*(p-0.5*(chem*(cg_x+cg_y)+Fx+Fy)); //double(100*n)+7.f;
gqbar[8*Np+n] = 0.0277777777777778*(p-0.5*(chem*(-cg_x-cg_y)-Fx-Fy)); //double(100*n)+8.f;
gqbar[9*Np+n] = 0.0277777777777778*(p-0.5*(chem*(cg_x-cg_y)+Fx-Fy)); //double(100*n)+9.f;
gqbar[10*Np+n] = 0.0277777777777778*(p-0.5*(chem*(-cg_x+cg_y)-Fx+Fy)); //double(100*n)+10.f;
gqbar[11*Np+n] = 0.0277777777777778*(p-0.5*(chem*(cg_x+cg_z)+Fx+Fz)); //double(100*n)+11.f;
gqbar[12*Np+n] = 0.0277777777777778*(p-0.5*(chem*(-cg_x-cg_z)-Fx-Fz)); //double(100*n)+12.f;
gqbar[13*Np+n] = 0.0277777777777778*(p-0.5*(chem*(cg_x-cg_z)+Fx-Fz)); //double(100*n)+13.f;
gqbar[14*Np+n] = 0.0277777777777778*(p-0.5*(chem*(-cg_x+cg_z)-Fx+Fz)); //double(100*n)+14.f;
gqbar[15*Np+n] = 0.0277777777777778*(p-0.5*(chem*(cg_y+cg_z)+Fy+Fz)); ; //double(100*n)+15.f;
gqbar[16*Np+n] = 0.0277777777777778*(p-0.5*(chem*(-cg_y-cg_z)-Fy-Fz));; //double(100*n)+16.f;
gqbar[17*Np+n] = 0.0277777777777778*(p-0.5*(chem*(cg_y-cg_z)+Fy-Fz)); ; //double(100*n)+17.f;
gqbar[18*Np+n] = 0.0277777777777778*(p-0.5*(chem*(-cg_y+cg_z)-Fy+Fz));; //double(100*n)+18.f;
}
}
extern "C" void ScaLBL_FreeLeeModel_PhaseField_Init(int *Map, double *Phi, double *Den, double *hq, double *ColorGrad,
double rhonA, double rhoB, double tauM, double W, int start, int finish, int Np){
int idx,n;
double phi;
double nx,ny,nz,cg_mag;
double theta;//anti-diffusion term
double cs2_inv = 4.5;//inverse of speed of sound for D3Q7
double M = 1.0/cs2_inv*(tauM-0.5);//diffusivity (or mobility)
for (idx=start; idx<finish; idx++){
n = Map[idx];
phi = Phi[n];
if (phi > 1.f) phi = 1.0;
if (phi < -1.f) phi = -1.0;
Den[idx] = rhoA + 0.5*(1.0-phi)*(rhoB-rhoA);
//compute unit normal of color gradient
nx = ColorGrad[idx+0*Np];
ny = ColorGrad[idx+1*Np];
nz = ColorGrad[idx+2*Np];
cg_mag = sqrt(nx*nx+ny*ny+nz*nz);
double ColorMag_temp = cg_mag;
if (cg_mag==0.0) ColorMag_temp=1.0;
nx = nx/ColorMag_temp;
ny = ny/ColorMag_temp;
nz = nz/ColorMag_temp;
theta = M*cs2_inv*(1-4.0*phi*phi)/W;
hq[0*Np+idx]=0.3333333333333333*(phi);
hq[1*Np+idx]=0.1111111111111111*(phi+theta*nx);
hq[2*Np+idx]=0.1111111111111111*(phi-theta*nx);
hq[3*Np+idx]=0.1111111111111111*(phi+theta*ny);
hq[4*Np+idx]=0.1111111111111111*(phi-theta*ny);
hq[5*Np+idx]=0.1111111111111111*(phi+theta*nz);
hq[6*Np+idx]=0.1111111111111111*(phi-theta*nz);
}
}
extern "C" void ScaLBL_D3Q7_AAodd_FreeLeeModel_PhaseField(int *neighborList, int *Map, double *hq, double *Den, double *Phi,
double rhoA, double rhoB, int start, int finish, int Np){
int idx,n,nread;
double fq,phi;
for (int n=start; n<finish; n++){
// q=0
fq = hq[n];
phi = fq;
// q=1
nread = neighborList[n];
fq = hq[nread];
phi += fq;
// q=2
nread = neighborList[n+Np];
fq = hq[nread];
phi += fq;
// q=3
nread = neighborList[n+2*Np];
fq = hq[nread];
phi += fq;
// q = 4
nread = neighborList[n+3*Np];
fq = hq[nread];
phi += fq;
// q=5
nread = neighborList[n+4*Np];
fq = hq[nread];
phi += fq;
// q = 6
nread = neighborList[n+5*Np];
fq = hq[nread];
phi += fq;
// save the number densities
Den[n] = rhoA + 0.5*(1.0-phi)*(rhoB-rhoA);
// save the phase indicator field
idx = Map[n];
Phi[idx] = phi;
}
}
extern "C" void ScaLBL_D3Q7_AAeven_FreeLeeModel_PhaseField(int *Map, double *hq, double *Den, double *Phi,
double rhoA, double rhoB, int start, int finish, int Np){
int idx,n;
double fq,phi;
for (int n=start; n<finish; n++){
// q=0
fq = hq[n];
phi = fq;
// q=1
fq = hq[2*Np+n];
phi += fq;
// f2 = hq[10*Np+n];
fq = hq[1*Np+n];
phi += fq;
// q=3
fq = hq[4*Np+n];
phi += fq;
// q = 4
fq = hq[3*Np+n];
phi += fq;
// q=5
fq = hq[6*Np+n];
phi += fq;
// q = 6
fq = hq[5*Np+n];
phi += fq;
// save the number densities
Den[n] = rhoA + 0.5*(1.0-phi)*(rhoB-rhoA);
// save the phase indicator field
idx = Map[n];
Phi[idx] = phi;
}
}
extern "C" void ScaLBL_D3Q19_AAodd_FreeLeeModel(int *neighborList, int *Map, double *dist, double *hq, double *Den, double *Phi, double *mu_phi, double *Vel, double *Pressure,
double rhoA, double rhoB, double tauA, double tauB, double tauM, double kappa, double beta, double W, double Fx, double Fy, double Fz,
int strideY, int strideZ, int start, int finish, int Np){
int n,nn,nn2x,ijk;
int nr1,nr2,nr3,nr4,nr5,nr6,nr7,nr8,nr9,nr10,nr11,nr12,nr13,nr14,nr15,nr16,nr17,nr18;
double ux,uy,uz;//fluid velocity
double p;//pressure
double chem;//chemical potential
double phi; //phase field
double rho0;//fluid density
// distribution functions
double m1,m2,m4,m6,m8,m9,m10,m11,m12,m13,m14,m15,m16,m17,m18;
double m0,m3,m5,m7;
double mm1,mm2,mm4,mm6,mm8,mm9,mm10,mm11,mm12,mm13,mm14,mm15,mm16,mm17,mm18;
double mm3,mm5,mm7;
double feq0,feq1,feq2,feq3,feq4,feq5,feq6,feq7,feq8,feq9,feq10,feq11,feq12,feq13,feq14,feq15,feq16,feq17,feq18;
double nx,ny,nz;//normal color gradient
double mgx,mgy,mgz;//mixed gradient reaching secondary neighbor
//double f0,f1,f2,f3,f4,f5,f6,f7,f8,f9,f10,f11,f12,f13,f14,f15,f16,f17,f18;
double h0,h1,h2,h3,h4,h5,h6;//distributions for LB phase field
double tau;//position dependent LB relaxation time for fluid
double C,theta;
double M = 2.0/9.0*(tauM-0.5);//diffusivity (or mobility) for the phase field D3Q7
for (int n=start; n<finish; n++){
rho0 = Den[n];//load density
phi = Phi[n];// load phase field
// local relaxation time
tau=tauA + 0.5*(1.0-phi)*(tauB-tauA);
// Get the 1D index based on regular data layout
ijk = Map[n];
// COMPUTE THE COLOR GRADIENT
//........................................................................
//.................Read Phase Indicator Values............................
//........................................................................
nn = ijk-1; // neighbor index (get convention)
m1 = Phi[nn]; // get neighbor for phi - 1
//........................................................................
nn = ijk+1; // neighbor index (get convention)
m2 = Phi[nn]; // get neighbor for phi - 2
//........................................................................
nn = ijk-strideY; // neighbor index (get convention)
m3 = Phi[nn]; // get neighbor for phi - 3
//........................................................................
nn = ijk+strideY; // neighbor index (get convention)
m4 = Phi[nn]; // get neighbor for phi - 4
//........................................................................
nn = ijk-strideZ; // neighbor index (get convention)
m5 = Phi[nn]; // get neighbor for phi - 5
//........................................................................
nn = ijk+strideZ; // neighbor index (get convention)
m6 = Phi[nn]; // get neighbor for phi - 6
//........................................................................
nn = ijk-strideY-1; // neighbor index (get convention)
m7 = Phi[nn]; // get neighbor for phi - 7
//........................................................................
nn = ijk+strideY+1; // neighbor index (get convention)
m8 = Phi[nn]; // get neighbor for phi - 8
//........................................................................
nn = ijk+strideY-1; // neighbor index (get convention)
m9 = Phi[nn]; // get neighbor for phi - 9
//........................................................................
nn = ijk-strideY+1; // neighbor index (get convention)
m10 = Phi[nn]; // get neighbor for phi - 10
//........................................................................
nn = ijk-strideZ-1; // neighbor index (get convention)
m11 = Phi[nn]; // get neighbor for phi - 11
//........................................................................
nn = ijk+strideZ+1; // neighbor index (get convention)
m12 = Phi[nn]; // get neighbor for phi - 12
//........................................................................
nn = ijk+strideZ-1; // neighbor index (get convention)
m13 = Phi[nn]; // get neighbor for phi - 13
//........................................................................
nn = ijk-strideZ+1; // neighbor index (get convention)
m14 = Phi[nn]; // get neighbor for phi - 14
//........................................................................
nn = ijk-strideZ-strideY; // neighbor index (get convention)
m15 = Phi[nn]; // get neighbor for phi - 15
//........................................................................
nn = ijk+strideZ+strideY; // neighbor index (get convention)
m16 = Phi[nn]; // get neighbor for phi - 16
//........................................................................
nn = ijk+strideZ-strideY; // neighbor index (get convention)
m17 = Phi[nn]; // get neighbor for phi - 17
//........................................................................
nn = ijk-strideZ+strideY; // neighbor index (get convention)
m18 = Phi[nn]; // get neighbor for phi - 18
// compute mixed difference (Eq.30, A.Fukhari et al. JCP 315(2016) 434-457)
//........................................................................
nn2x = ijk-2; // neighbor index (get convention)
mm1 = Phi[nn2x]; // get neighbor for phi - 1
mm1 = 0.25*(-mm1+5.0*m1-3.0*phi-m2);
//........................................................................
nn2x = ijk+2; // neighbor index (get convention)
mm2 = Phi[nn2x]; // get neighbor for phi - 2
mm2 = 0.25*(-mm2+5.0*m2-3.0*phi-m1);
//........................................................................
nn2x = ijk-strideY*2; // neighbor index (get convention)
mm3 = Phi[nn2x]; // get neighbor for phi - 3
mm3 = 0.25*(-mm3+5.0*m3-3.0*phi-m4);
//........................................................................
nn2x = ijk+strideY*2; // neighbor index (get convention)
mm4 = Phi[nn2x]; // get neighbor for phi - 4
mm4 = 0.25*(-mm4+5.0*m4-3.0*phi-m3);
//........................................................................
nn2x = ijk-strideZ*2; // neighbor index (get convention)
mm5 = Phi[nn2x]; // get neighbor for phi - 5
mm5 = 0.25*(-mm5+5.0*m5-3.0*phi-m6);
//........................................................................
nn2x = ijk+strideZ*2; // neighbor index (get convention)
mm6 = Phi[nn2x]; // get neighbor for phi - 6
mm6 = 0.25*(-mm6+5.0*m6-3.0*phi-m5);
//........................................................................
nn2x = ijk-strideY*2-2; // neighbor index (get convention)
mm7 = Phi[nn2x]; // get neighbor for phi - 7
mm7 = 0.25*(-mm7+5.0*m7-3.0*phi-m8);
//........................................................................
nn2x = ijk+strideY*2+2; // neighbor index (get convention)
mm8 = Phi[nn2x]; // get neighbor for phi - 8
mm8 = 0.25*(-mm8+5.0*m8-3.0*phi-m7);
//........................................................................
nn2x = ijk+strideY*2-2; // neighbor index (get convention)
mm9 = Phi[nn2x]; // get neighbor for phi - 9
mm9 = 0.25*(-mm9+5.0*m9-3.0*phi-m10);
//........................................................................
nn2x = ijk-strideY*2+2; // neighbor index (get convention)
mm10 = Phi[nn2x]; // get neighbor for phi - 10
mm10 = 0.25*(-mm10+5.0*m10-3.0*phi-m9);
//........................................................................
nn2x = ijk-strideZ*2-2; // neighbor index (get convention)
mm11 = Phi[nn2x]; // get neighbor for phi - 11
mm11 = 0.25*(-mm11+5.0*m11-3.0*phi-m12);
//........................................................................
nn2x = ijk+strideZ*2+2; // neighbor index (get convention)
mm12 = Phi[nn2x]; // get neighbor for phi - 12
mm12 = 0.25*(-mm12+5.0*m12-3.0*phi-m11);
//........................................................................
nn2x = ijk+strideZ*2-2; // neighbor index (get convention)
mm13 = Phi[nn2x]; // get neighbor for phi - 13
mm13 = 0.25*(-mm13+5.0*m13-3.0*phi-m14);
//........................................................................
nn2x = ijk-strideZ*2+2; // neighbor index (get convention)
mm14 = Phi[nn2x]; // get neighbor for phi - 14
mm14 = 0.25*(-mm14+5.0*m14-3.0*phi-m13);
//........................................................................
nn2x = ijk-strideZ*2-strideY*2; // neighbor index (get convention)
mm15 = Phi[nn2x]; // get neighbor for phi - 15
mm15 = 0.25*(-mm15+5.0*m15-3.0*phi-m16);
//........................................................................
nn2x = ijk+strideZ*2+strideY*2; // neighbor index (get convention)
mm16 = Phi[nn2x]; // get neighbor for phi - 16
mm16 = 0.25*(-mm16+5.0*m16-3.0*phi-m15);
//........................................................................
nn2x = ijk+strideZ*2-strideY*2; // neighbor index (get convention)
mm17 = Phi[nn2x]; // get neighbor for phi - 17
mm17 = 0.25*(-mm17+5.0*m17-3.0*phi-m18);
//........................................................................
nn2x = ijk-strideZ*2+strideY*2; // neighbor index (get convention)
mm18 = Phi[nn2x]; // get neighbor for phi - 18
mm18 = 0.25*(-mm18+5.0*m18-3.0*phi-m17);
//............Compute the Color Gradient...................................
nx = -3.0*1.0/18.0*(m1-m2+0.5*(m7-m8+m9-m10+m11-m12+m13-m14));
ny = -3.0*1.0/18.0*(m3-m4+0.5*(m7-m8-m9+m10+m15-m16+m17-m18));
nz = -3.0*1.0/18.0*(m5-m6+0.5*(m11-m12-m13+m14+m15-m16-m17+m18));
//............Compute the Chemical Potential...............................
chem = 2.0*3.0/18.0*(m1+m2+m3+m4+m5+m6-6*phi+0.5*(m7+m8+m9+m10+m11+m12+m13+m14+m15+m16+m17+m18-12*phi));//intermediate var, i.e. the laplacian
chem = 4.0*beta*phi*(phi+1.0)*(phi-1.0)-kappa*chem;
//............Compute the Mixed Gradient...................................
mgx = -3.0*1.0/18.0*(mm1-mm2+0.5*(mm7-mm8+mm9-mm10+mm11-mm12+mm13-mm14))*0.25;//the factor of 0.25 comes from the denominator of Eq.30
mgy = -3.0*1.0/18.0*(mm3-mm4+0.5*(mm7-mm8-mm9+mm10+mm15-mm16+mm17-mm18))*0.25;
mgz = -3.0*1.0/18.0*(mm5-mm6+0.5*(mm11-mm12-mm13+mm14+mm15-mm16-mm17+mm18))*0.25;
// q=0
m0 = dist[n];
// q=1
nr1 = neighborList[n]; // neighbor 2 ( > 10Np => odd part of dist)
m1 = dist[nr1]; // reading the f1 data into register fq
nr2 = neighborList[n+Np]; // neighbor 1 ( < 10Np => even part of dist)
m2 = dist[nr2]; // reading the f2 data into register fq
// q=3
nr3 = neighborList[n+2*Np]; // neighbor 4
m3 = dist[nr3];
// q = 4
nr4 = neighborList[n+3*Np]; // neighbor 3
m4 = dist[nr4];
// q=5
nr5 = neighborList[n+4*Np];
m5 = dist[nr5];
// q = 6
nr6 = neighborList[n+5*Np];
m6 = dist[nr6];
// q=7
nr7 = neighborList[n+6*Np];
m7 = dist[nr7];
// q = 8
nr8 = neighborList[n+7*Np];
m8 = dist[nr8];
// q=9
nr9 = neighborList[n+8*Np];
m9 = dist[nr9];
// q = 10
nr10 = neighborList[n+9*Np];
m10 = dist[nr10];
// q=11
nr11 = neighborList[n+10*Np];
m11 = dist[nr11];
// q=12
nr12 = neighborList[n+11*Np];
m12 = dist[nr12];
// q=13
nr13 = neighborList[n+12*Np];
m13 = dist[nr13];
// q=14
nr14 = neighborList[n+13*Np];
m14 = dist[nr14];
// q=15
nr15 = neighborList[n+14*Np];
m15 = dist[nr15];
// q=16
nr16 = neighborList[n+15*Np];
m16 = dist[nr16];
// q=17
nr17 = neighborList[n+16*Np];
m17 = dist[nr17];
// q=18
nr18 = neighborList[n+17*Np];
m18 = dist[nr18];
//compute fluid velocity
ux = 3.0/rho0*(m1-m2+m7-m8+m9-m10+m11-m12+m13-m14+0.5*(chem*nx+Fx));
uy = 3.0/rho0*(m3-m4+m7-m8-m9+m10+m15-m16+m17-m18+0.5*(chem*ny+Fy));
uz = 3.0/rho0*(m5-m6+m11-m12-m13+m14+m15-m16-m17+m18+0.5*(chem*nz+Fz));
//compute pressure
p = (m0+m2+m1+m4+m3+m6+m5+m8+m7+m10+m9+m12+m11+m14+m13+m16+m15+m18+m17)
+0.5*(rhoA-rhoB)/2.0/3.0*(ux*nx+uy*ny+uz*nz);
//compute equilibrium distributions
feq0 = 0.3333333333333333*p - 0.25*(Fx*ux + Fy*uy + Fz*uz)*(-0.6666666666666666 + ux*ux + uy*uy + uz*uz) -
0.16666666666666666*rho0*(ux*ux + uy*uy + uz*uz) - 0.5*(-(nx*ux) - ny*uy - nz*uz)*
(-0.08333333333333333*(rhoA - rhoB)*(ux*ux + uy*uy + uz*uz) + chem*(0.3333333333333333 - 0.5*(ux*ux + uy*uy + uz*uz)));
feq1 = 0.05555555555555555*p - 0.08333333333333333*rho0*(-ux*ux + 0.3333333333333333*(-2*ux + ux*ux + uy*uy + uz*uz)) -
0.125*(Fx*(-1. + ux) + Fy*uy + Fz*uz)*(-0.2222222222222222 - 1.*ux*ux +
0.3333333333333333*(-2.*ux + ux*ux + uy*uy + uz*uz)) - 0.0625*(nx - nx*ux - ny*uy - nz*uz)*
(2*chem*ux*ux - 0.3333333333333333*((-rhoA + rhoB)*ux*ux + 2*chem*(-2*ux + ux*ux + uy*uy + uz*uz)) +
0.1111111111111111*(4*chem - (rhoA - rhoB)*(-2*ux + ux*ux + uy*uy + uz*uz)));
feq2 = 0.05555555555555555*p - 0.08333333333333333*rho0*(-ux*ux + 0.3333333333333333*(2*ux + ux*ux + uy*uy + uz*uz)) -
0.125*(Fx + Fx*ux + Fy*uy + Fz*uz)*(-0.2222222222222222 - 1.*ux*ux +
0.3333333333333333*(2.*ux + ux*ux + uy*uy + uz*uz)) - 0.0625*(nx + nx*ux + ny*uy + nz*uz)*
(-2.*chem*ux*ux + 0.1111111111111111*(-4.*chem + rhoB*(-2.*ux - 1.*ux*ux - 1.*uy*uy - 1.*uz*uz) +
rhoA*(2.*ux + ux*ux + uy*uy + uz*uz)) + 0.3333333333333333*((-1.*rhoA + rhoB)*ux*ux +
chem*(4.*ux + 2.*ux*ux + 2.*uy*uy + 2.*uz*uz)));
feq3 = 0.05555555555555555*p - 0.08333333333333333*rho0*(-uy*uy + 0.3333333333333333*(ux*ux - 2*uy + uy*uy + uz*uz)) -
0.125*(Fx*ux + Fy*(-1. + uy) + Fz*uz)*(-0.2222222222222222 - 1.*uy*uy +
0.3333333333333333*(ux*ux - 2.*uy + uy*uy + uz*uz)) - 0.0625*(ny - nx*ux - ny*uy - nz*uz)*
(2*chem*uy*uy - 0.3333333333333333*((-rhoA + rhoB)*uy*uy + 2*chem*(ux*ux - 2*uy + uy*uy + uz*uz)) +
0.1111111111111111*(4*chem - (rhoA - rhoB)*(ux*ux - 2*uy + uy*uy + uz*uz)));
feq4 = 0.05555555555555555*p - 0.08333333333333333*rho0*(-uy*uy + 0.3333333333333333*(ux*ux + 2*uy + uy*uy + uz*uz)) -
0.125*(Fy + Fx*ux + Fy*uy + Fz*uz)*(-0.2222222222222222 - 1.*uy*uy +
0.3333333333333333*(ux*ux + 2.*uy + uy*uy + uz*uz)) - 0.0625*(ny + nx*ux + ny*uy + nz*uz)*
(-2.*chem*uy*uy + 0.1111111111111111*(-4.*chem + rhoB*(-1.*ux*ux - 2.*uy - 1.*uy*uy - 1.*uz*uz) +
rhoA*(ux*ux + 2.*uy + uy*uy + uz*uz)) + 0.3333333333333333*((-1.*rhoA + rhoB)*uy*uy +
chem*(2.*ux*ux + 4.*uy + 2.*uy*uy + 2.*uz*uz)));
feq5 = 0.05555555555555555*p - 0.08333333333333333*rho0*(-uz*uz + 0.3333333333333333*(ux*ux + uy*uy + (-2 + uz)*uz)) -
0.125*(Fx*ux + Fy*uy + Fz*(-1. + uz))*(-0.2222222222222222 - 1.*uz*uz +
0.3333333333333333*(ux*ux + uy*uy + (-2. + uz)*uz)) - 0.0625*(nx*ux + ny*uy + nz*(-1. + uz))*
(-2.*chem*uz*uz + 0.1111111111111111*(-4.*chem + rhoB*(-1.*ux*ux - 1.*uy*uy + (2. - 1.*uz)*uz) +
rhoA*(ux*ux + uy*uy + (-2. + uz)*uz)) + 0.3333333333333333*((-1.*rhoA + rhoB)*uz*uz +
chem*(2.*ux*ux + 2.*uy*uy + uz*(-4. + 2.*uz))));
feq6 = 0.05555555555555555*p - 0.08333333333333333*rho0*(-uz*uz + 0.3333333333333333*(ux*ux + uy*uy + uz*(2 + uz))) -
0.125*(Fz + Fx*ux + Fy*uy + Fz*uz)*(-0.2222222222222222 - 1.*uz*uz +
0.3333333333333333*(ux*ux + uy*uy + uz*(2. + uz))) - 0.0625*(nz + nx*ux + ny*uy + nz*uz)*
(-2.*chem*uz*uz + 0.1111111111111111*(-4.*chem + rhoB*(-1.*ux*ux - 1.*uy*uy + (-2. - 1.*uz)*uz) +
rhoA*(ux*ux + uy*uy + uz*(2. + uz))) + 0.3333333333333333*((-1.*rhoA + rhoB)*uz*uz +
chem*(2.*ux*ux + 2.*uy*uy + uz*(4. + 2.*uz))));
feq7 = 0.027777777777777776*p - 0.041666666666666664*rho0*
(-(ux + uy)*(ux + uy) + 0.3333333333333333*(-2*ux + ux*ux - 2*uy + uy*uy + uz*uz)) -
0.0625*(Fx*(-1. + ux) + Fy*(-1. + uy) + Fz*uz)*(-0.2222222222222222 - 1.*ux*ux - 2.*ux*uy - 1.*uy*uy +
0.3333333333333333*(-2.*ux + ux*ux - 2.*uy + uy*uy + uz*uz)) - 0.03125*(nx + ny - nx*ux - ny*uy - nz*uz)*
(2*chem*(ux + uy)*(ux + uy) + 0.3333333333333333*((rhoA - rhoB)*(ux + uy)*(ux + uy) - 2*chem*(-2*ux + ux*ux - 2*uy + uy*uy + uz*uz)) +
0.1111111111111111*(4*chem - (rhoA - rhoB)*(-2*ux + ux*ux - 2*uy + uy*uy + uz*uz)));
feq8 = 0.027777777777777776*p - 0.041666666666666664*rho0*
(-(ux + uy)*(ux + uy) + 0.3333333333333333*(2*ux + ux*ux + 2*uy + uy*uy + uz*uz)) -
0.0625*(Fx + Fy + Fx*ux + Fy*uy + Fz*uz)*(-0.2222222222222222 - 1.*ux*ux - 2.*ux*uy - 1.*uy*uy +
0.3333333333333333*(2.*ux + ux*ux + 2.*uy + uy*uy + uz*uz)) - 0.03125*(-(nx*(1 + ux)) - ny*(1 + uy) - nz*uz)*
(2*chem*(ux + uy)*(ux + uy) - 0.3333333333333333*(-((rhoA - rhoB)*(ux + uy)*(ux + uy)) +
2*chem*(2*ux + ux*ux + 2*uy + uy*uy + uz*uz)) + 0.1111111111111111*
(4*chem - (rhoA - rhoB)*(2*ux + ux*ux + 2*uy + uy*uy + uz*uz)));
feq9 = 0.027777777777777776*p - 0.041666666666666664*rho0*
(-(ux - uy)*(ux - uy) + 0.3333333333333333*(-2*ux + ux*ux + 2*uy + uy*uy + uz*uz)) -
0.0625*(Fy + Fx*(-1. + ux) + Fy*uy + Fz*uz)*(-0.2222222222222222 - 1.*ux*ux + 2.*ux*uy - 1.*uy*uy +
0.3333333333333333*(-2.*ux + ux*ux + 2.*uy + uy*uy + uz*uz)) - 0.03125*(nx - nx*ux - ny*(1 + uy) - nz*uz)*
(2*chem*(ux - uy)*(ux - uy) - 0.3333333333333333*(-((rhoA - rhoB)*(ux - uy)*(ux - uy)) +
2*chem*(-2*ux + ux*ux + 2*uy + uy*uy + uz*uz)) + 0.1111111111111111*
(4*chem - (rhoA - rhoB)*(-2*ux + ux*ux + 2*uy + uy*uy + uz*uz)));
feq10 = 0.027777777777777776*p - 0.041666666666666664*rho0*
(-(ux - uy)*(ux - uy) + 0.3333333333333333*(2*ux + ux*ux - 2*uy + uy*uy + uz*uz)) -
0.0625*(Fx*(1 + ux) + Fy*(-1. + uy) + Fz*uz)*(-0.2222222222222222 - 1.*ux*ux + 2.*ux*uy - 1.*uy*uy +
0.3333333333333333*(2.*ux + ux*ux - 2.*uy + uy*uy + uz*uz)) - 0.03125*(ny - nx*(1 + ux) - ny*uy - nz*uz)*
(2*chem*(ux - uy)*(ux - uy) - 0.3333333333333333*(-((rhoA - rhoB)*(ux - uy)*(ux - uy)) +
2*chem*(2*ux + ux*ux - 2*uy + uy*uy + uz*uz)) + 0.1111111111111111*
(4*chem - (rhoA - rhoB)*(2*ux + ux*ux - 2*uy + uy*uy + uz*uz)));
feq11 = 0.027777777777777776*p - 0.041666666666666664*rho0*
(-(ux + uz)*(ux + uz) + 0.3333333333333333*(-2*ux + ux*ux + uy*uy + (-2 + uz)*uz)) -
0.0625*(Fx*(-1. + ux) + Fy*uy + Fz*(-1. + uz))*(-0.2222222222222222 - 1.*ux*ux - 2.*ux*uz - 1.*uz*uz +
0.3333333333333333*(-2.*ux + ux*ux + uy*uy + (-2. + uz)*uz)) - 0.03125*(nx + nz - nx*ux - ny*uy - nz*uz)*
(2*chem*(ux + uz)*(ux + uz) + 0.3333333333333333*((rhoA - rhoB)*(ux + uz)*(ux + uz) - 2*chem*(-2*ux + ux*ux + uy*uy + (-2 + uz)*uz)) +
0.1111111111111111*(4*chem - (rhoA - rhoB)*(-2*ux + ux*ux + uy*uy + (-2 + uz)*uz)));
feq12 = 0.027777777777777776*p - 0.041666666666666664*rho0*
(-(ux + uz)*(ux + uz) + 0.3333333333333333*(2*ux + ux*ux + uy*uy + uz*(2 + uz))) -
0.0625*(Fx + Fz + Fx*ux + Fy*uy + Fz*uz)*(-0.2222222222222222 - 1.*ux*ux - 2.*ux*uz - 1.*uz*uz +
0.3333333333333333*(2.*ux + ux*ux + uy*uy + uz*(2. + uz))) - 0.03125*(-(nx*(1 + ux)) - ny*uy - nz*(1 + uz))*
(2*chem*(ux + uz)*(ux + uz) - 0.3333333333333333*(-((rhoA - rhoB)*(ux + uz)*(ux + uz)) +
2*chem*(2*ux + ux*ux + uy*uy + uz*(2 + uz))) + 0.1111111111111111*
(4*chem - (rhoA - rhoB)*(2*ux + ux*ux + uy*uy + uz*(2 + uz))));
feq13 = 0.027777777777777776*p - 0.041666666666666664*rho0*
(-(ux - uz)*(ux - uz) + 0.3333333333333333*(-2*ux + ux*ux + uy*uy + uz*(2 + uz))) -
0.0625*(Fz + Fx*(-1. + ux) + Fy*uy + Fz*uz)*(-0.2222222222222222 - 1.*ux*ux + 2.*ux*uz - 1.*uz*uz +
0.3333333333333333*(-2.*ux + ux*ux + uy*uy + uz*(2. + uz))) - 0.03125*(nx - nx*ux - ny*uy - nz*(1 + uz))*
(2*chem*(ux - uz)*(ux - uz) - 0.3333333333333333*(-((rhoA - rhoB)*(ux - uz)*(ux - uz)) +
2*chem*(-2*ux + ux*ux + uy*uy + uz*(2 + uz))) + 0.1111111111111111*
(4*chem - (rhoA - rhoB)*(-2*ux + ux*ux + uy*uy + uz*(2 + uz))));
feq14 = 0.027777777777777776*p - 0.041666666666666664*rho0*
(-(ux - uz)*(ux - uz) + 0.3333333333333333*(2*ux + ux*ux + uy*uy + (-2 + uz)*uz)) -
0.0625*(Fx*(1 + ux) + Fy*uy + Fz*(-1. + uz))*(-0.2222222222222222 - 1.*ux*ux + 2.*ux*uz - 1.*uz*uz +
0.3333333333333333*(2.*ux + ux*ux + uy*uy + (-2. + uz)*uz)) - 0.03125*(nz - nx*(1 + ux) - ny*uy - nz*uz)*
(2*chem*(ux - uz)*(ux - uz) - 0.3333333333333333*(-((rhoA - rhoB)*(ux - uz)*(ux - uz)) +
2*chem*(2*ux + ux*ux + uy*uy + (-2 + uz)*uz)) + 0.1111111111111111*
(4*chem - (rhoA - rhoB)*(2*ux + ux*ux + uy*uy + (-2 + uz)*uz)));
feq15 = 0.027777777777777776*p - 0.041666666666666664*rho0*
(-(uy + uz)*(uy + uz) + 0.3333333333333333*(ux*ux - 2*uy + uy*uy + (-2 + uz)*uz)) -
0.0625*(Fx*ux + Fy*(-1. + uy) + Fz*(-1. + uz))*(-0.2222222222222222 - 1.*uy*uy - 2.*uy*uz - 1.*uz*uz +
0.3333333333333333*(ux*ux - 2.*uy + uy*uy + (-2. + uz)*uz)) - 0.03125*(ny + nz - nx*ux - ny*uy - nz*uz)*
(2*chem*(uy + uz)*(uy + uz) + 0.3333333333333333*((rhoA - rhoB)*(uy + uz)*(uy + uz) - 2*chem*(ux*ux - 2*uy + uy*uy + (-2 + uz)*uz)) +
0.1111111111111111*(4*chem - (rhoA - rhoB)*(ux*ux - 2*uy + uy*uy + (-2 + uz)*uz)));
feq16 = 0.027777777777777776*p - 0.041666666666666664*rho0*
(-(uy + uz)*(uy + uz) + 0.3333333333333333*(ux*ux + 2*uy + uy*uy + uz*(2 + uz))) -
0.0625*(Fy + Fz + Fx*ux + Fy*uy + Fz*uz)*(-0.2222222222222222 - 1.*uy*uy - 2.*uy*uz - 1.*uz*uz +
0.3333333333333333*(ux*ux + 2.*uy + uy*uy + uz*(2. + uz))) - 0.03125*(-(nx*ux) - ny*(1 + uy) - nz*(1 + uz))*
(2*chem*(uy + uz)*(uy + uz) - 0.3333333333333333*(-((rhoA - rhoB)*(uy + uz)*(uy + uz)) +
2*chem*(ux*ux + 2*uy + uy*uy + uz*(2 + uz))) + 0.1111111111111111*
(4*chem - (rhoA - rhoB)*(ux*ux + 2*uy + uy*uy + uz*(2 + uz))));
feq17 = 0.027777777777777776*p - 0.041666666666666664*rho0*
(-(uy - uz)*(uy - uz) + 0.3333333333333333*(ux*ux - 2*uy + uy*uy + uz*(2 + uz))) -
0.0625*(Fz + Fx*ux + Fy*(-1. + uy) + Fz*uz)*(-0.2222222222222222 - 1.*uy*uy + 2.*uy*uz - 1.*uz*uz +
0.3333333333333333*(ux*ux - 2.*uy + uy*uy + uz*(2. + uz))) - 0.03125*(ny - nx*ux - ny*uy - nz*(1 + uz))*
(2*chem*(uy - uz)*(uy - uz) - 0.3333333333333333*(-((rhoA - rhoB)*(uy - uz)*(uy - uz)) +
2*chem*(ux*ux - 2*uy + uy*uy + uz*(2 + uz))) + 0.1111111111111111*
(4*chem - (rhoA - rhoB)*(ux*ux - 2*uy + uy*uy + uz*(2 + uz))));
feq18 = 0.027777777777777776*p - 0.041666666666666664*rho0*
(-(uy - uz)*(uy - uz) + 0.3333333333333333*(ux*ux + 2*uy + uy*uy + (-2 + uz)*uz)) -
0.0625*(Fx*ux + Fy*(1 + uy) + Fz*(-1. + uz))*(-0.2222222222222222 - 1.*uy*uy + 2.*uy*uz - 1.*uz*uz +
0.3333333333333333*(ux*ux + 2.*uy + uy*uy + (-2. + uz)*uz)) - 0.03125*(nz - nx*ux - ny*(1 + uy) - nz*uz)*
(2*chem*(uy - uz)*(uy - uz) - 0.3333333333333333*(-((rhoA - rhoB)*(uy - uz)*(uy - uz)) +
2*chem*(ux*ux + 2*uy + uy*uy + (-2 + uz)*uz)) + 0.1111111111111111*
(4*chem - (rhoA - rhoB)*(ux*ux + 2*uy + uy*uy + (-2 + uz)*uz)));
//------------------------------------------------- BCK collison ------------------------------------------------------------//
// q=0
dist[n] = m0 - (m0-feq0)/tau + 0.25*(-2*(Fx*ux + Fy*uy + Fz*uz)*(-0.6666666666666666 + ux*ux + uy*uy + uz*uz) +
(mgx*ux + mgy*uy + mgz*uz)*(2*chem*(ux*ux + uy*uy + uz*uz) + 0.3333333333333333*
(-4*chem + (rhoA - rhoB)*(ux*ux + uy*uy + uz*uz))));
// q = 1
dist[nr2] = m1 - (m1-feq1)/tau + 0.125*(2*(Fx*(-1 + ux) + Fy*uy + Fz*uz)*(0.2222222222222222 + ux*ux -
0.3333333333333333*(-2*ux + ux*ux + uy*uy + uz*uz)) + (mgx*(-1 + ux) + mgy*uy + mgz*uz)*
(-2*chem*ux*ux + 0.3333333333333333*((-rhoA + rhoB)*ux*ux + 2*chem*(-2*ux + ux*ux + uy*uy + uz*uz)) +
0.1111111111111111*(-4*chem + (rhoA - rhoB)*(-2*ux + ux*ux + uy*uy + uz*uz))));
// q=2
dist[nr1] = m2 - (m2-feq2)/tau + 0.125*(-2*(Fx + Fx*ux + Fy*uy + Fz*uz)*(-0.2222222222222222 - ux*ux + 0.3333333333333333*(2*ux + ux*ux + uy*uy + uz*uz)) +
(mgx + mgx*ux + mgy*uy + mgz*uz)*(-2*chem*ux*ux + 0.3333333333333333*((-rhoA + rhoB)*ux*ux +
2*chem*(2*ux + ux*ux + uy*uy + uz*uz)) + 0.1111111111111111*(-4*chem + (rhoA - rhoB)*(2*ux + ux*ux + uy*uy + uz*uz))));
// q = 3
dist[nr4] = m3 - (m3-feq3)/tau + 0.125*(2*(Fx*ux + Fy*(-1 + uy) + Fz*uz)*(0.2222222222222222 + uy*uy - 0.3333333333333333*(ux*ux - 2*uy + uy*uy + uz*uz)) +
(mgx*ux + mgy*(-1 + uy) + mgz*uz)*(-2*chem*uy*uy + 0.3333333333333333*((-rhoA + rhoB)*uy*uy +
2*chem*(ux*ux - 2*uy + uy*uy + uz*uz)) + 0.1111111111111111*(-4*chem + (rhoA - rhoB)*(ux*ux - 2*uy + uy*uy + uz*uz))));
// q = 4
dist[nr3] = m4 - (m4-feq4)/tau + 0.125*(-2*(Fy + Fx*ux + Fy*uy + Fz*uz)*(-0.2222222222222222 - uy*uy + 0.3333333333333333*(ux*ux + 2*uy + uy*uy + uz*uz)) +
(mgy + mgx*ux + mgy*uy + mgz*uz)*(-2*chem*uy*uy + 0.3333333333333333*((-rhoA + rhoB)*uy*uy +
2*chem*(ux*ux + 2*uy + uy*uy + uz*uz)) + 0.1111111111111111*(-4*chem + (rhoA - rhoB)*(ux*ux + 2*uy + uy*uy + uz*uz))));
// q = 5
dist[nr6] = m5 - (m5-feq5)/tau + 0.125*(2*(Fx*ux + Fy*uy + Fz*(-1 + uz))*(0.2222222222222222 + uz*uz -
0.3333333333333333*(ux*ux + uy*uy + (-2 + uz)*uz)) + (mgx*ux + mgy*uy + mgz*(-1 + uz))*
(-2*chem*uz*uz + 0.3333333333333333*((-rhoA + rhoB)*uz*uz + 2*chem*(ux*ux + uy*uy + (-2 + uz)*uz)) +
0.1111111111111111*(-4*chem + (rhoA - rhoB)*(ux*ux + uy*uy + (-2 + uz)*uz))));
// q = 6
dist[nr5] = m6 - (m6-feq6)/tau + 0.125*(-2*(Fz + Fx*ux + Fy*uy + Fz*uz)*(-0.2222222222222222 - uz*uz + 0.3333333333333333*(ux*ux + uy*uy + uz*(2 + uz))) +
(mgz + mgx*ux + mgy*uy + mgz*uz)*(-2*chem*uz*uz + 0.3333333333333333*((-rhoA + rhoB)*uz*uz +
2*chem*(ux*ux + uy*uy + uz*(2 + uz))) + 0.1111111111111111*(-4*chem + (rhoA - rhoB)*(ux*ux + uy*uy + uz*(2 + uz)))));
// q = 7
dist[nr8] = m7 - (m7-feq7)/tau + 0.0625*(2*(Fx*(-1 + ux) + Fy*(-1 + uy) + Fz*uz)*(0.2222222222222222 + (ux + uy)*(ux + uy) -
0.3333333333333333*(-2*ux + ux*ux - 2*uy + uy*uy + uz*uz)) + (mgx*(-1 + ux) + mgy*(-1 + uy) + mgz*uz)*
(-2*chem*(ux + uy)*(ux + uy) + 0.3333333333333333*(-((rhoA - rhoB)*(ux + uy)*(ux + uy)) +
2*chem*(-2*ux + ux*ux - 2*uy + uy*uy + uz*uz)) + 0.1111111111111111*
(-4*chem + (rhoA - rhoB)*(-2*ux + ux*ux - 2*uy + uy*uy + uz*uz))));
// q = 8
dist[nr7] = m8 - (m8-feq8)/tau + 0.0625*(2*(Fx + Fy + Fx*ux + Fy*uy + Fz*uz)*(0.2222222222222222 + (ux + uy)*(ux + uy) -
0.3333333333333333*(2*ux + ux*ux + 2*uy + uy*uy + uz*uz)) + (mgx + mgy + mgx*ux + mgy*uy + mgz*uz)*
(-2*chem*(ux + uy)*(ux + uy) + 0.3333333333333333*(-((rhoA - rhoB)*(ux + uy)*(ux + uy)) +
2*chem*(2*ux + ux*ux + 2*uy + uy*uy + uz*uz)) + 0.1111111111111111*
(-4*chem + (rhoA - rhoB)*(2*ux + ux*ux + 2*uy + uy*uy + uz*uz))));
// q = 9
dist[nr10] = m9 - (m9-feq9)/tau + 0.0625*(2*(Fy + Fx*(-1 + ux) + Fy*uy + Fz*uz)*(0.2222222222222222 + (ux - uy)*(ux - uy) -
0.3333333333333333*(-2*ux + ux*ux + 2*uy + uy*uy + uz*uz)) + (mgy + mgx*(-1 + ux) + mgy*uy + mgz*uz)*
(-2*chem*(ux - uy)*(ux - uy) + 0.3333333333333333*(-((rhoA - rhoB)*(ux - uy)*(ux - uy)) +
2*chem*(-2*ux + ux*ux + 2*uy + uy*uy + uz*uz)) + 0.1111111111111111*
(-4*chem + (rhoA - rhoB)*(-2*ux + ux*ux + 2*uy + uy*uy + uz*uz))));
// q = 10
dist[nr9] = m10 - (m10-feq10)/tau + 0.0625*(2*(Fx*(1 + ux) + Fy*(-1 + uy) + Fz*uz)*(0.2222222222222222 + (ux - uy)*(ux - uy) -
0.3333333333333333*(2*ux + ux*ux - 2*uy + uy*uy + uz*uz)) + (mgx*(1 + ux) + mgy*(-1 + uy) + mgz*uz)*
(-2*chem*(ux - uy)*(ux - uy) + 0.3333333333333333*(-((rhoA - rhoB)*(ux - uy)*(ux - uy)) +
2*chem*(2*ux + ux*ux - 2*uy + uy*uy + uz*uz)) + 0.1111111111111111*
(-4*chem + (rhoA - rhoB)*(2*ux + ux*ux - 2*uy + uy*uy + uz*uz))));
// q = 11
dist[nr12] = m11 - (m11-feq11)/tau + 0.0625*(2*(Fx*(-1 + ux) + Fy*uy + Fz*(-1 + uz))*(0.2222222222222222 + (ux + uz)*(ux + uz) -
0.3333333333333333*(-2*ux + ux*ux + uy*uy + (-2 + uz)*uz)) + (mgx*(-1 + ux) + mgy*uy + mgz*(-1 + uz))*
(-2*chem*(ux + uz)*(ux + uz) + 0.3333333333333333*(-((rhoA - rhoB)*(ux + uz)*(ux + uz)) +
2*chem*(-2*ux + ux*ux + uy*uy + (-2 + uz)*uz)) + 0.1111111111111111*
(-4*chem + (rhoA - rhoB)*(-2*ux + ux*ux + uy*uy + (-2 + uz)*uz))));
// q = 12
dist[nr11] = m12 - (m12-feq12)/tau + 0.0625*(2*(Fx + Fz + Fx*ux + Fy*uy + Fz*uz)*(0.2222222222222222 + (ux + uz)*(ux + uz) -
0.3333333333333333*(2*ux + ux*ux + uy*uy + uz*(2 + uz))) + (mgx + mgz + mgx*ux + mgy*uy + mgz*uz)*
(-2*chem*(ux + uz)*(ux + uz) + 0.3333333333333333*(-((rhoA - rhoB)*(ux + uz)*(ux + uz)) +
2*chem*(2*ux + ux*ux + uy*uy + uz*(2 + uz))) + 0.1111111111111111*
(-4*chem + (rhoA - rhoB)*(2*ux + ux*ux + uy*uy + uz*(2 + uz)))));
// q = 13
dist[nr14] = m13 - (m13-feq13)/tau + 0.0625*(2*(Fz + Fx*(-1 + ux) + Fy*uy + Fz*uz)*(0.2222222222222222 + (ux - uz)*(ux - uz) -
0.3333333333333333*(-2*ux + ux*ux + uy*uy + uz*(2 + uz))) + (mgz + mgx*(-1 + ux) + mgy*uy + mgz*uz)*
(-2*chem*(ux - uz)*(ux - uz) + 0.3333333333333333*(-((rhoA - rhoB)*(ux - uz)*(ux - uz)) +
2*chem*(-2*ux + ux*ux + uy*uy + uz*(2 + uz))) + 0.1111111111111111*
(-4*chem + (rhoA - rhoB)*(-2*ux + ux*ux + uy*uy + uz*(2 + uz)))));
// q= 14
dist[nr13] = m14 - (m14-feq14)/tau + 0.0625*(2*(Fx*(1 + ux) + Fy*uy + Fz*(-1 + uz))*(0.2222222222222222 + (ux - uz)*(ux - uz) -
0.3333333333333333*(2*ux + ux*ux + uy*uy + (-2 + uz)*uz)) + (mgx*(1 + ux) + mgy*uy + mgz*(-1 + uz))*
(-2*chem*(ux - uz)*(ux - uz) + 0.3333333333333333*(-((rhoA - rhoB)*(ux - uz)*(ux - uz)) +
2*chem*(2*ux + ux*ux + uy*uy + (-2 + uz)*uz)) + 0.1111111111111111*
(-4*chem + (rhoA - rhoB)*(2*ux + ux*ux + uy*uy + (-2 + uz)*uz))));
// q = 15
dist[nr16] = m15 - (m15-feq15)/tau + 0.0625*(2*(Fx*ux + Fy*(-1 + uy) + Fz*(-1 + uz))*(0.2222222222222222 + (uy + uz)(uy + uz) -
0.3333333333333333*(ux*ux - 2*uy + uy*uy + (-2 + uz)*uz)) + (mgx*ux + mgy*(-1 + uy) + mgz*(-1 + uz))*
(-2*chem*(uy + uz)*(uy + uz) + 0.3333333333333333*(-((rhoA - rhoB)*(uy + uz)*(uy + uz)) +
2*chem*(ux*ux - 2*uy + uy*uy + (-2 + uz)*uz)) + 0.1111111111111111*
(-4*chem + (rhoA - rhoB)*(ux*ux - 2*uy + uy*uy + (-2 + uz)*uz))));
// q = 16
dist[nr15] = m16 - (m16-feq16)/tau + 0.0625*(2*(Fy + Fz + Fx*ux + Fy*uy + Fz*uz)*(0.2222222222222222 + (uy + uz)*(uy + uz) -
0.3333333333333333*(ux*ux + 2*uy + uy*uy + uz*(2 + uz))) + (mgy + mgz + mgx*ux + mgy*uy + mgz*uz)*
(-2*chem*(uy + uz)*(uy + uz) + 0.3333333333333333*(-((rhoA - rhoB)*(uy + uz)*(uy + uz)) +
2*chem*(ux*ux + 2*uy + uy*uy + uz*(2 + uz))) + 0.1111111111111111*
(-4*chem + (rhoA - rhoB)*(ux*ux + 2*uy + uy*uy + uz*(2 + uz)))));
// q = 17
dist[nr18] = m17 - (m17-feq17)/tau + 0.0625*(2*(Fz + Fx*ux + Fy*(-1 + uy) + Fz*uz)*(0.2222222222222222 + (uy - uz)*(uy - uz) -
0.3333333333333333*(ux*ux - 2*uy + uy*uy + uz*(2 + uz))) + (mgz + mgx*ux + mgy*(-1 + uy) + mgz*uz)*
(-2*chem*(uy - uz)*(uy - uz) + 0.3333333333333333*(-((rhoA - rhoB)*(uy - uz)*(uy - uz)) +
2*chem*(ux*ux - 2*uy + uy*uy + uz*(2 + uz))) + 0.1111111111111111*
(-4*chem + (rhoA - rhoB)*(ux*ux - 2*uy + uy*uy + uz*(2 + uz)))));
// q = 18
dist[nr17] = m18 - (m18-feq18)/tau + 0.0625*(2*(Fx*ux + Fy*(1 + uy) + Fz*(-1 + uz))*(0.2222222222222222 + (uy - uz)*(uy - uz) -
0.3333333333333333*(ux*ux + 2*uy + uy*uy + (-2 + uz)*uz)) + (mgx*ux + mgy*(1 + uy) + mgz*(-1 + uz))*
(-2*chem*(uy - uz)*(uy - uz) + 0.3333333333333333*(-((rhoA - rhoB)*(uy - uz)*(uy - uz)) +
2*chem*(ux*ux + 2*uy + uy*uy + (-2 + uz)*uz)) + 0.1111111111111111*
(-4*chem + (rhoA - rhoB)*(ux*ux + 2*uy + uy*uy + (-2 + uz)*uz))));
//----------------------------------------------------------------------------------------------------------------------------------------//
// ----------------------------- compute phase field evolution ----------------------------------------
//Normalize the Color Gradient
C = sqrt(nx*nx+ny*ny+nz*nz);
double ColorMag = C;
if (C==0.0) ColorMag=1.0;
nx = nx/ColorMag;
ny = ny/ColorMag;
nz = nz/ColorMag;
//compute surface tension-related parameter
theta = M*4.5*(1-4.0*phi*phi)/W;
//load distributions of phase field
//q=0
h0 = hq[n];
//q=1
h1 = hq[nr1];
//q=2
h2 = hq[nr2];
//q=3
h3 = hq[nr3];
//q=4
h4 = hq[nr4];
//q=5
h5 = hq[nr5];
//q=6
h6 = hq[nr6];
//-------------------------------- BGK collison for phase field ---------------------------------//
// q = 0
hq[n] = h0 - (h0 - 0.3333333333333333*phi)/tauM;
// q = 1
hq[nr2] = h1 - (h1 - phi*(0.1111111111111111 + 0.5*ux) - (0.5*M*nx*(1 - 4*phi*phi))/W)/tauM;
// q = 2
hq[nr1] = h2 - (h2 - phi*(0.1111111111111111 - 0.5*ux) + (0.5*M*nx*(1 - 4*phi*phi))/W)/tauM;
// q = 3
hq[nr4] = h3 - (h3 - phi*(0.1111111111111111 + 0.5*uy) - (0.5*M*ny*(1 - 4*phi*phi))/W)/tauM;
// q = 4
hq[nr3] = h4 - (h4 - phi*(0.1111111111111111 - 0.5*uy) + (0.5*M*ny*(1 - 4*phi*phi))/W)/tauM;
// q = 5
hq[nr6] = h5 - (h5 - phi*(0.1111111111111111 + 0.5*uz) - (0.5*M*nz*(1 - 4*phi*phi))/W)/tauM;
// q = 6
hq[nr5] = h6 - (h6 - phi*(0.1111111111111111 - 0.5*uz) + (0.5*M*nz*(1 - 4*phi*phi))/W)/tauM;
//........................................................................
//Update velocity on device
Velocity[0*Np+n] = ux;
Velocity[1*Np+n] = uy;
Velocity[2*Np+n] = uz;
//Update pressure on device
Pressure[n] = p;
//Update chemical potential on device
mu_phi[n] = chem;
//Update color gradient on device
ColorGrad[0*Np+n] = nx;
ColorGrad[1*Np+n] = ny;
ColorGrad[2*Np+n] = nz;
}
}
extern "C" void ScaLBL_D3Q19_AAeven_FreeLeeModel(int *Map, double *dist, double *hq, double *Den, double *Phi, double *mu_phi, double *Vel, double *Pressure,
double rhoA, double rhoB, double tauA, double tauB, double tauM, double kappa, double beta, double W, double Fx, double Fy, double Fz,
int strideY, int strideZ, int start, int finish, int Np){
int n,nn,nn2x,ijk;
//int nr1,nr2,nr3,nr4,nr5,nr6,nr7,nr8,nr9,nr10,nr11,nr12,nr13,nr14,nr15,nr16,nr17,nr18;
double ux,uy,uz;//fluid velocity
double p;//pressure
double chem;//chemical potential
double phi; //phase field
double rho0;//fluid density
// distribution functions
double m1,m2,m4,m6,m8,m9,m10,m11,m12,m13,m14,m15,m16,m17,m18;
double m0,m3,m5,m7;
double mm1,mm2,mm4,mm6,mm8,mm9,mm10,mm11,mm12,mm13,mm14,mm15,mm16,mm17,mm18;
double mm3,mm5,mm7;
double feq0,feq1,feq2,feq3,feq4,feq5,feq6,feq7,feq8,feq9,feq10,feq11,feq12,feq13,feq14,feq15,feq16,feq17,feq18;
double nx,ny,nz;//normal color gradient
double mgx,mgy,mgz;//mixed gradient reaching secondary neighbor
//double f0,f1,f2,f3,f4,f5,f6,f7,f8,f9,f10,f11,f12,f13,f14,f15,f16,f17,f18;
double h0,h1,h2,h3,h4,h5,h6;//distributions for LB phase field
double tau;//position dependent LB relaxation time for fluid
double C,theta;
double M = 2.0/9.0*(tauM-0.5);//diffusivity (or mobility) for the phase field D3Q7
for (int n=start; n<finish; n++){
rho0 = Den[n];//load density
phi = Phi[n];// load phase field
// local relaxation time
tau=tauA + 0.5*(1.0-phi)*(tauB-tauA);
// Get the 1D index based on regular data layout
ijk = Map[n];
// COMPUTE THE COLOR GRADIENT
//........................................................................
//.................Read Phase Indicator Values............................
//........................................................................
nn = ijk-1; // neighbor index (get convention)
m1 = Phi[nn]; // get neighbor for phi - 1
//........................................................................
nn = ijk+1; // neighbor index (get convention)
m2 = Phi[nn]; // get neighbor for phi - 2
//........................................................................
nn = ijk-strideY; // neighbor index (get convention)
m3 = Phi[nn]; // get neighbor for phi - 3
//........................................................................
nn = ijk+strideY; // neighbor index (get convention)
m4 = Phi[nn]; // get neighbor for phi - 4
//........................................................................
nn = ijk-strideZ; // neighbor index (get convention)
m5 = Phi[nn]; // get neighbor for phi - 5
//........................................................................
nn = ijk+strideZ; // neighbor index (get convention)
m6 = Phi[nn]; // get neighbor for phi - 6
//........................................................................
nn = ijk-strideY-1; // neighbor index (get convention)
m7 = Phi[nn]; // get neighbor for phi - 7
//........................................................................
nn = ijk+strideY+1; // neighbor index (get convention)
m8 = Phi[nn]; // get neighbor for phi - 8
//........................................................................
nn = ijk+strideY-1; // neighbor index (get convention)
m9 = Phi[nn]; // get neighbor for phi - 9
//........................................................................
nn = ijk-strideY+1; // neighbor index (get convention)
m10 = Phi[nn]; // get neighbor for phi - 10
//........................................................................
nn = ijk-strideZ-1; // neighbor index (get convention)
m11 = Phi[nn]; // get neighbor for phi - 11
//........................................................................
nn = ijk+strideZ+1; // neighbor index (get convention)
m12 = Phi[nn]; // get neighbor for phi - 12
//........................................................................
nn = ijk+strideZ-1; // neighbor index (get convention)
m13 = Phi[nn]; // get neighbor for phi - 13
//........................................................................
nn = ijk-strideZ+1; // neighbor index (get convention)
m14 = Phi[nn]; // get neighbor for phi - 14
//........................................................................
nn = ijk-strideZ-strideY; // neighbor index (get convention)
m15 = Phi[nn]; // get neighbor for phi - 15
//........................................................................
nn = ijk+strideZ+strideY; // neighbor index (get convention)
m16 = Phi[nn]; // get neighbor for phi - 16
//........................................................................
nn = ijk+strideZ-strideY; // neighbor index (get convention)
m17 = Phi[nn]; // get neighbor for phi - 17
//........................................................................
nn = ijk-strideZ+strideY; // neighbor index (get convention)
m18 = Phi[nn]; // get neighbor for phi - 18
// compute mixed difference (Eq.30, A.Fukhari et al. JCP 315(2016) 434-457)
//........................................................................
nn2x = ijk-2; // neighbor index (get convention)
mm1 = Phi[nn2x]; // get neighbor for phi - 1
mm1 = 0.25*(-mm1+5.0*m1-3.0*phi-m2);
//........................................................................
nn2x = ijk+2; // neighbor index (get convention)
mm2 = Phi[nn2x]; // get neighbor for phi - 2
mm2 = 0.25*(-mm2+5.0*m2-3.0*phi-m1);
//........................................................................
nn2x = ijk-strideY*2; // neighbor index (get convention)
mm3 = Phi[nn2x]; // get neighbor for phi - 3
mm3 = 0.25*(-mm3+5.0*m3-3.0*phi-m4);
//........................................................................
nn2x = ijk+strideY*2; // neighbor index (get convention)
mm4 = Phi[nn2x]; // get neighbor for phi - 4
mm4 = 0.25*(-mm4+5.0*m4-3.0*phi-m3);
//........................................................................
nn2x = ijk-strideZ*2; // neighbor index (get convention)
mm5 = Phi[nn2x]; // get neighbor for phi - 5
mm5 = 0.25*(-mm5+5.0*m5-3.0*phi-m6);
//........................................................................
nn2x = ijk+strideZ*2; // neighbor index (get convention)
mm6 = Phi[nn2x]; // get neighbor for phi - 6
mm6 = 0.25*(-mm6+5.0*m6-3.0*phi-m5);
//........................................................................
nn2x = ijk-strideY*2-2; // neighbor index (get convention)
mm7 = Phi[nn2x]; // get neighbor for phi - 7
mm7 = 0.25*(-mm7+5.0*m7-3.0*phi-m8);
//........................................................................
nn2x = ijk+strideY*2+2; // neighbor index (get convention)
mm8 = Phi[nn2x]; // get neighbor for phi - 8
mm8 = 0.25*(-mm8+5.0*m8-3.0*phi-m7);
//........................................................................
nn2x = ijk+strideY*2-2; // neighbor index (get convention)
mm9 = Phi[nn2x]; // get neighbor for phi - 9
mm9 = 0.25*(-mm9+5.0*m9-3.0*phi-m10);
//........................................................................
nn2x = ijk-strideY*2+2; // neighbor index (get convention)
mm10 = Phi[nn2x]; // get neighbor for phi - 10
mm10 = 0.25*(-mm10+5.0*m10-3.0*phi-m9);
//........................................................................
nn2x = ijk-strideZ*2-2; // neighbor index (get convention)
mm11 = Phi[nn2x]; // get neighbor for phi - 11
mm11 = 0.25*(-mm11+5.0*m11-3.0*phi-m12);
//........................................................................
nn2x = ijk+strideZ*2+2; // neighbor index (get convention)
mm12 = Phi[nn2x]; // get neighbor for phi - 12
mm12 = 0.25*(-mm12+5.0*m12-3.0*phi-m11);
//........................................................................
nn2x = ijk+strideZ*2-2; // neighbor index (get convention)
mm13 = Phi[nn2x]; // get neighbor for phi - 13
mm13 = 0.25*(-mm13+5.0*m13-3.0*phi-m14);
//........................................................................
nn2x = ijk-strideZ*2+2; // neighbor index (get convention)
mm14 = Phi[nn2x]; // get neighbor for phi - 14
mm14 = 0.25*(-mm14+5.0*m14-3.0*phi-m13);
//........................................................................
nn2x = ijk-strideZ*2-strideY*2; // neighbor index (get convention)
mm15 = Phi[nn2x]; // get neighbor for phi - 15
mm15 = 0.25*(-mm15+5.0*m15-3.0*phi-m16);
//........................................................................
nn2x = ijk+strideZ*2+strideY*2; // neighbor index (get convention)
mm16 = Phi[nn2x]; // get neighbor for phi - 16
mm16 = 0.25*(-mm16+5.0*m16-3.0*phi-m15);
//........................................................................
nn2x = ijk+strideZ*2-strideY*2; // neighbor index (get convention)
mm17 = Phi[nn2x]; // get neighbor for phi - 17
mm17 = 0.25*(-mm17+5.0*m17-3.0*phi-m18);
//........................................................................
nn2x = ijk-strideZ*2+strideY*2; // neighbor index (get convention)
mm18 = Phi[nn2x]; // get neighbor for phi - 18
mm18 = 0.25*(-mm18+5.0*m18-3.0*phi-m17);
//............Compute the Color Gradient...................................
nx = -3.0*1.0/18.0*(m1-m2+0.5*(m7-m8+m9-m10+m11-m12+m13-m14));
ny = -3.0*1.0/18.0*(m3-m4+0.5*(m7-m8-m9+m10+m15-m16+m17-m18));
nz = -3.0*1.0/18.0*(m5-m6+0.5*(m11-m12-m13+m14+m15-m16-m17+m18));
//............Compute the Chemical Potential...............................
chem = 2.0*3.0/18.0*(m1+m2+m3+m4+m5+m6-6*phi+0.5*(m7+m8+m9+m10+m11+m12+m13+m14+m15+m16+m17+m18-12*phi));//intermediate var, i.e. the laplacian
chem = 4.0*beta*phi*(phi+1.0)*(phi-1.0)-kappa*chem;
//............Compute the Mixed Gradient...................................
mgx = -3.0*1.0/18.0*(mm1-mm2+0.5*(mm7-mm8+mm9-mm10+mm11-mm12+mm13-mm14))*0.25;//the factor of 0.25 comes from the denominator of Eq.30
mgy = -3.0*1.0/18.0*(mm3-mm4+0.5*(mm7-mm8-mm9+mm10+mm15-mm16+mm17-mm18))*0.25;
mgz = -3.0*1.0/18.0*(mm5-mm6+0.5*(mm11-mm12-mm13+mm14+mm15-mm16-mm17+mm18))*0.25;
// q=0
m0 = dist[n];
// q=1
m1 = dist[2*Np+n];
// q=2
m2 = dist[1*Np+n];
// q=3
m3 = dist[4*Np+n];
// q = 4
m4 = dist[3*Np+n];
// q=5
m5 = dist[6*Np+n];
// q = 6
m6 = dist[5*Np+n];
// q=7
m7 = dist[8*Np+n];
// q = 8
m8 = dist[7*Np+n];
// q=9
m9 = dist[10*Np+n];
// q = 10
m10 = dist[9*Np+n];
// q=11
m11 = dist[12*Np+n];
// q=12
m12 = dist[11*Np+n];
// q=13
m13 = dist[14*Np+n];
// q=14
m14 = dist[13*Np+n];
// q=15
m15 = dist[16*Np+n];
// q=16
m16 = dist[15*Np+n];
// q=17
m17 = dist[18*Np+n];
// q=18
m18 = dist[17*Np+n];
//compute fluid velocity
ux = 3.0/rho0*(m1-m2+m7-m8+m9-m10+m11-m12+m13-m14+0.5*(chem*nx+Fx));
uy = 3.0/rho0*(m3-m4+m7-m8-m9+m10+m15-m16+m17-m18+0.5*(chem*ny+Fy));
uz = 3.0/rho0*(m5-m6+m11-m12-m13+m14+m15-m16-m17+m18+0.5*(chem*nz+Fz));
//compute pressure
p = (m0+m2+m1+m4+m3+m6+m5+m8+m7+m10+m9+m12+m11+m14+m13+m16+m15+m18+m17)
+0.5*(rhoA-rhoB)/2.0/3.0*(ux*nx+uy*ny+uz*nz);
//compute equilibrium distributions
feq0 = 0.3333333333333333*p - 0.25*(Fx*ux + Fy*uy + Fz*uz)*(-0.6666666666666666 + ux*ux + uy*uy + uz*uz) -
0.16666666666666666*rho0*(ux*ux + uy*uy + uz*uz) - 0.5*(-(nx*ux) - ny*uy - nz*uz)*
(-0.08333333333333333*(rhoA - rhoB)*(ux*ux + uy*uy + uz*uz) + chem*(0.3333333333333333 - 0.5*(ux*ux + uy*uy + uz*uz)));
feq1 = 0.05555555555555555*p - 0.08333333333333333*rho0*(-ux*ux + 0.3333333333333333*(-2*ux + ux*ux + uy*uy + uz*uz)) -
0.125*(Fx*(-1. + ux) + Fy*uy + Fz*uz)*(-0.2222222222222222 - 1.*ux*ux +
0.3333333333333333*(-2.*ux + ux*ux + uy*uy + uz*uz)) - 0.0625*(nx - nx*ux - ny*uy - nz*uz)*
(2*chem*ux*ux - 0.3333333333333333*((-rhoA + rhoB)*ux*ux + 2*chem*(-2*ux + ux*ux + uy*uy + uz*uz)) +
0.1111111111111111*(4*chem - (rhoA - rhoB)*(-2*ux + ux*ux + uy*uy + uz*uz)));
feq2 = 0.05555555555555555*p - 0.08333333333333333*rho0*(-ux*ux + 0.3333333333333333*(2*ux + ux*ux + uy*uy + uz*uz)) -
0.125*(Fx + Fx*ux + Fy*uy + Fz*uz)*(-0.2222222222222222 - 1.*ux*ux +
0.3333333333333333*(2.*ux + ux*ux + uy*uy + uz*uz)) - 0.0625*(nx + nx*ux + ny*uy + nz*uz)*
(-2.*chem*ux*ux + 0.1111111111111111*(-4.*chem + rhoB*(-2.*ux - 1.*ux*ux - 1.*uy*uy - 1.*uz*uz) +
rhoA*(2.*ux + ux*ux + uy*uy + uz*uz)) + 0.3333333333333333*((-1.*rhoA + rhoB)*ux*ux +
chem*(4.*ux + 2.*ux*ux + 2.*uy*uy + 2.*uz*uz)));
feq3 = 0.05555555555555555*p - 0.08333333333333333*rho0*(-uy*uy + 0.3333333333333333*(ux*ux - 2*uy + uy*uy + uz*uz)) -
0.125*(Fx*ux + Fy*(-1. + uy) + Fz*uz)*(-0.2222222222222222 - 1.*uy*uy +
0.3333333333333333*(ux*ux - 2.*uy + uy*uy + uz*uz)) - 0.0625*(ny - nx*ux - ny*uy - nz*uz)*
(2*chem*uy*uy - 0.3333333333333333*((-rhoA + rhoB)*uy*uy + 2*chem*(ux*ux - 2*uy + uy*uy + uz*uz)) +
0.1111111111111111*(4*chem - (rhoA - rhoB)*(ux*ux - 2*uy + uy*uy + uz*uz)));
feq4 = 0.05555555555555555*p - 0.08333333333333333*rho0*(-uy*uy + 0.3333333333333333*(ux*ux + 2*uy + uy*uy + uz*uz)) -
0.125*(Fy + Fx*ux + Fy*uy + Fz*uz)*(-0.2222222222222222 - 1.*uy*uy +
0.3333333333333333*(ux*ux + 2.*uy + uy*uy + uz*uz)) - 0.0625*(ny + nx*ux + ny*uy + nz*uz)*
(-2.*chem*uy*uy + 0.1111111111111111*(-4.*chem + rhoB*(-1.*ux*ux - 2.*uy - 1.*uy*uy - 1.*uz*uz) +
rhoA*(ux*ux + 2.*uy + uy*uy + uz*uz)) + 0.3333333333333333*((-1.*rhoA + rhoB)*uy*uy +
chem*(2.*ux*ux + 4.*uy + 2.*uy*uy + 2.*uz*uz)));
feq5 = 0.05555555555555555*p - 0.08333333333333333*rho0*(-uz*uz + 0.3333333333333333*(ux*ux + uy*uy + (-2 + uz)*uz)) -
0.125*(Fx*ux + Fy*uy + Fz*(-1. + uz))*(-0.2222222222222222 - 1.*uz*uz +
0.3333333333333333*(ux*ux + uy*uy + (-2. + uz)*uz)) - 0.0625*(nx*ux + ny*uy + nz*(-1. + uz))*
(-2.*chem*uz*uz + 0.1111111111111111*(-4.*chem + rhoB*(-1.*ux*ux - 1.*uy*uy + (2. - 1.*uz)*uz) +
rhoA*(ux*ux + uy*uy + (-2. + uz)*uz)) + 0.3333333333333333*((-1.*rhoA + rhoB)*uz*uz +
chem*(2.*ux*ux + 2.*uy*uy + uz*(-4. + 2.*uz))));
feq6 = 0.05555555555555555*p - 0.08333333333333333*rho0*(-uz*uz + 0.3333333333333333*(ux*ux + uy*uy + uz*(2 + uz))) -
0.125*(Fz + Fx*ux + Fy*uy + Fz*uz)*(-0.2222222222222222 - 1.*uz*uz +
0.3333333333333333*(ux*ux + uy*uy + uz*(2. + uz))) - 0.0625*(nz + nx*ux + ny*uy + nz*uz)*
(-2.*chem*uz*uz + 0.1111111111111111*(-4.*chem + rhoB*(-1.*ux*ux - 1.*uy*uy + (-2. - 1.*uz)*uz) +
rhoA*(ux*ux + uy*uy + uz*(2. + uz))) + 0.3333333333333333*((-1.*rhoA + rhoB)*uz*uz +
chem*(2.*ux*ux + 2.*uy*uy + uz*(4. + 2.*uz))));
feq7 = 0.027777777777777776*p - 0.041666666666666664*rho0*
(-(ux + uy)*(ux + uy) + 0.3333333333333333*(-2*ux + ux*ux - 2*uy + uy*uy + uz*uz)) -
0.0625*(Fx*(-1. + ux) + Fy*(-1. + uy) + Fz*uz)*(-0.2222222222222222 - 1.*ux*ux - 2.*ux*uy - 1.*uy*uy +
0.3333333333333333*(-2.*ux + ux*ux - 2.*uy + uy*uy + uz*uz)) - 0.03125*(nx + ny - nx*ux - ny*uy - nz*uz)*
(2*chem*(ux + uy)*(ux + uy) + 0.3333333333333333*((rhoA - rhoB)*(ux + uy)*(ux + uy) - 2*chem*(-2*ux + ux*ux - 2*uy + uy*uy + uz*uz)) +
0.1111111111111111*(4*chem - (rhoA - rhoB)*(-2*ux + ux*ux - 2*uy + uy*uy + uz*uz)));
feq8 = 0.027777777777777776*p - 0.041666666666666664*rho0*
(-(ux + uy)*(ux + uy) + 0.3333333333333333*(2*ux + ux*ux + 2*uy + uy*uy + uz*uz)) -
0.0625*(Fx + Fy + Fx*ux + Fy*uy + Fz*uz)*(-0.2222222222222222 - 1.*ux*ux - 2.*ux*uy - 1.*uy*uy +
0.3333333333333333*(2.*ux + ux*ux + 2.*uy + uy*uy + uz*uz)) - 0.03125*(-(nx*(1 + ux)) - ny*(1 + uy) - nz*uz)*
(2*chem*(ux + uy)*(ux + uy) - 0.3333333333333333*(-((rhoA - rhoB)*(ux + uy)*(ux + uy)) +
2*chem*(2*ux + ux*ux + 2*uy + uy*uy + uz*uz)) + 0.1111111111111111*
(4*chem - (rhoA - rhoB)*(2*ux + ux*ux + 2*uy + uy*uy + uz*uz)));
feq9 = 0.027777777777777776*p - 0.041666666666666664*rho0*
(-(ux - uy)*(ux - uy) + 0.3333333333333333*(-2*ux + ux*ux + 2*uy + uy*uy + uz*uz)) -
0.0625*(Fy + Fx*(-1. + ux) + Fy*uy + Fz*uz)*(-0.2222222222222222 - 1.*ux*ux + 2.*ux*uy - 1.*uy*uy +
0.3333333333333333*(-2.*ux + ux*ux + 2.*uy + uy*uy + uz*uz)) - 0.03125*(nx - nx*ux - ny*(1 + uy) - nz*uz)*
(2*chem*(ux - uy)*(ux - uy) - 0.3333333333333333*(-((rhoA - rhoB)*(ux - uy)*(ux - uy)) +
2*chem*(-2*ux + ux*ux + 2*uy + uy*uy + uz*uz)) + 0.1111111111111111*
(4*chem - (rhoA - rhoB)*(-2*ux + ux*ux + 2*uy + uy*uy + uz*uz)));
feq10 = 0.027777777777777776*p - 0.041666666666666664*rho0*
(-(ux - uy)*(ux - uy) + 0.3333333333333333*(2*ux + ux*ux - 2*uy + uy*uy + uz*uz)) -
0.0625*(Fx*(1 + ux) + Fy*(-1. + uy) + Fz*uz)*(-0.2222222222222222 - 1.*ux*ux + 2.*ux*uy - 1.*uy*uy +
0.3333333333333333*(2.*ux + ux*ux - 2.*uy + uy*uy + uz*uz)) - 0.03125*(ny - nx*(1 + ux) - ny*uy - nz*uz)*
(2*chem*(ux - uy)*(ux - uy) - 0.3333333333333333*(-((rhoA - rhoB)*(ux - uy)*(ux - uy)) +
2*chem*(2*ux + ux*ux - 2*uy + uy*uy + uz*uz)) + 0.1111111111111111*
(4*chem - (rhoA - rhoB)*(2*ux + ux*ux - 2*uy + uy*uy + uz*uz)));
feq11 = 0.027777777777777776*p - 0.041666666666666664*rho0*
(-(ux + uz)*(ux + uz) + 0.3333333333333333*(-2*ux + ux*ux + uy*uy + (-2 + uz)*uz)) -
0.0625*(Fx*(-1. + ux) + Fy*uy + Fz*(-1. + uz))*(-0.2222222222222222 - 1.*ux*ux - 2.*ux*uz - 1.*uz*uz +
0.3333333333333333*(-2.*ux + ux*ux + uy*uy + (-2. + uz)*uz)) - 0.03125*(nx + nz - nx*ux - ny*uy - nz*uz)*
(2*chem*(ux + uz)*(ux + uz) + 0.3333333333333333*((rhoA - rhoB)*(ux + uz)*(ux + uz) - 2*chem*(-2*ux + ux*ux + uy*uy + (-2 + uz)*uz)) +
0.1111111111111111*(4*chem - (rhoA - rhoB)*(-2*ux + ux*ux + uy*uy + (-2 + uz)*uz)));
feq12 = 0.027777777777777776*p - 0.041666666666666664*rho0*
(-(ux + uz)*(ux + uz) + 0.3333333333333333*(2*ux + ux*ux + uy*uy + uz*(2 + uz))) -
0.0625*(Fx + Fz + Fx*ux + Fy*uy + Fz*uz)*(-0.2222222222222222 - 1.*ux*ux - 2.*ux*uz - 1.*uz*uz +
0.3333333333333333*(2.*ux + ux*ux + uy*uy + uz*(2. + uz))) - 0.03125*(-(nx*(1 + ux)) - ny*uy - nz*(1 + uz))*
(2*chem*(ux + uz)*(ux + uz) - 0.3333333333333333*(-((rhoA - rhoB)*(ux + uz)*(ux + uz)) +
2*chem*(2*ux + ux*ux + uy*uy + uz*(2 + uz))) + 0.1111111111111111*
(4*chem - (rhoA - rhoB)*(2*ux + ux*ux + uy*uy + uz*(2 + uz))));
feq13 = 0.027777777777777776*p - 0.041666666666666664*rho0*
(-(ux - uz)*(ux - uz) + 0.3333333333333333*(-2*ux + ux*ux + uy*uy + uz*(2 + uz))) -
0.0625*(Fz + Fx*(-1. + ux) + Fy*uy + Fz*uz)*(-0.2222222222222222 - 1.*ux*ux + 2.*ux*uz - 1.*uz*uz +
0.3333333333333333*(-2.*ux + ux*ux + uy*uy + uz*(2. + uz))) - 0.03125*(nx - nx*ux - ny*uy - nz*(1 + uz))*
(2*chem*(ux - uz)*(ux - uz) - 0.3333333333333333*(-((rhoA - rhoB)*(ux - uz)*(ux - uz)) +
2*chem*(-2*ux + ux*ux + uy*uy + uz*(2 + uz))) + 0.1111111111111111*
(4*chem - (rhoA - rhoB)*(-2*ux + ux*ux + uy*uy + uz*(2 + uz))));
feq14 = 0.027777777777777776*p - 0.041666666666666664*rho0*
(-(ux - uz)*(ux - uz) + 0.3333333333333333*(2*ux + ux*ux + uy*uy + (-2 + uz)*uz)) -
0.0625*(Fx*(1 + ux) + Fy*uy + Fz*(-1. + uz))*(-0.2222222222222222 - 1.*ux*ux + 2.*ux*uz - 1.*uz*uz +
0.3333333333333333*(2.*ux + ux*ux + uy*uy + (-2. + uz)*uz)) - 0.03125*(nz - nx*(1 + ux) - ny*uy - nz*uz)*
(2*chem*(ux - uz)*(ux - uz) - 0.3333333333333333*(-((rhoA - rhoB)*(ux - uz)*(ux - uz)) +
2*chem*(2*ux + ux*ux + uy*uy + (-2 + uz)*uz)) + 0.1111111111111111*
(4*chem - (rhoA - rhoB)*(2*ux + ux*ux + uy*uy + (-2 + uz)*uz)));
feq15 = 0.027777777777777776*p - 0.041666666666666664*rho0*
(-(uy + uz)*(uy + uz) + 0.3333333333333333*(ux*ux - 2*uy + uy*uy + (-2 + uz)*uz)) -
0.0625*(Fx*ux + Fy*(-1. + uy) + Fz*(-1. + uz))*(-0.2222222222222222 - 1.*uy*uy - 2.*uy*uz - 1.*uz*uz +
0.3333333333333333*(ux*ux - 2.*uy + uy*uy + (-2. + uz)*uz)) - 0.03125*(ny + nz - nx*ux - ny*uy - nz*uz)*
(2*chem*(uy + uz)*(uy + uz) + 0.3333333333333333*((rhoA - rhoB)*(uy + uz)*(uy + uz) - 2*chem*(ux*ux - 2*uy + uy*uy + (-2 + uz)*uz)) +
0.1111111111111111*(4*chem - (rhoA - rhoB)*(ux*ux - 2*uy + uy*uy + (-2 + uz)*uz)));
feq16 = 0.027777777777777776*p - 0.041666666666666664*rho0*
(-(uy + uz)*(uy + uz) + 0.3333333333333333*(ux*ux + 2*uy + uy*uy + uz*(2 + uz))) -
0.0625*(Fy + Fz + Fx*ux + Fy*uy + Fz*uz)*(-0.2222222222222222 - 1.*uy*uy - 2.*uy*uz - 1.*uz*uz +
0.3333333333333333*(ux*ux + 2.*uy + uy*uy + uz*(2. + uz))) - 0.03125*(-(nx*ux) - ny*(1 + uy) - nz*(1 + uz))*
(2*chem*(uy + uz)*(uy + uz) - 0.3333333333333333*(-((rhoA - rhoB)*(uy + uz)*(uy + uz)) +
2*chem*(ux*ux + 2*uy + uy*uy + uz*(2 + uz))) + 0.1111111111111111*
(4*chem - (rhoA - rhoB)*(ux*ux + 2*uy + uy*uy + uz*(2 + uz))));
feq17 = 0.027777777777777776*p - 0.041666666666666664*rho0*
(-(uy - uz)*(uy - uz) + 0.3333333333333333*(ux*ux - 2*uy + uy*uy + uz*(2 + uz))) -
0.0625*(Fz + Fx*ux + Fy*(-1. + uy) + Fz*uz)*(-0.2222222222222222 - 1.*uy*uy + 2.*uy*uz - 1.*uz*uz +
0.3333333333333333*(ux*ux - 2.*uy + uy*uy + uz*(2. + uz))) - 0.03125*(ny - nx*ux - ny*uy - nz*(1 + uz))*
(2*chem*(uy - uz)*(uy - uz) - 0.3333333333333333*(-((rhoA - rhoB)*(uy - uz)*(uy - uz)) +
2*chem*(ux*ux - 2*uy + uy*uy + uz*(2 + uz))) + 0.1111111111111111*
(4*chem - (rhoA - rhoB)*(ux*ux - 2*uy + uy*uy + uz*(2 + uz))));
feq18 = 0.027777777777777776*p - 0.041666666666666664*rho0*
(-(uy - uz)*(uy - uz) + 0.3333333333333333*(ux*ux + 2*uy + uy*uy + (-2 + uz)*uz)) -
0.0625*(Fx*ux + Fy*(1 + uy) + Fz*(-1. + uz))*(-0.2222222222222222 - 1.*uy*uy + 2.*uy*uz - 1.*uz*uz +
0.3333333333333333*(ux*ux + 2.*uy + uy*uy + (-2. + uz)*uz)) - 0.03125*(nz - nx*ux - ny*(1 + uy) - nz*uz)*
(2*chem*(uy - uz)*(uy - uz) - 0.3333333333333333*(-((rhoA - rhoB)*(uy - uz)*(uy - uz)) +
2*chem*(ux*ux + 2*uy + uy*uy + (-2 + uz)*uz)) + 0.1111111111111111*
(4*chem - (rhoA - rhoB)*(ux*ux + 2*uy + uy*uy + (-2 + uz)*uz)));
//------------------------------------------------- BCK collison ------------------------------------------------------------//
// q=0
dist[n] = m0 - (m0-feq0)/tau + 0.25*(-2*(Fx*ux + Fy*uy + Fz*uz)*(-0.6666666666666666 + ux*ux + uy*uy + uz*uz) +
(mgx*ux + mgy*uy + mgz*uz)*(2*chem*(ux*ux + uy*uy + uz*uz) + 0.3333333333333333*
(-4*chem + (rhoA - rhoB)*(ux*ux + uy*uy + uz*uz))));
// q = 1
dist[1*Np+n] = m1 - (m1-feq1)/tau + 0.125*(2*(Fx*(-1 + ux) + Fy*uy + Fz*uz)*(0.2222222222222222 + ux*ux -
0.3333333333333333*(-2*ux + ux*ux + uy*uy + uz*uz)) + (mgx*(-1 + ux) + mgy*uy + mgz*uz)*
(-2*chem*ux*ux + 0.3333333333333333*((-rhoA + rhoB)*ux*ux + 2*chem*(-2*ux + ux*ux + uy*uy + uz*uz)) +
0.1111111111111111*(-4*chem + (rhoA - rhoB)*(-2*ux + ux*ux + uy*uy + uz*uz))));
// q=2
dist[2*Np+n] = m2 - (m2-feq2)/tau + 0.125*(-2*(Fx + Fx*ux + Fy*uy + Fz*uz)*(-0.2222222222222222 - ux*ux + 0.3333333333333333*(2*ux + ux*ux + uy*uy + uz*uz)) +
(mgx + mgx*ux + mgy*uy + mgz*uz)*(-2*chem*ux*ux + 0.3333333333333333*((-rhoA + rhoB)*ux*ux +
2*chem*(2*ux + ux*ux + uy*uy + uz*uz)) + 0.1111111111111111*(-4*chem + (rhoA - rhoB)*(2*ux + ux*ux + uy*uy + uz*uz))));
// q = 3
dist[3*Np+n] = m3 - (m3-feq3)/tau + 0.125*(2*(Fx*ux + Fy*(-1 + uy) + Fz*uz)*(0.2222222222222222 + uy*uy - 0.3333333333333333*(ux*ux - 2*uy + uy*uy + uz*uz)) +
(mgx*ux + mgy*(-1 + uy) + mgz*uz)*(-2*chem*uy*uy + 0.3333333333333333*((-rhoA + rhoB)*uy*uy +
2*chem*(ux*ux - 2*uy + uy*uy + uz*uz)) + 0.1111111111111111*(-4*chem + (rhoA - rhoB)*(ux*ux - 2*uy + uy*uy + uz*uz))));
// q = 4
dist[4*Np+n] = m4 - (m4-feq4)/tau + 0.125*(-2*(Fy + Fx*ux + Fy*uy + Fz*uz)*(-0.2222222222222222 - uy*uy + 0.3333333333333333*(ux*ux + 2*uy + uy*uy + uz*uz)) +
(mgy + mgx*ux + mgy*uy + mgz*uz)*(-2*chem*uy*uy + 0.3333333333333333*((-rhoA + rhoB)*uy*uy +
2*chem*(ux*ux + 2*uy + uy*uy + uz*uz)) + 0.1111111111111111*(-4*chem + (rhoA - rhoB)*(ux*ux + 2*uy + uy*uy + uz*uz))));
// q = 5
dist[5*Np+n] = m5 - (m5-feq5)/tau + 0.125*(2*(Fx*ux + Fy*uy + Fz*(-1 + uz))*(0.2222222222222222 + uz*uz -
0.3333333333333333*(ux*ux + uy*uy + (-2 + uz)*uz)) + (mgx*ux + mgy*uy + mgz*(-1 + uz))*
(-2*chem*uz*uz + 0.3333333333333333*((-rhoA + rhoB)*uz*uz + 2*chem*(ux*ux + uy*uy + (-2 + uz)*uz)) +
0.1111111111111111*(-4*chem + (rhoA - rhoB)*(ux*ux + uy*uy + (-2 + uz)*uz))));
// q = 6
dist[6*Np+n] = m6 - (m6-feq6)/tau + 0.125*(-2*(Fz + Fx*ux + Fy*uy + Fz*uz)*(-0.2222222222222222 - uz*uz + 0.3333333333333333*(ux*ux + uy*uy + uz*(2 + uz))) +
(mgz + mgx*ux + mgy*uy + mgz*uz)*(-2*chem*uz*uz + 0.3333333333333333*((-rhoA + rhoB)*uz*uz +
2*chem*(ux*ux + uy*uy + uz*(2 + uz))) + 0.1111111111111111*(-4*chem + (rhoA - rhoB)*(ux*ux + uy*uy + uz*(2 + uz)))));
// q = 7
dist[7*Np+n] = m7 - (m7-feq7)/tau + 0.0625*(2*(Fx*(-1 + ux) + Fy*(-1 + uy) + Fz*uz)*(0.2222222222222222 + (ux + uy)*(ux + uy) -
0.3333333333333333*(-2*ux + ux*ux - 2*uy + uy*uy + uz*uz)) + (mgx*(-1 + ux) + mgy*(-1 + uy) + mgz*uz)*
(-2*chem*(ux + uy)*(ux + uy) + 0.3333333333333333*(-((rhoA - rhoB)*(ux + uy)*(ux + uy)) +
2*chem*(-2*ux + ux*ux - 2*uy + uy*uy + uz*uz)) + 0.1111111111111111*
(-4*chem + (rhoA - rhoB)*(-2*ux + ux*ux - 2*uy + uy*uy + uz*uz))));
// q = 8
dist[8*Np+n] = m8 - (m8-feq8)/tau + 0.0625*(2*(Fx + Fy + Fx*ux + Fy*uy + Fz*uz)*(0.2222222222222222 + (ux + uy)*(ux + uy) -
0.3333333333333333*(2*ux + ux*ux + 2*uy + uy*uy + uz*uz)) + (mgx + mgy + mgx*ux + mgy*uy + mgz*uz)*
(-2*chem*(ux + uy)*(ux + uy) + 0.3333333333333333*(-((rhoA - rhoB)*(ux + uy)*(ux + uy)) +
2*chem*(2*ux + ux*ux + 2*uy + uy*uy + uz*uz)) + 0.1111111111111111*
(-4*chem + (rhoA - rhoB)*(2*ux + ux*ux + 2*uy + uy*uy + uz*uz))));
// q = 9
dist[9*Np+n] = m9 - (m9-feq9)/tau + 0.0625*(2*(Fy + Fx*(-1 + ux) + Fy*uy + Fz*uz)*(0.2222222222222222 + (ux - uy)*(ux - uy) -
0.3333333333333333*(-2*ux + ux*ux + 2*uy + uy*uy + uz*uz)) + (mgy + mgx*(-1 + ux) + mgy*uy + mgz*uz)*
(-2*chem*(ux - uy)*(ux - uy) + 0.3333333333333333*(-((rhoA - rhoB)*(ux - uy)*(ux - uy)) +
2*chem*(-2*ux + ux*ux + 2*uy + uy*uy + uz*uz)) + 0.1111111111111111*
(-4*chem + (rhoA - rhoB)*(-2*ux + ux*ux + 2*uy + uy*uy + uz*uz))));
// q = 10
dist[10*Np+n] = m10 - (m10-feq10)/tau + 0.0625*(2*(Fx*(1 + ux) + Fy*(-1 + uy) + Fz*uz)*(0.2222222222222222 + (ux - uy)*(ux - uy) -
0.3333333333333333*(2*ux + ux*ux - 2*uy + uy*uy + uz*uz)) + (mgx*(1 + ux) + mgy*(-1 + uy) + mgz*uz)*
(-2*chem*(ux - uy)*(ux - uy) + 0.3333333333333333*(-((rhoA - rhoB)*(ux - uy)*(ux - uy)) +
2*chem*(2*ux + ux*ux - 2*uy + uy*uy + uz*uz)) + 0.1111111111111111*
(-4*chem + (rhoA - rhoB)*(2*ux + ux*ux - 2*uy + uy*uy + uz*uz))));
// q = 11
dist[11*Np+n] = m11 - (m11-feq11)/tau + 0.0625*(2*(Fx*(-1 + ux) + Fy*uy + Fz*(-1 + uz))*(0.2222222222222222 + (ux + uz)*(ux + uz) -
0.3333333333333333*(-2*ux + ux*ux + uy*uy + (-2 + uz)*uz)) + (mgx*(-1 + ux) + mgy*uy + mgz*(-1 + uz))*
(-2*chem*(ux + uz)*(ux + uz) + 0.3333333333333333*(-((rhoA - rhoB)*(ux + uz)*(ux + uz)) +
2*chem*(-2*ux + ux*ux + uy*uy + (-2 + uz)*uz)) + 0.1111111111111111*
(-4*chem + (rhoA - rhoB)*(-2*ux + ux*ux + uy*uy + (-2 + uz)*uz))));
// q = 12
dist[12*Np+n] = m12 - (m12-feq12)/tau + 0.0625*(2*(Fx + Fz + Fx*ux + Fy*uy + Fz*uz)*(0.2222222222222222 + (ux + uz)*(ux + uz) -
0.3333333333333333*(2*ux + ux*ux + uy*uy + uz*(2 + uz))) + (mgx + mgz + mgx*ux + mgy*uy + mgz*uz)*
(-2*chem*(ux + uz)*(ux + uz) + 0.3333333333333333*(-((rhoA - rhoB)*(ux + uz)*(ux + uz)) +
2*chem*(2*ux + ux*ux + uy*uy + uz*(2 + uz))) + 0.1111111111111111*
(-4*chem + (rhoA - rhoB)*(2*ux + ux*ux + uy*uy + uz*(2 + uz)))));
// q = 13
dist[13*Np+n] = m13 - (m13-feq13)/tau + 0.0625*(2*(Fz + Fx*(-1 + ux) + Fy*uy + Fz*uz)*(0.2222222222222222 + (ux - uz)*(ux - uz) -
0.3333333333333333*(-2*ux + ux*ux + uy*uy + uz*(2 + uz))) + (mgz + mgx*(-1 + ux) + mgy*uy + mgz*uz)*
(-2*chem*(ux - uz)*(ux - uz) + 0.3333333333333333*(-((rhoA - rhoB)*(ux - uz)*(ux - uz)) +
2*chem*(-2*ux + ux*ux + uy*uy + uz*(2 + uz))) + 0.1111111111111111*
(-4*chem + (rhoA - rhoB)*(-2*ux + ux*ux + uy*uy + uz*(2 + uz)))));
// q= 14
dist[14*Np+n] = m14 - (m14-feq14)/tau + 0.0625*(2*(Fx*(1 + ux) + Fy*uy + Fz*(-1 + uz))*(0.2222222222222222 + (ux - uz)*(ux - uz) -
0.3333333333333333*(2*ux + ux*ux + uy*uy + (-2 + uz)*uz)) + (mgx*(1 + ux) + mgy*uy + mgz*(-1 + uz))*
(-2*chem*(ux - uz)*(ux - uz) + 0.3333333333333333*(-((rhoA - rhoB)*(ux - uz)*(ux - uz)) +
2*chem*(2*ux + ux*ux + uy*uy + (-2 + uz)*uz)) + 0.1111111111111111*
(-4*chem + (rhoA - rhoB)*(2*ux + ux*ux + uy*uy + (-2 + uz)*uz))));
// q = 15
dist[15*Np+n] = m15 - (m15-feq15)/tau + 0.0625*(2*(Fx*ux + Fy*(-1 + uy) + Fz*(-1 + uz))*(0.2222222222222222 + (uy + uz)(uy + uz) -
0.3333333333333333*(ux*ux - 2*uy + uy*uy + (-2 + uz)*uz)) + (mgx*ux + mgy*(-1 + uy) + mgz*(-1 + uz))*
(-2*chem*(uy + uz)*(uy + uz) + 0.3333333333333333*(-((rhoA - rhoB)*(uy + uz)*(uy + uz)) +
2*chem*(ux*ux - 2*uy + uy*uy + (-2 + uz)*uz)) + 0.1111111111111111*
(-4*chem + (rhoA - rhoB)*(ux*ux - 2*uy + uy*uy + (-2 + uz)*uz))));
// q = 16
dist[16*Np+n] = m16 - (m16-feq16)/tau + 0.0625*(2*(Fy + Fz + Fx*ux + Fy*uy + Fz*uz)*(0.2222222222222222 + (uy + uz)*(uy + uz) -
0.3333333333333333*(ux*ux + 2*uy + uy*uy + uz*(2 + uz))) + (mgy + mgz + mgx*ux + mgy*uy + mgz*uz)*
(-2*chem*(uy + uz)*(uy + uz) + 0.3333333333333333*(-((rhoA - rhoB)*(uy + uz)*(uy + uz)) +
2*chem*(ux*ux + 2*uy + uy*uy + uz*(2 + uz))) + 0.1111111111111111*
(-4*chem + (rhoA - rhoB)*(ux*ux + 2*uy + uy*uy + uz*(2 + uz)))));
// q = 17
dist[17*Np+n] = m17 - (m17-feq17)/tau + 0.0625*(2*(Fz + Fx*ux + Fy*(-1 + uy) + Fz*uz)*(0.2222222222222222 + (uy - uz)*(uy - uz) -
0.3333333333333333*(ux*ux - 2*uy + uy*uy + uz*(2 + uz))) + (mgz + mgx*ux + mgy*(-1 + uy) + mgz*uz)*
(-2*chem*(uy - uz)*(uy - uz) + 0.3333333333333333*(-((rhoA - rhoB)*(uy - uz)*(uy - uz)) +
2*chem*(ux*ux - 2*uy + uy*uy + uz*(2 + uz))) + 0.1111111111111111*
(-4*chem + (rhoA - rhoB)*(ux*ux - 2*uy + uy*uy + uz*(2 + uz)))));
// q = 18
dist[18*Np+n] = m18 - (m18-feq18)/tau + 0.0625*(2*(Fx*ux + Fy*(1 + uy) + Fz*(-1 + uz))*(0.2222222222222222 + (uy - uz)*(uy - uz) -
0.3333333333333333*(ux*ux + 2*uy + uy*uy + (-2 + uz)*uz)) + (mgx*ux + mgy*(1 + uy) + mgz*(-1 + uz))*
(-2*chem*(uy - uz)*(uy - uz) + 0.3333333333333333*(-((rhoA - rhoB)*(uy - uz)*(uy - uz)) +
2*chem*(ux*ux + 2*uy + uy*uy + (-2 + uz)*uz)) + 0.1111111111111111*
(-4*chem + (rhoA - rhoB)*(ux*ux + 2*uy + uy*uy + (-2 + uz)*uz))));
//----------------------------------------------------------------------------------------------------------------------------------------//
// ----------------------------- compute phase field evolution ----------------------------------------
//Normalize the Color Gradient
C = sqrt(nx*nx+ny*ny+nz*nz);
double ColorMag = C;
if (C==0.0) ColorMag=1.0;
nx = nx/ColorMag;
ny = ny/ColorMag;
nz = nz/ColorMag;
//compute surface tension-related parameter
theta = M*4.5*(1-4.0*phi*phi)/W;
//load distributions of phase field
//q=0
h0 = hq[n];
//q=1
h1 = hq[2*Np+n];
//q=2
h2 = hq[1*Np+n];
//q=3
h3 = hq[4*Np+n];
//q=4
h4 = hq[3*Np+n];
//q=5
h5 = hq[6*Np+n];
//q=6
h6 = hq[5*Np+n];
//-------------------------------- BGK collison for phase field ---------------------------------//
// q = 0
hq[n] = h0 - (h0 - 0.3333333333333333*phi)/tauM;
// q = 1
hq[1*Np+n] = h1 - (h1 - phi*(0.1111111111111111 + 0.5*ux) - (0.5*M*nx*(1 - 4*phi*phi))/W)/tauM;
// q = 2
hq[2*Np+n] = h2 - (h2 - phi*(0.1111111111111111 - 0.5*ux) + (0.5*M*nx*(1 - 4*phi*phi))/W)/tauM;
// q = 3
hq[3*Np+n] = h3 - (h3 - phi*(0.1111111111111111 + 0.5*uy) - (0.5*M*ny*(1 - 4*phi*phi))/W)/tauM;
// q = 4
hq[4*Np+n] = h4 - (h4 - phi*(0.1111111111111111 - 0.5*uy) + (0.5*M*ny*(1 - 4*phi*phi))/W)/tauM;
// q = 5
hq[5*Np+n] = h5 - (h5 - phi*(0.1111111111111111 + 0.5*uz) - (0.5*M*nz*(1 - 4*phi*phi))/W)/tauM;
// q = 6
hq[6*Np+n] = h6 - (h6 - phi*(0.1111111111111111 - 0.5*uz) + (0.5*M*nz*(1 - 4*phi*phi))/W)/tauM;
//........................................................................
//Update velocity on device
Velocity[0*Np+n] = ux;
Velocity[1*Np+n] = uy;
Velocity[2*Np+n] = uz;
//Update pressure on device
Pressure[n] = p;
//Update chemical potential on device
mu_phi[n] = chem;
//Update color gradient on device
ColorGrad[0*Np+n] = nx;
ColorGrad[1*Np+n] = ny;
ColorGrad[2*Np+n] = nz;
}
}
extern "C" void ScaLBL_Color_Init(char *ID, double *Den, double *Phi, double das, double dbs, int Nx, int Ny, int Nz)
{
int n,N;
N = Nx*Ny*Nz;
for (n=0; n<N; n++){
if ( ID[n] == 1){
Den[n] = 1.0;
Den[N+n] = 0.0;
Phi[n] = 1.0;
}
else if ( ID[n] == 2){
Den[n] = 0.0;
Den[N+n] = 1.0;
Phi[n] = -1.0;
}
else{
Den[n] = das;
Den[N+n] = dbs;
Phi[n] = (das-dbs)/(das+dbs);
}
}
}
extern "C" void ScaLBL_Color_InitDistancePacked(char *ID, double *Den, double *Phi, double *Distance,
double das, double dbs, double beta, double xp, int Nx, int Ny, int Nz)
{
int i,j,k,n,N;
double d;
N = Nx*Ny*Nz;
for (n=0; n<N; n++){
//.......Back out the 3-D indices for node n..............
k = n/(Nx*Ny);
j = (n-Nx*Ny*k)/Nx;
i = n-Nx*Ny*k-Nx*j;
if ( ID[n] == 1){
Den[2*n] = 1.0;
Den[2*n+1] = 0.0;
Phi[n] = 1.0;
}
if (i == 0 || j == 0 || k == 0 || i == Nx-1 || j == Ny-1 || k == Nz-1){
Den[2*n] = 0.0;
Den[2*n+1] = 0.0;
}
else if ( ID[n] == 1){
Den[2*n] = 1.0;
Den[2*n+1] = 0.0;
Phi[n] = 1.0;
}
else if ( ID[n] == 2){
Den[2*n] = 0.0;
Den[2*n+1] = 1.0;
Phi[n] = -1.0;
}
else{
Den[2*n] = das;
Den[2*n+1] = dbs;
Phi[n] = (das-dbs)/(das+dbs);
d = fabs(Distance[n]);
Phi[n] = (2.f*(exp(-2.f*beta*(d+xp)))/(1.f+exp(-2.f*beta*(d+xp))) - 1.f);
}
}
}
extern "C" void ScaLBL_Color_InitDistance(char *ID, double *Den, double *Phi, double *Distance,
double das, double dbs, double beta, double xp, int Nx, int Ny, int Nz)
{
int n,N;
double d;
N = Nx*Ny*Nz;
for (n=0; n<N; n++){
if ( ID[n] == 1){
Den[n] = 1.0;
Den[N+n] = 0.0;
Phi[n] = 1.0;
}
else if ( ID[n] == 2){
Den[n] = 0.0;
Den[N+n] = 1.0;
Phi[n] = -1.0;
}
else{
Den[n] = das;
Den[N+n] = dbs;
Phi[n] = (das-dbs)/(das+dbs);
d = fabs(Distance[n]);
Phi[n] = (2.f*(exp(-2.f*beta*(d+xp)))/(1.f+exp(-2.f*beta*(d+xp))) - 1.f);
}
}
}
//*************************************************************************
//*************************************************************************
extern "C" void ScaLBL_Color_BC(int *list, int *Map, double *Phi, double *Den, double vA, double vB, int count, int Np)
{
int idx,n,nm;
// Fill the outlet with component b
for (idx=0; idx<count; idx++){
n = list[idx];
Den[n] = vA;
Den[Np+n] = vB;
nm = Map[n];
Phi[nm] = (vA-vB)/(vA+vB);
}
}
extern "C" void ScaLBL_Color_BC_z(int *list, int *Map, double *Phi, double *Den, double vA, double vB, int count, int Np)
{
int idx,n,nm;
// Fill the outlet with component b
for (idx=0; idx<count; idx++){
n = list[idx];
Den[n] = vA;
Den[Np+n] = vB;
//double valB = Den[Np+n]; // mass that reaches inlet is conserved
nm = Map[n];
Phi[nm] = (vA-vB)/(vA+vB);
}
}
extern "C" void ScaLBL_Color_BC_Z(int *list, int *Map, double *Phi, double *Den, double vA, double vB, int count, int Np)
{
int idx,n,nm;
// Fill the outlet with component b
for (idx=0; idx<count; idx++){
n = list[idx];
Den[n] = vA;
Den[Np+n] = vB;
nm = Map[n];
Phi[nm] = (vA-vB)/(vA+vB);
}
}
//*************************************************************************
//*************************************************************************
extern "C" void ScaLBL_D3Q19_ColorGradient(char *ID, double *phi, double *ColorGrad, int Nx, int Ny, int Nz)
{
int n,N,i,j,k,nn;
// distributions
double f1,f2,f3,f4,f5,f6,f7,f8,f9;
double f10,f11,f12,f13,f14,f15,f16,f17,f18;
double nx,ny,nz;
// non-conserved moments
// additional variables needed for computations
N = Nx*Ny*Nz;
for (n=0; n<N; n++){
//.......Back out the 3-D indices for node n..............
k = n/(Nx*Ny);
j = (n-Nx*Ny*k)/Nx;
i = n-Nx*Ny*k-Nx*j;
//........................................................................
//........Get 1-D index for this thread....................
// n = S*blockIdx.x*blockDim.x + s*blockDim.x + threadIdx.x;
//........................................................................
// COMPUTE THE COLOR GRADIENT
//........................................................................
//.................Read Phase Indicator Values............................
//........................................................................
nn = n-1; // neighbor index (get convention)
if (i-1<0) nn += Nx; // periodic BC along the x-boundary
f1 = phi[nn]; // get neighbor for phi - 1
//........................................................................
nn = n+1; // neighbor index (get convention)
if (!(i+1<Nx)) nn -= Nx; // periodic BC along the x-boundary
f2 = phi[nn]; // get neighbor for phi - 2
//........................................................................
nn = n-Nx; // neighbor index (get convention)
if (j-1<0) nn += Nx*Ny; // Perioidic BC along the y-boundary
f3 = phi[nn]; // get neighbor for phi - 3
//........................................................................
nn = n+Nx; // neighbor index (get convention)
if (!(j+1<Ny)) nn -= Nx*Ny; // Perioidic BC along the y-boundary
f4 = phi[nn]; // get neighbor for phi - 4
//........................................................................
nn = n-Nx*Ny; // neighbor index (get convention)
if (k-1<0) nn += Nx*Ny*Nz; // Perioidic BC along the z-boundary
f5 = phi[nn]; // get neighbor for phi - 5
//........................................................................
nn = n+Nx*Ny; // neighbor index (get convention)
if (!(k+1<Nz)) nn -= Nx*Ny*Nz; // Perioidic BC along the z-boundary
f6 = phi[nn]; // get neighbor for phi - 6
//........................................................................
nn = n-Nx-1; // neighbor index (get convention)
if (i-1<0) nn += Nx; // periodic BC along the x-boundary
if (j-1<0) nn += Nx*Ny; // Perioidic BC along the y-boundary
f7 = phi[nn]; // get neighbor for phi - 7
//........................................................................
nn = n+Nx+1; // neighbor index (get convention)
if (!(i+1<Nx)) nn -= Nx; // periodic BC along the x-boundary
if (!(j+1<Ny)) nn -= Nx*Ny; // Perioidic BC along the y-boundary
f8 = phi[nn]; // get neighbor for phi - 8
//........................................................................
nn = n+Nx-1; // neighbor index (get convention)
if (i-1<0) nn += Nx; // periodic BC along the x-boundary
if (!(j+1<Ny)) nn -= Nx*Ny; // Perioidic BC along the y-boundary
f9 = phi[nn]; // get neighbor for phi - 9
//........................................................................
nn = n-Nx+1; // neighbor index (get convention)
if (!(i+1<Nx)) nn -= Nx; // periodic BC along the x-boundary
if (j-1<0) nn += Nx*Ny; // Perioidic BC along the y-boundary
f10 = phi[nn]; // get neighbor for phi - 10
//........................................................................
nn = n-Nx*Ny-1; // neighbor index (get convention)
if (i-1<0) nn += Nx; // periodic BC along the x-boundary
if (k-1<0) nn += Nx*Ny*Nz; // Perioidic BC along the z-boundary
f11 = phi[nn]; // get neighbor for phi - 11
//........................................................................
nn = n+Nx*Ny+1; // neighbor index (get convention)
if (!(i+1<Nx)) nn -= Nx; // periodic BC along the x-boundary
if (!(k+1<Nz)) nn -= Nx*Ny*Nz; // Perioidic BC along the z-boundary
f12 = phi[nn]; // get neighbor for phi - 12
//........................................................................
nn = n+Nx*Ny-1; // neighbor index (get convention)
if (i-1<0) nn += Nx; // periodic BC along the x-boundary
if (!(k+1<Nz)) nn -= Nx*Ny*Nz; // Perioidic BC along the z-boundary
f13 = phi[nn]; // get neighbor for phi - 13
//........................................................................
nn = n-Nx*Ny+1; // neighbor index (get convention)
if (!(i+1<Nx)) nn -= Nx; // periodic BC along the x-boundary
if (k-1<0) nn += Nx*Ny*Nz; // Perioidic BC along the z-boundary
f14 = phi[nn]; // get neighbor for phi - 14
//........................................................................
nn = n-Nx*Ny-Nx; // neighbor index (get convention)
if (j-1<0) nn += Nx*Ny; // Perioidic BC along the y-boundary
if (k-1<0) nn += Nx*Ny*Nz; // Perioidic BC along the z-boundary
f15 = phi[nn]; // get neighbor for phi - 15
//........................................................................
nn = n+Nx*Ny+Nx; // neighbor index (get convention)
if (!(j+1<Ny)) nn -= Nx*Ny; // Perioidic BC along the y-boundary
if (!(k+1<Nz)) nn -= Nx*Ny*Nz; // Perioidic BC along the z-boundary
f16 = phi[nn]; // get neighbor for phi - 16
//........................................................................
nn = n+Nx*Ny-Nx; // neighbor index (get convention)
if (j-1<0) nn += Nx*Ny; // Perioidic BC along the y-boundary
if (!(k+1<Nz)) nn -= Nx*Ny*Nz; // Perioidic BC along the z-boundary
f17 = phi[nn]; // get neighbor for phi - 17
//........................................................................
nn = n-Nx*Ny+Nx; // neighbor index (get convention)
if (!(j+1<Ny)) nn -= Nx*Ny; // Perioidic BC along the y-boundary
if (k-1<0) nn += Nx*Ny*Nz; // Perioidic BC along the z-boundary
f18 = phi[nn]; // get neighbor for phi - 18
//............Compute the Color Gradient...................................
nx = -(f1-f2+0.5*(f7-f8+f9-f10+f11-f12+f13-f14));
ny = -(f3-f4+0.5*(f7-f8-f9+f10+f15-f16+f17-f18));
nz = -(f5-f6+0.5*(f11-f12-f13+f14+f15-f16-f17+f18));
//...........Normalize the Color Gradient.................................
// C = sqrt(nx*nx+ny*ny+nz*nz);
// nx = nx/C;
// ny = ny/C;
// nz = nz/C;
//...Store the Color Gradient....................
ColorGrad[n] = nx;
ColorGrad[N+n] = ny;
ColorGrad[2*N+n] = nz;
//...............................................
}
}
//*************************************************************************
extern "C" void ColorCollide( char *ID, double *disteven, double *distodd, double *ColorGrad,
double *Velocity, int Nx, int Ny, int Nz, double rlx_setA, double rlx_setB,
double alpha, double beta, double Fx, double Fy, double Fz, bool pBC)
{
int n,N;
// distributions
double f0,f1,f2,f3,f4,f5,f6,f7,f8,f9;
double f10,f11,f12,f13,f14,f15,f16,f17,f18;
// non-conserved moments
double m1,m2,m4,m6,m8,m9,m10,m11,m12,m13,m14,m15,m16,m17,m18;
// additional variables needed for computations
double rho,jx,jy,jz,C,nx,ny,nz;
N = Nx*Ny*Nz;
char id;
for (n=0; n<N; n++){
id = ID[n];
if (id > 0){
// Retrieve the color gradient
nx = ColorGrad[n];
ny = ColorGrad[N+n];
nz = ColorGrad[2*N+n];
//...........Normalize the Color Gradient.................................
C = sqrt(nx*nx+ny*ny+nz*nz);
if (C==0.0) C=1.0;
nx = nx/C;
ny = ny/C;
nz = nz/C;
//......No color gradient at z-boundary if pressure BC are set.............
// if (pBC && k==0) nx = ny = nz = 0.f;
// if (pBC && k==Nz-1) nx = ny = nz = 0.f;
//........................................................................
// READ THE DISTRIBUTIONS
// (read from opposite array due to previous swap operation)
//........................................................................
f2 = distodd[n];
f4 = distodd[N+n];
f6 = distodd[2*N+n];
f8 = distodd[3*N+n];
f10 = distodd[4*N+n];
f12 = distodd[5*N+n];
f14 = distodd[6*N+n];
f16 = distodd[7*N+n];
f18 = distodd[8*N+n];
//........................................................................
f0 = disteven[n];
f1 = disteven[N+n];
f3 = disteven[2*N+n];
f5 = disteven[3*N+n];
f7 = disteven[4*N+n];
f9 = disteven[5*N+n];
f11 = disteven[6*N+n];
f13 = disteven[7*N+n];
f15 = disteven[8*N+n];
f17 = disteven[9*N+n];
//........................................................................
// PERFORM RELAXATION PROCESS
//........................................................................
//....................compute the moments...............................................
rho = f0+f2+f1+f4+f3+f6+f5+f8+f7+f10+f9+f12+f11+f14+f13+f16+f15+f18+f17;
m1 = -30*f0-11*(f2+f1+f4+f3+f6+f5)+8*(f8+f7+f10+f9+f12+f11+f14+f13+f16+f15+f18 +f17);
m2 = 12*f0-4*(f2+f1 +f4+f3+f6 +f5)+f8+f7+f10+f9+f12+f11+f14+f13+f16+f15+f18+f17;
jx = f1-f2+f7-f8+f9-f10+f11-f12+f13-f14;
m4 = 4*(-f1+f2)+f7-f8+f9-f10+f11-f12+f13-f14;
jy = f3-f4+f7-f8-f9+f10+f15-f16+f17-f18;
m6 = -4*(f3-f4)+f7-f8-f9+f10+f15-f16+f17-f18;
jz = f5-f6+f11-f12-f13+f14+f15-f16-f17+f18;
m8 = -4*(f5-f6)+f11-f12-f13+f14+f15-f16-f17+f18;
m9 = 2*(f1+f2)-f3-f4-f5-f6+f7+f8+f9+f10+f11+f12+f13+f14-2*(f15+f16+f17+f18);
m10 = -4*(f1+f2)+2*(f4+f3+f6+f5)+f8+f7+f10+f9+f12+f11+f14+f13-2*(f16+f15+f18+f17);
m11 = f4+f3-f6-f5+f8+f7+f10+f9-f12-f11-f14-f13;
m12 = -2*(f4+f3-f6-f5)+f8+f7+f10+f9-f12-f11-f14-f13;
m13 = f8+f7-f10-f9;
m14 = f16+f15-f18-f17;
m15 = f12+f11-f14-f13;
m16 = f7-f8+f9-f10-f11+f12-f13+f14;
m17 = -f7+f8+f9-f10+f15-f16+f17-f18;
m18 = f11-f12-f13+f14-f15+f16+f17-f18;
//..........Toelke, Fruediger et. al. 2006...............
if (C == 0.0) nx = ny = nz = 1.0;
#ifdef STOKES
m1 = m1 + rlx_setA*(- 11*rho -alpha*C - m1);
m2 = m2 + rlx_setA*(3*rho - 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*( 0.5*alpha*C*(2*nx*nx-ny*ny-nz*nz) - m9);
m10 = m10 + rlx_setA*( - m10);
m11 = m11 + rlx_setA*( 0.5*alpha*C*(ny*ny-nz*nz)- m11);
m12 = m12 + rlx_setA*( - m12);
m13 = m13 + rlx_setA*( 0.5*alpha*C*nx*ny - m13);
m14 = m14 + rlx_setA*( 0.5*alpha*C*ny*nz - m14);
m15 = m15 + rlx_setA*( 0.5*alpha*C*nx*nz - m15);
m16 = m16 + rlx_setB*( - m16);
m17 = m17 + rlx_setB*( - m17);
m18 = m18 + rlx_setB*( - m18);
#else
m1 = m1 + rlx_setA*((19*(jx*jx+jy*jy+jz*jz)/rho - 11*rho) -alpha*C - m1);
m2 = m2 + rlx_setA*((3*rho - 5.5*(jx*jx+jy*jy+jz*jz)/rho)- 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)/rho) + 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)/rho) + 0.5*alpha*C*(ny*ny-nz*nz)- m11);
m12 = m12 + rlx_setA*( - m12);
m13 = m13 + rlx_setA*( (jx*jy/rho) + 0.5*alpha*C*nx*ny - m13);
m14 = m14 + rlx_setA*( (jy*jz/rho) + 0.5*alpha*C*ny*nz - m14);
m15 = m15 + rlx_setA*( (jx*jz/rho) + 0.5*alpha*C*nx*nz - m15);
m16 = m16 + rlx_setB*( - m16);
m17 = m17 + rlx_setB*( - m17);
m18 = m18 + rlx_setB*( - m18);
#endif
//.................inverse transformation......................................................
f0 = 0.05263157894736842*rho-0.012531328320802*m1+0.04761904761904762*m2;
f1 = 0.05263157894736842*rho-0.004594820384294068*m1-0.01587301587301587*m2
+0.1*(jx-m4)+0.0555555555555555555555555*(m9-m10);
f2 = 0.05263157894736842*rho-0.004594820384294068*m1-0.01587301587301587*m2
+0.1*(m4-jx)+0.0555555555555555555555555*(m9-m10);
f3 = 0.05263157894736842*rho-0.004594820384294068*m1-0.01587301587301587*m2
+0.1*(jy-m6)+0.02777777777777778*(m10-m9)+0.08333333333333333*(m11-m12);
f4 = 0.05263157894736842*rho-0.004594820384294068*m1-0.01587301587301587*m2
+0.1*(m6-jy)+0.02777777777777778*(m10-m9)+0.08333333333333333*(m11-m12);
f5 = 0.05263157894736842*rho-0.004594820384294068*m1-0.01587301587301587*m2
+0.1*(jz-m8)+0.02777777777777778*(m10-m9)+0.08333333333333333*(m12-m11);
f6 = 0.05263157894736842*rho-0.004594820384294068*m1-0.01587301587301587*m2
+0.1*(m8-jz)+0.02777777777777778*(m10-m9)+0.08333333333333333*(m12-m11);
f7 = 0.05263157894736842*rho+0.003341687552213868*m1+0.003968253968253968*m2+0.1*(jx+jy)+0.025*(m4+m6)
+0.02777777777777778*m9+0.01388888888888889*m10+0.08333333333333333*m11
+0.04166666666666666*m12+0.25*m13+0.125*(m16-m17);
f8 = 0.05263157894736842*rho+0.003341687552213868*m1+0.003968253968253968*m2-0.1*(jx+jy)-0.025*(m4+m6)
+0.02777777777777778*m9+0.01388888888888889*m10+0.08333333333333333*m11
+0.04166666666666666*m12+0.25*m13+0.125*(m17-m16);
f9 = 0.05263157894736842*rho+0.003341687552213868*m1+0.003968253968253968*m2+0.1*(jx-jy)+0.025*(m4-m6)
+0.02777777777777778*m9+0.01388888888888889*m10+0.08333333333333333*m11
+0.04166666666666666*m12-0.25*m13+0.125*(m16+m17);
f10 = 0.05263157894736842*rho+0.003341687552213868*m1+0.003968253968253968*m2+0.1*(jy-jx)+0.025*(m6-m4)
+0.02777777777777778*m9+0.01388888888888889*m10+0.08333333333333333*m11
+0.04166666666666666*m12-0.25*m13-0.125*(m16+m17);
f11 = 0.05263157894736842*rho+0.003341687552213868*m1
+0.003968253968253968*m2+0.1*(jx+jz)+0.025*(m4+m8)
+0.02777777777777778*m9+0.01388888888888889*m10-0.08333333333333333*m11
-0.04166666666666666*m12+0.25*m15+0.125*(m18-m16);
f12 = 0.05263157894736842*rho+0.003341687552213868*m1
+0.003968253968253968*m2-0.1*(jx+jz)-0.025*(m4+m8)
+0.02777777777777778*m9+0.01388888888888889*m10-0.08333333333333333*m11
-0.04166666666666666*m12+0.25*m15+0.125*(m16-m18);
f13 = 0.05263157894736842*rho+0.003341687552213868*m1
+0.003968253968253968*m2+0.1*(jx-jz)+0.025*(m4-m8)
+0.02777777777777778*m9+0.01388888888888889*m10-0.08333333333333333*m11
-0.04166666666666666*m12-0.25*m15-0.125*(m16+m18);
f14 = 0.05263157894736842*rho+0.003341687552213868*m1
+0.003968253968253968*m2+0.1*(jz-jx)+0.025*(m8-m4)
+0.02777777777777778*m9+0.01388888888888889*m10-0.08333333333333333*m11
-0.04166666666666666*m12-0.25*m15+0.125*(m16+m18);
f15 = 0.05263157894736842*rho+0.003341687552213868*m1
+0.003968253968253968*m2+0.1*(jy+jz)+0.025*(m6+m8)
-0.0555555555555555555555555*m9-0.02777777777777778*m10+0.25*m14+0.125*(m17-m18);
f16 = 0.05263157894736842*rho+0.003341687552213868*m1
+0.003968253968253968*m2-0.1*(jy+jz)-0.025*(m6+m8)
-0.0555555555555555555555555*m9-0.02777777777777778*m10+0.25*m14+0.125*(m18-m17);
f17 = 0.05263157894736842*rho+0.003341687552213868*m1
+0.003968253968253968*m2+0.1*(jy-jz)+0.025*(m6-m8)
-0.0555555555555555555555555*m9-0.02777777777777778*m10-0.25*m14+0.125*(m17+m18);
f18 = 0.05263157894736842*rho+0.003341687552213868*m1
+0.003968253968253968*m2+0.1*(jz-jy)+0.025*(m8-m6)
-0.0555555555555555555555555*m9-0.02777777777777778*m10-0.25*m14-0.125*(m17+m18);
//.......................................................................................................
// incorporate external force
f1 += 0.16666666*Fx;
f2 -= 0.16666666*Fx;
f3 += 0.16666666*Fy;
f4 -= 0.16666666*Fy;
f5 += 0.16666666*Fz;
f6 -= 0.16666666*Fz;
f7 += 0.08333333333*(Fx+Fy);
f8 -= 0.08333333333*(Fx+Fy);
f9 += 0.08333333333*(Fx-Fy);
f10 -= 0.08333333333*(Fx-Fy);
f11 += 0.08333333333*(Fx+Fz);
f12 -= 0.08333333333*(Fx+Fz);
f13 += 0.08333333333*(Fx-Fz);
f14 -= 0.08333333333*(Fx-Fz);
f15 += 0.08333333333*(Fy+Fz);
f16 -= 0.08333333333*(Fy+Fz);
f17 += 0.08333333333*(Fy-Fz);
f18 -= 0.08333333333*(Fy-Fz);
//*********** WRITE UPDATED VALUES TO MEMORY ******************
// Write the updated distributions
//....EVEN.....................................
disteven[n] = f0;
disteven[N+n] = f2;
disteven[2*N+n] = f4;
disteven[3*N+n] = f6;
disteven[4*N+n] = f8;
disteven[5*N+n] = f10;
disteven[6*N+n] = f12;
disteven[7*N+n] = f14;
disteven[8*N+n] = f16;
disteven[9*N+n] = f18;
//....ODD......................................
distodd[n] = f1;
distodd[N+n] = f3;
distodd[2*N+n] = f5;
distodd[3*N+n] = f7;
distodd[4*N+n] = f9;
distodd[5*N+n] = f11;
distodd[6*N+n] = f13;
distodd[7*N+n] = f15;
distodd[8*N+n] = f17;
//...Store the Velocity..........................
Velocity[n] = jx;
Velocity[N+n] = jy;
Velocity[2*N+n] = jz;
/* Velocity[3*n] = jx;
Velocity[3*n+1] = jy;
Velocity[3*n+2] = jz;
*/ //...Store the Color Gradient....................
// ColorGrad[3*n] = nx*C;
// ColorGrad[3*n+1] = ny*C;
// ColorGrad[3*n+2] = nz*C;
//...............................................
//***************************************************************
} // check if n is in the solid
} // loop over n
}
extern "C" void ScaLBL_D3Q19_ColorCollide( char *ID, double *disteven, double *distodd, double *phi, double *ColorGrad,
double *Velocity, int Nx, int Ny, int Nz, double rlx_setA, double rlx_setB,
double alpha, double beta, double Fx, double Fy, double Fz)
{
int i,j,k,n,nn,N;
// distributions
double f0,f1,f2,f3,f4,f5,f6,f7,f8,f9;
double f10,f11,f12,f13,f14,f15,f16,f17,f18;
// non-conserved moments
double m1,m2,m4,m6,m8,m9,m10,m11,m12,m13,m14,m15,m16,m17,m18;
// additional variables needed for computations
double rho,jx,jy,jz,C,nx,ny,nz;
N = Nx*Ny*Nz;
char id;
for (n=0; n<N; n++){
id = ID[n];
if (id > 0){
//.......Back out the 3-D indices for node n..............
k = n/(Nx*Ny);
j = (n-Nx*Ny*k)/Nx;
i = n-Nx*Ny*k-Nx*j;
//........................................................................
//........Get 1-D index for this thread....................
// n = S*blockIdx.x*blockDim.x + s*blockDim.x + threadIdx.x;
//........................................................................
// COMPUTE THE COLOR GRADIENT
//........................................................................
//.................Read Phase Indicator Values............................
//........................................................................
nn = n-1; // neighbor index (get convention)
if (i-1<0) nn += Nx; // periodic BC along the x-boundary
f1 = phi[nn]; // get neighbor for phi - 1
//........................................................................
nn = n+1; // neighbor index (get convention)
if (!(i+1<Nx)) nn -= Nx; // periodic BC along the x-boundary
f2 = phi[nn]; // get neighbor for phi - 2
//........................................................................
nn = n-Nx; // neighbor index (get convention)
if (j-1<0) nn += Nx*Ny; // Perioidic BC along the y-boundary
f3 = phi[nn]; // get neighbor for phi - 3
//........................................................................
nn = n+Nx; // neighbor index (get convention)
if (!(j+1<Ny)) nn -= Nx*Ny; // Perioidic BC along the y-boundary
f4 = phi[nn]; // get neighbor for phi - 4
//........................................................................
nn = n-Nx*Ny; // neighbor index (get convention)
if (k-1<0) nn += Nx*Ny*Nz; // Perioidic BC along the z-boundary
f5 = phi[nn]; // get neighbor for phi - 5
//........................................................................
nn = n+Nx*Ny; // neighbor index (get convention)
if (!(k+1<Nz)) nn -= Nx*Ny*Nz; // Perioidic BC along the z-boundary
f6 = phi[nn]; // get neighbor for phi - 6
//........................................................................
nn = n-Nx-1; // neighbor index (get convention)
if (i-1<0) nn += Nx; // periodic BC along the x-boundary
if (j-1<0) nn += Nx*Ny; // Perioidic BC along the y-boundary
f7 = phi[nn]; // get neighbor for phi - 7
//........................................................................
nn = n+Nx+1; // neighbor index (get convention)
if (!(i+1<Nx)) nn -= Nx; // periodic BC along the x-boundary
if (!(j+1<Ny)) nn -= Nx*Ny; // Perioidic BC along the y-boundary
f8 = phi[nn]; // get neighbor for phi - 8
//........................................................................
nn = n+Nx-1; // neighbor index (get convention)
if (i-1<0) nn += Nx; // periodic BC along the x-boundary
if (!(j+1<Ny)) nn -= Nx*Ny; // Perioidic BC along the y-boundary
f9 = phi[nn]; // get neighbor for phi - 9
//........................................................................
nn = n-Nx+1; // neighbor index (get convention)
if (!(i+1<Nx)) nn -= Nx; // periodic BC along the x-boundary
if (j-1<0) nn += Nx*Ny; // Perioidic BC along the y-boundary
f10 = phi[nn]; // get neighbor for phi - 10
//........................................................................
nn = n-Nx*Ny-1; // neighbor index (get convention)
if (i-1<0) nn += Nx; // periodic BC along the x-boundary
if (k-1<0) nn += Nx*Ny*Nz; // Perioidic BC along the z-boundary
f11 = phi[nn]; // get neighbor for phi - 11
//........................................................................
nn = n+Nx*Ny+1; // neighbor index (get convention)
if (!(i+1<Nx)) nn -= Nx; // periodic BC along the x-boundary
if (!(k+1<Nz)) nn -= Nx*Ny*Nz; // Perioidic BC along the z-boundary
f12 = phi[nn]; // get neighbor for phi - 12
//........................................................................
nn = n+Nx*Ny-1; // neighbor index (get convention)
if (i-1<0) nn += Nx; // periodic BC along the x-boundary
if (!(k+1<Nz)) nn -= Nx*Ny*Nz; // Perioidic BC along the z-boundary
f13 = phi[nn]; // get neighbor for phi - 13
//........................................................................
nn = n-Nx*Ny+1; // neighbor index (get convention)
if (!(i+1<Nx)) nn -= Nx; // periodic BC along the x-boundary
if (k-1<0) nn += Nx*Ny*Nz; // Perioidic BC along the z-boundary
f14 = phi[nn]; // get neighbor for phi - 14
//........................................................................
nn = n-Nx*Ny-Nx; // neighbor index (get convention)
if (j-1<0) nn += Nx*Ny; // Perioidic BC along the y-boundary
if (k-1<0) nn += Nx*Ny*Nz; // Perioidic BC along the z-boundary
f15 = phi[nn]; // get neighbor for phi - 15
//........................................................................
nn = n+Nx*Ny+Nx; // neighbor index (get convention)
if (!(j+1<Ny)) nn -= Nx*Ny; // Perioidic BC along the y-boundary
if (!(k+1<Nz)) nn -= Nx*Ny*Nz; // Perioidic BC along the z-boundary
f16 = phi[nn]; // get neighbor for phi - 16
//........................................................................
nn = n+Nx*Ny-Nx; // neighbor index (get convention)
if (j-1<0) nn += Nx*Ny; // Perioidic BC along the y-boundary
if (!(k+1<Nz)) nn -= Nx*Ny*Nz; // Perioidic BC along the z-boundary
f17 = phi[nn]; // get neighbor for phi - 17
//........................................................................
nn = n-Nx*Ny+Nx; // neighbor index (get convention)
if (!(j+1<Ny)) nn -= Nx*Ny; // Perioidic BC along the y-boundary
if (k-1<0) nn += Nx*Ny*Nz; // Perioidic BC along the z-boundary
f18 = phi[nn]; // get neighbor for phi - 18
//............Compute the Color Gradient...................................
nx = -(f1-f2+0.5*(f7-f8+f9-f10+f11-f12+f13-f14));
ny = -(f3-f4+0.5*(f7-f8-f9+f10+f15-f16+f17-f18));
nz = -(f5-f6+0.5*(f11-f12-f13+f14+f15-f16-f17+f18));
//...Store the Color Gradient....................
ColorGrad[n] = nx;
ColorGrad[N+n] = ny;
ColorGrad[2*N+n] = nz;
//...............................................
//...........Normalize the Color Gradient.................................
C = sqrt(nx*nx+ny*ny+nz*nz);
if (C==0.0) C=1.0;
nx = nx/C;
ny = ny/C;
nz = nz/C;
//......No color gradient at z-boundary if pressure BC are set.............
// if (pBC && k==0) nx = ny = nz = 0.f;
// if (pBC && k==Nz-1) nx = ny = nz = 0.f;
//........................................................................
// READ THE DISTRIBUTIONS
// (read from opposite array due to previous swap operation)
//........................................................................
f2 = distodd[n];
f4 = distodd[N+n];
f6 = distodd[2*N+n];
f0 = disteven[n];
f1 = disteven[N+n];
f3 = disteven[2*N+n];
f5 = disteven[3*N+n];
//........................................................................
//....................compute the moments...............................................
rho = f0+f2+f1+f4+f3+f6+f5;
m1 = -30*f0-11*(f2+f1+f4+f3+f6+f5);
m2 = 12*f0-4*(f2+f1 +f4+f3+f6 +f5);
jx = f1-f2;
m4 = 4*(-f1+f2);
jy = f3-f4;
m6 = -4*(f3-f4);
jz = f5-f6;
m8 = -4*(f5-f6);
m9 = 2*(f1+f2)-f3-f4-f5-f6;
m10 = -4*(f1+f2)+2*(f4+f3+f6+f5);
m11 = f4+f3-f6-f5;
m12 = -2*(f4+f3-f6-f5);
//........................................................................
f8 = distodd[3*N+n];
f10 = distodd[4*N+n];
f7 = disteven[4*N+n];
f9 = disteven[5*N+n];
//........................................................................
rho += f8+f7+f10+f9;
m1 += 8*(f8+f7+f10+f9);
m2 += f8+f7+f10+f9;
jx += f7-f8+f9-f10;
m4 += f7-f8+f9-f10;
jy += f7-f8-f9+f10;
m6 += f7-f8-f9+f10;
m9 += f7+f8+f9+f10;
m10 += f8+f7+f10+f9;
m11 += f8+f7+f10+f9;
m12 += f8+f7+f10+f9;
m13 = f8+f7-f10-f9;
m16 = f7-f8+f9-f10;
m17 = -f7+f8+f9-f10;
//........................................................................
f11 = disteven[6*N+n];
f13 = disteven[7*N+n];
f12 = distodd[5*N+n];
f14 = distodd[6*N+n];
//........................................................................
//........................................................................
f15 = disteven[8*N+n];
f17 = disteven[9*N+n];
f16 = distodd[7*N+n];
f18 = distodd[8*N+n];
//........................................................................
//....................compute the moments...............................................
rho += f12+f11+f14+f13+f16+f15+f18+f17;
m1 += 8*(f12+f11+f14+f13+f16+f15+f18+f17);
m2 += f12+f11+f14+f13+f16+f15+f18+f17;
jx += f11-f12+f13-f14;
m4 += f11-f12+f13-f14;
jy += f15-f16+f17-f18;
m6 += f15-f16+f17-f18;
jz += f11-f12-f13+f14+f15-f16-f17+f18;
m8 += f11-f12-f13+f14+f15-f16-f17+f18;
m9 += f11+f12+f13+f14-2*(f15+f16+f17+f18);
m10 += f12+f11+f14+f13-2*(f16+f15+f18+f17);
m11 += -f12-f11-f14-f13;
m12 += -f12-f11-f14-f13;
m14 = f16+f15-f18-f17;
m15 = f12+f11-f14-f13;
m16 += -f11+f12-f13+f14;
m17 += f15-f16+f17-f18;
m18 = f11-f12-f13+f14-f15+f16+f17-f18;
//........................................................................
/* f2 = distodd[n];
f4 = distodd[N+n];
f6 = distodd[2*N+n];
f8 = distodd[3*N+n];
//........................................................................
f0 = disteven[n];
f1 = disteven[N+n];
f3 = disteven[2*N+n];
f5 = disteven[3*N+n];
f7 = disteven[4*N+n];
//........................................................................
//........................................................................
//....................compute the moments...............................................
rho = f0+f2+f1+f4+f3+f6+f5+f8+f7;
m1 = -30*f0-11*(f2+f1+f4+f3+f6+f5)+8*(f8+f7);
m2 = 12*f0-4*(f2+f1 +f4+f3+f6 +f5)+f8+f7;
jx = f1-f2+f7-f8;
m4 = 4*(-f1+f2)+f7-f8;
jy = f3-f4+f7-f8;
m6 = -4*(f3-f4)+f7-f8;
jz = f5-f6;
m8 = -4*(f5-f6);
m9 = 2*(f1+f2)-f3-f4-f5-f6+f7+f8;
m10 = -4*(f1+f2)+2*(f4+f3+f6+f5)+f8+f7;
m11 = f4+f3-f6-f5+f8+f7;
m12 = -2*(f4+f3-f6-f5)+f8+f7;
m13 = f8+f7;
m16 = f7-f8;
m17 = -f7+f8;
//........................................................................
f9 = disteven[5*N+n];
f11 = disteven[6*N+n];
f13 = disteven[7*N+n];
f15 = disteven[8*N+n];
f17 = disteven[9*N+n];
f10 = distodd[4*N+n];
f12 = distodd[5*N+n];
f14 = distodd[6*N+n];
f16 = distodd[7*N+n];
f18 = distodd[8*N+n];
//........................................................................
rho += f10+f9+f12+f11+f14+f13+f16+f15+f18+f17;
m1 += 8*(f10+f9+f12+f11+f14+f13+f16+f15+f18 +f17);
m2 += f10+f9+f12+f11+f14+f13+f16+f15+f18+f17;
jx += f9-f10+f11-f12+f13-f14;
m4 += f9-f10+f11-f12+f13-f14;
jy += -f9+f10+f15-f16+f17-f18;
m6 += -f9+f10+f15-f16+f17-f18;
jz += f11-f12-f13+f14+f15-f16-f17+f18;
m8 += f11-f12-f13+f14+f15-f16-f17+f18;
m9 += f9+f10+f11+f12+f13+f14-2*(f15+f16+f17+f18);
m10 += f10+f9+f12+f11+f14+f13-2*(f16+f15+f18+f17);
m11 += f10+f9-f12-f11-f14-f13;
m12 += f10+f9-f12-f11-f14-f13;
m13 += -f10-f9;
m14 = f16+f15-f18-f17;
m15 = f12+f11-f14-f13;
m16 += f9-f10-f11+f12-f13+f14;
m17 += f9-f10+f15-f16+f17-f18;
m18 = f11-f12-f13+f14-f15+f16+f17-f18;
*/ //........................................................................
// PERFORM 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)/rho - 11*rho) -alpha*C - m1);
m2 = m2 + rlx_setA*((3*rho - 5.5*(jx*jx+jy*jy+jz*jz)/rho)- 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)/rho) + 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)/rho) + 0.5*alpha*C*(ny*ny-nz*nz)- m11);
m12 = m12 + rlx_setA*( - m12);
m13 = m13 + rlx_setA*( (jx*jy/rho) + 0.5*alpha*C*nx*ny - m13);
m14 = m14 + rlx_setA*( (jy*jz/rho) + 0.5*alpha*C*ny*nz - m14);
m15 = m15 + rlx_setA*( (jx*jz/rho) + 0.5*alpha*C*nx*nz - m15);
m16 = m16 + rlx_setB*( - m16);
m17 = m17 + rlx_setB*( - m17);
m18 = m18 + rlx_setB*( - m18);
//.................inverse transformation......................................................
f0 = 0.05263157894736842*rho-0.012531328320802*m1+0.04761904761904762*m2;
f1 = 0.05263157894736842*rho-0.004594820384294068*m1-0.01587301587301587*m2
+0.1*(jx-m4)+0.0555555555555555555555555*(m9-m10);
f2 = 0.05263157894736842*rho-0.004594820384294068*m1-0.01587301587301587*m2
+0.1*(m4-jx)+0.0555555555555555555555555*(m9-m10);
f3 = 0.05263157894736842*rho-0.004594820384294068*m1-0.01587301587301587*m2
+0.1*(jy-m6)+0.02777777777777778*(m10-m9)+0.08333333333333333*(m11-m12);
f4 = 0.05263157894736842*rho-0.004594820384294068*m1-0.01587301587301587*m2
+0.1*(m6-jy)+0.02777777777777778*(m10-m9)+0.08333333333333333*(m11-m12);
f5 = 0.05263157894736842*rho-0.004594820384294068*m1-0.01587301587301587*m2
+0.1*(jz-m8)+0.02777777777777778*(m10-m9)+0.08333333333333333*(m12-m11);
f6 = 0.05263157894736842*rho-0.004594820384294068*m1-0.01587301587301587*m2
+0.1*(m8-jz)+0.02777777777777778*(m10-m9)+0.08333333333333333*(m12-m11);
f7 = 0.05263157894736842*rho+0.003341687552213868*m1+0.003968253968253968*m2+0.1*(jx+jy)+0.025*(m4+m6)
+0.02777777777777778*m9+0.01388888888888889*m10+0.08333333333333333*m11
+0.04166666666666666*m12+0.25*m13+0.125*(m16-m17);
f8 = 0.05263157894736842*rho+0.003341687552213868*m1+0.003968253968253968*m2-0.1*(jx+jy)-0.025*(m4+m6)
+0.02777777777777778*m9+0.01388888888888889*m10+0.08333333333333333*m11
+0.04166666666666666*m12+0.25*m13+0.125*(m17-m16);
f9 = 0.05263157894736842*rho+0.003341687552213868*m1+0.003968253968253968*m2+0.1*(jx-jy)+0.025*(m4-m6)
+0.02777777777777778*m9+0.01388888888888889*m10+0.08333333333333333*m11
+0.04166666666666666*m12-0.25*m13+0.125*(m16+m17);
f10 = 0.05263157894736842*rho+0.003341687552213868*m1+0.003968253968253968*m2+0.1*(jy-jx)+0.025*(m6-m4)
+0.02777777777777778*m9+0.01388888888888889*m10+0.08333333333333333*m11
+0.04166666666666666*m12-0.25*m13-0.125*(m16+m17);
f11 = 0.05263157894736842*rho+0.003341687552213868*m1
+0.003968253968253968*m2+0.1*(jx+jz)+0.025*(m4+m8)
+0.02777777777777778*m9+0.01388888888888889*m10-0.08333333333333333*m11
-0.04166666666666666*m12+0.25*m15+0.125*(m18-m16);
f12 = 0.05263157894736842*rho+0.003341687552213868*m1
+0.003968253968253968*m2-0.1*(jx+jz)-0.025*(m4+m8)
+0.02777777777777778*m9+0.01388888888888889*m10-0.08333333333333333*m11
-0.04166666666666666*m12+0.25*m15+0.125*(m16-m18);
f13 = 0.05263157894736842*rho+0.003341687552213868*m1
+0.003968253968253968*m2+0.1*(jx-jz)+0.025*(m4-m8)
+0.02777777777777778*m9+0.01388888888888889*m10-0.08333333333333333*m11
-0.04166666666666666*m12-0.25*m15-0.125*(m16+m18);
f14 = 0.05263157894736842*rho+0.003341687552213868*m1
+0.003968253968253968*m2+0.1*(jz-jx)+0.025*(m8-m4)
+0.02777777777777778*m9+0.01388888888888889*m10-0.08333333333333333*m11
-0.04166666666666666*m12-0.25*m15+0.125*(m16+m18);
f15 = 0.05263157894736842*rho+0.003341687552213868*m1
+0.003968253968253968*m2+0.1*(jy+jz)+0.025*(m6+m8)
-0.0555555555555555555555555*m9-0.02777777777777778*m10+0.25*m14+0.125*(m17-m18);
f16 = 0.05263157894736842*rho+0.003341687552213868*m1
+0.003968253968253968*m2-0.1*(jy+jz)-0.025*(m6+m8)
-0.0555555555555555555555555*m9-0.02777777777777778*m10+0.25*m14+0.125*(m18-m17);
f17 = 0.05263157894736842*rho+0.003341687552213868*m1
+0.003968253968253968*m2+0.1*(jy-jz)+0.025*(m6-m8)
-0.0555555555555555555555555*m9-0.02777777777777778*m10-0.25*m14+0.125*(m17+m18);
f18 = 0.05263157894736842*rho+0.003341687552213868*m1
+0.003968253968253968*m2+0.1*(jz-jy)+0.025*(m8-m6)
-0.0555555555555555555555555*m9-0.02777777777777778*m10-0.25*m14-0.125*(m17+m18);
//.......................................................................................................
// incorporate external force
f1 += 0.16666666*Fx;
f2 -= 0.16666666*Fx;
f3 += 0.16666666*Fy;
f4 -= 0.16666666*Fy;
f5 += 0.16666666*Fz;
f6 -= 0.16666666*Fz;
f7 += 0.08333333333*(Fx+Fy);
f8 -= 0.08333333333*(Fx+Fy);
f9 += 0.08333333333*(Fx-Fy);
f10 -= 0.08333333333*(Fx-Fy);
f11 += 0.08333333333*(Fx+Fz);
f12 -= 0.08333333333*(Fx+Fz);
f13 += 0.08333333333*(Fx-Fz);
f14 -= 0.08333333333*(Fx-Fz);
f15 += 0.08333333333*(Fy+Fz);
f16 -= 0.08333333333*(Fy+Fz);
f17 += 0.08333333333*(Fy-Fz);
f18 -= 0.08333333333*(Fy-Fz);
//*********** WRITE UPDATED VALUES TO MEMORY ******************
// Write the updated distributions
//....EVEN.....................................
disteven[n] = f0;
disteven[N+n] = f2;
disteven[2*N+n] = f4;
disteven[3*N+n] = f6;
disteven[4*N+n] = f8;
disteven[5*N+n] = f10;
disteven[6*N+n] = f12;
disteven[7*N+n] = f14;
disteven[8*N+n] = f16;
disteven[9*N+n] = f18;
//....ODD......................................
distodd[n] = f1;
distodd[N+n] = f3;
distodd[2*N+n] = f5;
distodd[3*N+n] = f7;
distodd[4*N+n] = f9;
distodd[5*N+n] = f11;
distodd[6*N+n] = f13;
distodd[7*N+n] = f15;
distodd[8*N+n] = f17;
//...Store the Velocity..........................
Velocity[n] = jx;
Velocity[N+n] = jy;
Velocity[2*N+n] = jz;
//***************************************************************
} // check if n is in the solid
} // loop over n
}
extern "C" void ScaLBL_D3Q7_ColorCollideMass(char *ID, double *A_even, double *A_odd, double *B_even, double *B_odd,
double *Den, double *Phi, double *ColorGrad, double *Velocity, double beta, int N, bool pBC)
{
char id;
int idx,n,q,Cqx,Cqy,Cqz;
// int sendLoc;
double f0,f1,f2,f3,f4,f5,f6;
double na,nb,nab; // density values
double ux,uy,uz; // flow velocity
double nx,ny,nz,C; // color gradient components
double a1,a2,b1,b2;
double sp,delta;
//double feq[6]; // equilibrium distributions
// Set of Discrete velocities for the D3Q19 Model
//int D3Q7[3][3]={{1,0,0},{0,1,0},{0,0,1}};
for (n=0; n<N; n++){
id = ID[n];
if (id != 0 ){
//.....Load the Color gradient.........
nx = ColorGrad[n];
ny = ColorGrad[N+n];
nz = ColorGrad[2*N+n];
C = sqrt(nx*nx+ny*ny+nz*nz);
if (C==0.0) C=1.0;
nx = nx/C;
ny = ny/C;
nz = nz/C;
//....Load the flow velocity...........
ux = Velocity[n];
uy = Velocity[N+n];
uz = Velocity[2*N+n];
//........................................................................
// READ THE DISTRIBUTIONS
// (read from opposite array due to previous swap operation)
//........................................................................
f2 = A_odd[n];
f4 = A_odd[N+n];
f6 = A_odd[2*N+n];
f0 = A_even[n];
f1 = A_even[N+n];
f3 = A_even[2*N+n];
f5 = A_even[3*N+n];
na = f0+f1+f2+f3+f4+f5+f6;
//........................................................................
f2 = B_odd[n];
f4 = B_odd[N+n];
f6 = B_odd[2*N+n];
f0 = B_even[n];
f1 = B_even[N+n];
f3 = B_even[2*N+n];
f5 = B_even[3*N+n];
nb = f0+f1+f2+f3+f4+f5+f6;
nab = 1.0/(na+nb);
//........................................................................
//....Instantiate the density distributions
// Generate Equilibrium Distributions and stream
// Stationary value - distribution 0
A_even[n] = 0.3333333333333333*na;
B_even[n] = 0.3333333333333333*nb;
// Non-Stationary equilibrium distributions
//feq[0] = 0.1111111111111111*(1+4.5*ux);
//feq[1] = 0.1111111111111111*(1-4.5*ux);
//feq[2] = 0.1111111111111111*(1+4.5*uy);
//feq[3] = 0.1111111111111111*(1-4.5*uy);
//feq[4] = 0.1111111111111111*(1+4.5*uz);
//feq[5] = 0.1111111111111111*(1-4.5*uz);
//...............................................
// q = 0,2,4
// Cq = {1,0,0}, {0,1,0}, {0,0,1}
delta = beta*na*nb*nab*0.1111111111111111*nx;
if (!(na*nb*nab>0)) delta=0;
a1 = na*(0.1111111111111111*(1+4.5*ux))+delta;
b1 = nb*(0.1111111111111111*(1+4.5*ux))-delta;
a2 = na*(0.1111111111111111*(1-4.5*ux))-delta;
b2 = nb*(0.1111111111111111*(1-4.5*ux))+delta;
A_odd[n] = a1;
A_even[N+n] = a2;
B_odd[n] = b1;
B_even[N+n] = b2;
//...............................................
// q = 2
// Cq = {0,1,0}
delta = beta*na*nb*nab*0.1111111111111111*ny;
if (!(na*nb*nab>0)) delta=0;
a1 = na*(0.1111111111111111*(1+4.5*uy))+delta;
b1 = nb*(0.1111111111111111*(1+4.5*uy))-delta;
a2 = na*(0.1111111111111111*(1-4.5*uy))-delta;
b2 = nb*(0.1111111111111111*(1-4.5*uy))+delta;
A_odd[N+n] = a1;
A_even[2*N+n] = a2;
B_odd[N+n] = b1;
B_even[2*N+n] = b2;
//...............................................
// q = 4
// Cq = {0,0,1}
delta = beta*na*nb*nab*0.1111111111111111*nz;
if (!(na*nb*nab>0)) delta=0;
a1 = na*(0.1111111111111111*(1+4.5*uz))+delta;
b1 = nb*(0.1111111111111111*(1+4.5*uz))-delta;
a2 = na*(0.1111111111111111*(1-4.5*uz))-delta;
b2 = nb*(0.1111111111111111*(1-4.5*uz))+delta;
A_odd[2*N+n] = a1;
A_even[3*N+n] = a2;
B_odd[2*N+n] = b1;
B_even[3*N+n] = b2;
//...............................................
/* // Construction and streaming for the components
for (idx=0; idx<3; idx++){
//...............................................
// Distribution index
q = 2*idx;
// Associated discrete velocity
Cqx = D3Q7[idx][0];
Cqy = D3Q7[idx][1];
Cqz = D3Q7[idx][2];
// Generate the Equilibrium Distribution
a1 = na*feq[q];
b1 = nb*feq[q];
a2 = na*feq[q+1];
b2 = nb*feq[q+1];
// Recolor the distributions
if (C > 0.0){
sp = nx*double(Cqx)+ny*double(Cqy)+nz*double(Cqz);
//if (idx > 2) sp = 0.7071067811865475*sp;
//delta = sp*min( min(a1,a2), min(b1,b2) );
delta = na*nb/(na+nb)*0.1111111111111111*sp;
//if (a1>0 && b1>0){
a1 += beta*delta;
a2 -= beta*delta;
b1 -= beta*delta;
b2 += beta*delta;
}
// Save the re-colored distributions
A_odd[N*idx+n] = a1;
A_even[N*(idx+1)+n] = a2;
B_odd[N*idx+n] = b1;
B_even[N*(idx+1)+n] = b2;
//...............................................
}
*/
}
}
}
//*************************************************************************
extern "C" void DensityStreamD3Q7(char *ID, double *Den, double *Copy, double *Phi, double *ColorGrad, double *Velocity,
double beta, int Nx, int Ny, int Nz, bool pBC, int S)
{
char id;
int idx;
int in,jn,kn,n,nn,N;
int q,Cqx,Cqy,Cqz;
// int sendLoc;
double na,nb; // density values
double ux,uy,uz; // flow velocity
double nx,ny,nz,C; // color gradient components
double a1,a2,b1,b2;
double sp,delta;
double feq[6]; // equilibrium distributions
// Set of Discrete velocities for the D3Q19 Model
int D3Q7[3][3]={{1,0,0},{0,1,0},{0,0,1}};
N = Nx*Ny*Nz;
for (n=0; n<N; n++){
id = ID[n];
// Local Density Values
na = Copy[2*n];
nb = Copy[2*n+1];
if (id > 0 && na+nb > 0.0){
//.......Back out the 3-D indices for node n..............
int k = n/(Nx*Ny);
int j = (n-Nx*Ny*k)/Nx;
int i = n-Nx*Ny*k-Nx*j;
//.....Load the Color gradient.........
nx = ColorGrad[n];
ny = ColorGrad[N+n];
nz = ColorGrad[2*N+n];
C = sqrt(nx*nx+ny*ny+nz*nz);
nx = nx/C;
ny = ny/C;
nz = nz/C;
//....Load the flow velocity...........
ux = Velocity[n];
uy = Velocity[N+n];
uz = Velocity[2*N+n];
//....Instantiate the density distributions
// Generate Equilibrium Distributions and stream
// Stationary value - distribution 0
// Den[2*n] += 0.3333333333333333*na;
// Den[2*n+1] += 0.3333333333333333*nb;
Den[2*n] += 0.3333333333333333*na;
Den[2*n+1] += 0.3333333333333333*nb;
// Non-Stationary equilibrium distributions
feq[0] = 0.1111111111111111*(1+3*ux);
feq[1] = 0.1111111111111111*(1-3*ux);
feq[2] = 0.1111111111111111*(1+3*uy);
feq[3] = 0.1111111111111111*(1-3*uy);
feq[4] = 0.1111111111111111*(1+3*uz);
feq[5] = 0.1111111111111111*(1-3*uz);
// Construction and streaming for the components
for (idx=0; idx<3; idx++){
// Distribution index
q = 2*idx;
// Associated discrete velocity
Cqx = D3Q7[idx][0];
Cqy = D3Q7[idx][1];
Cqz = D3Q7[idx][2];
// Generate the Equilibrium Distribution
a1 = na*feq[q];
b1 = nb*feq[q];
a2 = na*feq[q+1];
b2 = nb*feq[q+1];
// Recolor the distributions
if (C > 0.0){
sp = nx*double(Cqx)+ny*double(Cqy)+nz*double(Cqz);
//if (idx > 2) sp = 0.7071067811865475*sp;
//delta = sp*min( min(a1,a2), min(b1,b2) );
delta = na*nb/(na+nb)*0.1111111111111111*sp;
//if (a1>0 && b1>0){
a1 += beta*delta;
a2 -= beta*delta;
b1 -= beta*delta;
b2 += beta*delta;
}
// .......Get the neighbor node..............
//nn = n + Stride[idx];
in = i+Cqx;
jn = j+Cqy;
kn = k+Cqz;
// Adjust for periodic BC, if necessary
// if (in<0) in+= Nx;
// if (jn<0) jn+= Ny;
// if (kn<0) kn+= Nz;
// if (!(in<Nx)) in-= Nx;
// if (!(jn<Ny)) jn-= Ny;
// if (!(kn<Nz)) kn-= Nz;
// Perform streaming or bounce-back as needed
id = ID[kn*Nx*Ny+jn*Nx+in];
if (id == 0){ //.....Bounce-back Rule...........
// Den[2*n] += a1;
// Den[2*n+1] += b1;
Den[2*n] += a1;
Den[2*n+1] += b1;
}
else{
//......Push the "distribution" to neighboring node...........
// Index of the neighbor in the local process
//nn = (kn-zmin[rank]+1)*Nxp*Nyp + (jn-ymin[rank]+1)*Nxp + (in-xmin[rank]+1);
nn = kn*Nx*Ny+jn*Nx+in;
// Push to neighboring node
// Den[2*nn] += a1;
// Den[2*nn+1] += b1;
Den[2*nn] += a1;
Den[2*nn+1] += b1;
}
// .......Get the neighbor node..............
q = 2*idx+1;
in = i-Cqx;
jn = j-Cqy;
kn = k-Cqz;
// Adjust for periodic BC, if necessary
// if (in<0) in+= Nx;
// if (jn<0) jn+= Ny;
// if (kn<0) kn+= Nz;
// if (!(in<Nx)) in-= Nx;
// if (!(jn<Ny)) jn-= Ny;
// if (!(kn<Nz)) kn-= Nz;
// Perform streaming or bounce-back as needed
id = ID[kn*Nx*Ny+jn*Nx+in];
if (id == 0){
//.....Bounce-back Rule...........
// Den[2*n] += a2;
// Den[2*n+1] += b2;
Den[2*n] += a2;
Den[2*n+1] += b2;
}
else{
//......Push the "distribution" to neighboring node...........
// Index of the neighbor in the local process
//nn = (kn-zmin[rank]+1)*Nxp*Nyp + (jn-ymin[rank]+1)*Nxp + (in-xmin[rank]+1);
nn = kn*Nx*Ny+jn*Nx+in;
// Push to neighboring node
// Den[2*nn] += a2;
// Den[2*nn+1] += b2;
Den[2*nn] += a2;
Den[2*nn+1] += b2;
}
}
}
}
}
extern "C" void ScaLBL_ComputePhaseField(char *ID, double *Phi, double *Den, int N)
{
int n;
double Na,Nb;
//...................................................................
// Update Phi
for (n=0; n<N; n++){
if (ID[n] > 0 ){
// Get the density value (Streaming already performed)
Na = Den[n];
Nb = Den[N+n];
Phi[n] = (Na-Nb)/(Na+Nb);
}
}
//...................................................................
}
extern "C" void ScaLBL_SetSlice_z(double *Phi, double value, int Nx, int Ny, int Nz, int Slice){
int n;
for (n=Slice*Nx*Ny; n<(Slice+1)*Nx*Ny; n++){
Phi[n] = value;
}
}
//extern "C" void ScaLBL_D3Q19_AAeven_Color(double *dist, double *Aq, double *Bq, double *Den, double *Velocity,
// double *ColorGrad, double rhoA, double rhoB, double tauA, double tauB, double alpha, double beta,
// double Fx, double Fy, double Fz, int start, int finish, int Np){
extern "C" void ScaLBL_D3Q19_AAeven_Color(int *Map, double *dist, double *Aq, double *Bq, double *Den, double *Phi,
double *Vel, double rhoA, double rhoB, double tauA, double tauB, double alpha, double beta,
double Fx, double Fy, double Fz, int strideY, int strideZ, int start, int finish, int Np){
int ijk,nn,n;
double fq;
// conserved momemnts
double rho,jx,jy,jz;
// non-conserved moments
double m1,m2,m4,m6,m8,m9,m10,m11,m12,m13,m14,m15,m16,m17,m18;
double m3,m5,m7;
double nA,nB; // number density
double a1,b1,a2,b2,nAB,delta;
double C,nx,ny,nz; //color gradient magnitude and direction
double ux,uy,uz;
double phi,tau,rho0,rlx_setA,rlx_setB;
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 component number densities
nA = Den[n];
nB = Den[Np + n];
// compute phase indicator field
phi=(nA-nB)/(nA+nB);
// local density
rho0=rhoA + 0.5*(1.0-phi)*(rhoB-rhoA);
// local relaxation time
tau=tauA + 0.5*(1.0-phi)*(tauB-tauA);
rlx_setA = 1.f/tau;
rlx_setB = 8.f*(2.f-rlx_setA)/(8.f-rlx_setA);
// Get the 1D index based on regular data layout
ijk = Map[n];
// COMPUTE THE COLOR GRADIENT
//........................................................................
//.................Read Phase Indicator Values............................
//........................................................................
nn = ijk-1; // neighbor index (get convention)
m1 = Phi[nn]; // get neighbor for phi - 1
//........................................................................
nn = ijk+1; // neighbor index (get convention)
m2 = Phi[nn]; // get neighbor for phi - 2
//........................................................................
nn = ijk-strideY; // neighbor index (get convention)
m3 = Phi[nn]; // get neighbor for phi - 3
//........................................................................
nn = ijk+strideY; // neighbor index (get convention)
m4 = Phi[nn]; // get neighbor for phi - 4
//........................................................................
nn = ijk-strideZ; // neighbor index (get convention)
m5 = Phi[nn]; // get neighbor for phi - 5
//........................................................................
nn = ijk+strideZ; // neighbor index (get convention)
m6 = Phi[nn]; // get neighbor for phi - 6
//........................................................................
nn = ijk-strideY-1; // neighbor index (get convention)
m7 = Phi[nn]; // get neighbor for phi - 7
//........................................................................
nn = ijk+strideY+1; // neighbor index (get convention)
m8 = Phi[nn]; // get neighbor for phi - 8
//........................................................................
nn = ijk+strideY-1; // neighbor index (get convention)
m9 = Phi[nn]; // get neighbor for phi - 9
//........................................................................
nn = ijk-strideY+1; // neighbor index (get convention)
m10 = Phi[nn]; // get neighbor for phi - 10
//........................................................................
nn = ijk-strideZ-1; // neighbor index (get convention)
m11 = Phi[nn]; // get neighbor for phi - 11
//........................................................................
nn = ijk+strideZ+1; // neighbor index (get convention)
m12 = Phi[nn]; // get neighbor for phi - 12
//........................................................................
nn = ijk+strideZ-1; // neighbor index (get convention)
m13 = Phi[nn]; // get neighbor for phi - 13
//........................................................................
nn = ijk-strideZ+1; // neighbor index (get convention)
m14 = Phi[nn]; // get neighbor for phi - 14
//........................................................................
nn = ijk-strideZ-strideY; // neighbor index (get convention)
m15 = Phi[nn]; // get neighbor for phi - 15
//........................................................................
nn = ijk+strideZ+strideY; // neighbor index (get convention)
m16 = Phi[nn]; // get neighbor for phi - 16
//........................................................................
nn = ijk+strideZ-strideY; // neighbor index (get convention)
m17 = Phi[nn]; // get neighbor for phi - 17
//........................................................................
nn = ijk-strideZ+strideY; // neighbor index (get convention)
m18 = Phi[nn]; // get neighbor for phi - 18
//............Compute the Color Gradient...................................
nx = -(m1-m2+0.5*(m7-m8+m9-m10+m11-m12+m13-m14));
ny = -(m3-m4+0.5*(m7-m8-m9+m10+m15-m16+m17-m18));
nz = -(m5-m6+0.5*(m11-m12-m13+m14+m15-m16-m17+m18));
//...........Normalize the Color Gradient.................................
C = sqrt(nx*nx+ny*ny+nz*nz);
double ColorMag = C;
if (C==0.0) ColorMag=1.0;
nx = nx/ColorMag;
ny = ny/ColorMag;
nz = nz/ColorMag;
// q=0
fq = dist[n];
rho = fq;
m1 = -30.0*fq;
m2 = 12.0*fq;
// q=1
fq = dist[2*Np+n];
rho += fq;
m1 -= 11.0*fq;
m2 -= 4.0*fq;
jx = fq;
m4 = -4.0*fq;
m9 = 2.0*fq;
m10 = -4.0*fq;
// f2 = dist[10*Np+n];
fq = dist[1*Np+n];
rho += fq;
m1 -= 11.0*(fq);
m2 -= 4.0*(fq);
jx -= fq;
m4 += 4.0*(fq);
m9 += 2.0*(fq);
m10 -= 4.0*(fq);
// q=3
fq = dist[4*Np+n];
rho += fq;
m1 -= 11.0*fq;
m2 -= 4.0*fq;
jy = fq;
m6 = -4.0*fq;
m9 -= fq;
m10 += 2.0*fq;
m11 = fq;
m12 = -2.0*fq;
// q = 4
fq = dist[3*Np+n];
rho+= fq;
m1 -= 11.0*fq;
m2 -= 4.0*fq;
jy -= fq;
m6 += 4.0*fq;
m9 -= fq;
m10 += 2.0*fq;
m11 += fq;
m12 -= 2.0*fq;
// q=5
fq = dist[6*Np+n];
rho += fq;
m1 -= 11.0*fq;
m2 -= 4.0*fq;
jz = fq;
m8 = -4.0*fq;
m9 -= fq;
m10 += 2.0*fq;
m11 -= fq;
m12 += 2.0*fq;
// q = 6
fq = dist[5*Np+n];
rho+= fq;
m1 -= 11.0*fq;
m2 -= 4.0*fq;
jz -= fq;
m8 += 4.0*fq;
m9 -= fq;
m10 += 2.0*fq;
m11 -= fq;
m12 += 2.0*fq;
// q=7
fq = dist[8*Np+n];
rho += fq;
m1 += 8.0*fq;
m2 += fq;
jx += fq;
m4 += fq;
jy += fq;
m6 += fq;
m9 += fq;
m10 += fq;
m11 += fq;
m12 += fq;
m13 = fq;
m16 = fq;
m17 = -fq;
// q = 8
fq = dist[7*Np+n];
rho += fq;
m1 += 8.0*fq;
m2 += fq;
jx -= fq;
m4 -= fq;
jy -= fq;
m6 -= fq;
m9 += fq;
m10 += fq;
m11 += fq;
m12 += fq;
m13 += fq;
m16 -= fq;
m17 += fq;
// q=9
fq = dist[10*Np+n];
rho += fq;
m1 += 8.0*fq;
m2 += fq;
jx += fq;
m4 += fq;
jy -= fq;
m6 -= fq;
m9 += fq;
m10 += fq;
m11 += fq;
m12 += fq;
m13 -= fq;
m16 += fq;
m17 += fq;
// q = 10
fq = dist[9*Np+n];
rho += fq;
m1 += 8.0*fq;
m2 += fq;
jx -= fq;
m4 -= fq;
jy += fq;
m6 += fq;
m9 += fq;
m10 += fq;
m11 += fq;
m12 += fq;
m13 -= fq;
m16 -= fq;
m17 -= fq;
// q=11
fq = dist[12*Np+n];
rho += fq;
m1 += 8.0*fq;
m2 += fq;
jx += fq;
m4 += fq;
jz += fq;
m8 += fq;
m9 += fq;
m10 += fq;
m11 -= fq;
m12 -= fq;
m15 = fq;
m16 -= fq;
m18 = fq;
// q=12
fq = dist[11*Np+n];
rho += fq;
m1 += 8.0*fq;
m2 += fq;
jx -= fq;
m4 -= fq;
jz -= fq;
m8 -= fq;
m9 += fq;
m10 += fq;
m11 -= fq;
m12 -= fq;
m15 += fq;
m16 += fq;
m18 -= fq;
// q=13
fq = dist[14*Np+n];
rho += fq;
m1 += 8.0*fq;
m2 += fq;
jx += fq;
m4 += fq;
jz -= fq;
m8 -= fq;
m9 += fq;
m10 += fq;
m11 -= fq;
m12 -= fq;
m15 -= fq;
m16 -= fq;
m18 -= fq;
// q=14
fq = dist[13*Np+n];
rho += fq;
m1 += 8.0*fq;
m2 += fq;
jx -= fq;
m4 -= fq;
jz += fq;
m8 += fq;
m9 += fq;
m10 += fq;
m11 -= fq;
m12 -= fq;
m15 -= fq;
m16 += fq;
m18 += fq;
// q=15
fq = dist[16*Np+n];
rho += fq;
m1 += 8.0*fq;
m2 += fq;
jy += fq;
m6 += fq;
jz += fq;
m8 += fq;
m9 -= 2.0*fq;
m10 -= 2.0*fq;
m14 = fq;
m17 += fq;
m18 -= fq;
// q=16
fq = dist[15*Np+n];
rho += fq;
m1 += 8.0*fq;
m2 += fq;
jy -= fq;
m6 -= fq;
jz -= fq;
m8 -= fq;
m9 -= 2.0*fq;
m10 -= 2.0*fq;
m14 += fq;
m17 -= fq;
m18 += fq;
// q=17
fq = dist[18*Np+n];
rho += fq;
m1 += 8.0*fq;
m2 += fq;
jy += fq;
m6 += fq;
jz -= fq;
m8 -= fq;
m9 -= 2.0*fq;
m10 -= 2.0*fq;
m14 -= fq;
m17 += fq;
m18 += fq;
// q=18
fq = dist[17*Np+n];
rho += fq;
m1 += 8.0*fq;
m2 += fq;
jy -= fq;
m6 -= fq;
jz += fq;
m8 += fq;
m9 -= 2.0*fq;
m10 -= 2.0*fq;
m14 -= fq;
m17 -= fq;
m18 -= fq;
//........................................................................
//..............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);
//.......................................................................................................
//.................inverse transformation......................................................
// q=0
fq = mrt_V1*rho-mrt_V2*m1+mrt_V3*m2;
dist[n] = fq;
// q = 1
fq = mrt_V1*rho-mrt_V4*m1-mrt_V5*m2+0.1*(jx-m4)+mrt_V6*(m9-m10) + 0.16666666*Fx;
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;
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;
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;
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;
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;
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);
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);
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);
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);
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);
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);
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);
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);
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);
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);
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);
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);
dist[18*Np+n] = fq;
//........................................................................
// write the velocity
ux = jx / rho0;
uy = jy / rho0;
uz = jz / rho0;
Vel[n] = ux;
Vel[Np+n] = uy;
Vel[2*Np+n] = uz;
// Instantiate mass transport distributions
// Stationary value - distribution 0
nAB = 1.0/(nA+nB);
Aq[n] = 0.3333333333333333*nA;
Bq[n] = 0.3333333333333333*nB;
//...............................................
// q = 0,2,4
// Cq = {1,0,0}, {0,1,0}, {0,0,1}
delta = beta*nA*nB*nAB*0.1111111111111111*nx;
if (!(nA*nB*nAB>0)) delta=0;
a1 = nA*(0.1111111111111111*(1+4.5*ux))+delta;
b1 = nB*(0.1111111111111111*(1+4.5*ux))-delta;
a2 = nA*(0.1111111111111111*(1-4.5*ux))-delta;
b2 = nB*(0.1111111111111111*(1-4.5*ux))+delta;
Aq[1*Np+n] = a1;
Bq[1*Np+n] = b1;
Aq[2*Np+n] = a2;
Bq[2*Np+n] = b2;
//...............................................
// q = 2
// Cq = {0,1,0}
delta = beta*nA*nB*nAB*0.1111111111111111*ny;
if (!(nA*nB*nAB>0)) delta=0;
a1 = nA*(0.1111111111111111*(1+4.5*uy))+delta;
b1 = nB*(0.1111111111111111*(1+4.5*uy))-delta;
a2 = nA*(0.1111111111111111*(1-4.5*uy))-delta;
b2 = nB*(0.1111111111111111*(1-4.5*uy))+delta;
Aq[3*Np+n] = a1;
Bq[3*Np+n] = b1;
Aq[4*Np+n] = a2;
Bq[4*Np+n] = b2;
//...............................................
// q = 4
// Cq = {0,0,1}
delta = beta*nA*nB*nAB*0.1111111111111111*nz;
if (!(nA*nB*nAB>0)) delta=0;
a1 = nA*(0.1111111111111111*(1+4.5*uz))+delta;
b1 = nB*(0.1111111111111111*(1+4.5*uz))-delta;
a2 = nA*(0.1111111111111111*(1-4.5*uz))-delta;
b2 = nB*(0.1111111111111111*(1-4.5*uz))+delta;
Aq[5*Np+n] = a1;
Bq[5*Np+n] = b1;
Aq[6*Np+n] = a2;
Bq[6*Np+n] = b2;
//...............................................
}
}
//extern "C" void ScaLBL_D3Q19_AAodd_Color(int *neighborList, double *dist, double *Aq, double *Bq, double *Den, double *Velocity,
// double *ColorGrad, double rhoA, double rhoB, double tauA, double tauB, double alpha, double beta,
// double Fx, double Fy, double Fz, int start, int finish, int Np){
extern "C" void ScaLBL_D3Q7_AAeven_PhaseField(int *Map, double *Aq, double *Bq, double *Den, double *Phi,
int start, int finish, int Np){
int idx,n,nread;
double fq,nA,nB;
for (int n=start; n<finish; n++){
// compute number density for component A
// q=0
fq = Aq[n];
nA = fq;
// q=1
fq = Aq[2*Np+n];
nA += fq;
// f2 = Aq[10*Np+n];
fq = Aq[1*Np+n];
nA += fq;
// q=3
fq = Aq[4*Np+n];
nA += fq;
// q = 4
fq = Aq[3*Np+n];
nA += fq;
// q=5
fq = Aq[6*Np+n];
nA += fq;
// q = 6
fq = Aq[5*Np+n];
nA += fq;
// compute number density for component B
// q=0
fq = Bq[n];
nB = fq;
// q=1
fq = Bq[2*Np+n];
nB += fq;
// f2 = Bq[10*Np+n];
fq = Bq[1*Np+n];
nB += fq;
// q=3
fq = Bq[4*Np+n];
nB += fq;
// q = 4
fq = Bq[3*Np+n];
nB += fq;
// q=5
fq = Bq[6*Np+n];
nB += fq;
// q = 6
fq = Bq[5*Np+n];
nB += fq;
// save the number densities
Den[n] = nA;
Den[Np+n] = nB;
// save the phase indicator field
idx = Map[n];
Phi[idx] = (nA-nB)/(nA+nB);
}
}
extern "C" void ScaLBL_D3Q19_Gradient(int *Map, double *phi, double *ColorGrad, int start, int finish, int Np, int Nx, int Ny, int Nz){
int idx,n,N,i,j,k,nn;
// distributions
double f1,f2,f3,f4,f5,f6,f7,f8,f9;
double f10,f11,f12,f13,f14,f15,f16,f17,f18;
double nx,ny,nz;
for (idx=0; idx<Np; idx++){
// Get the 1D index based on regular data layout
n = Map[idx];
//.......Back out the 3D indices for node n..............
k = n/(Nx*Ny);
j = (n-Nx*Ny*k)/Nx;
i = n-Nx*Ny*k-Nx*j;
//........................................................................
//........Get 1-D index for this thread....................
// n = S*blockIdx.x*blockDim.x + s*blockDim.x + threadIdx.x;
//........................................................................
// COMPUTE THE COLOR GRADIENT
//........................................................................
//.................Read Phase Indicator Values............................
//........................................................................
nn = n-1; // neighbor index (get convention)
if (i-1<0) nn += Nx; // periodic BC along the x-boundary
f1 = phi[nn]; // get neighbor for phi - 1
//........................................................................
nn = n+1; // neighbor index (get convention)
if (!(i+1<Nx)) nn -= Nx; // periodic BC along the x-boundary
f2 = phi[nn]; // get neighbor for phi - 2
//........................................................................
nn = n-Nx; // neighbor index (get convention)
if (j-1<0) nn += Nx*Ny; // Perioidic BC along the y-boundary
f3 = phi[nn]; // get neighbor for phi - 3
//........................................................................
nn = n+Nx; // neighbor index (get convention)
if (!(j+1<Ny)) nn -= Nx*Ny; // Perioidic BC along the y-boundary
f4 = phi[nn]; // get neighbor for phi - 4
//........................................................................
nn = n-Nx*Ny; // neighbor index (get convention)
if (k-1<0) nn += Nx*Ny*Nz; // Perioidic BC along the z-boundary
f5 = phi[nn]; // get neighbor for phi - 5
//........................................................................
nn = n+Nx*Ny; // neighbor index (get convention)
if (!(k+1<Nz)) nn -= Nx*Ny*Nz; // Perioidic BC along the z-boundary
f6 = phi[nn]; // get neighbor for phi - 6
//........................................................................
nn = n-Nx-1; // neighbor index (get convention)
if (i-1<0) nn += Nx; // periodic BC along the x-boundary
if (j-1<0) nn += Nx*Ny; // Perioidic BC along the y-boundary
f7 = phi[nn]; // get neighbor for phi - 7
//........................................................................
nn = n+Nx+1; // neighbor index (get convention)
if (!(i+1<Nx)) nn -= Nx; // periodic BC along the x-boundary
if (!(j+1<Ny)) nn -= Nx*Ny; // Perioidic BC along the y-boundary
f8 = phi[nn]; // get neighbor for phi - 8
//........................................................................
nn = n+Nx-1; // neighbor index (get convention)
if (i-1<0) nn += Nx; // periodic BC along the x-boundary
if (!(j+1<Ny)) nn -= Nx*Ny; // Perioidic BC along the y-boundary
f9 = phi[nn]; // get neighbor for phi - 9
//........................................................................
nn = n-Nx+1; // neighbor index (get convention)
if (!(i+1<Nx)) nn -= Nx; // periodic BC along the x-boundary
if (j-1<0) nn += Nx*Ny; // Perioidic BC along the y-boundary
f10 = phi[nn]; // get neighbor for phi - 10
//........................................................................
nn = n-Nx*Ny-1; // neighbor index (get convention)
if (i-1<0) nn += Nx; // periodic BC along the x-boundary
if (k-1<0) nn += Nx*Ny*Nz; // Perioidic BC along the z-boundary
f11 = phi[nn]; // get neighbor for phi - 11
//........................................................................
nn = n+Nx*Ny+1; // neighbor index (get convention)
if (!(i+1<Nx)) nn -= Nx; // periodic BC along the x-boundary
if (!(k+1<Nz)) nn -= Nx*Ny*Nz; // Perioidic BC along the z-boundary
f12 = phi[nn]; // get neighbor for phi - 12
//........................................................................
nn = n+Nx*Ny-1; // neighbor index (get convention)
if (i-1<0) nn += Nx; // periodic BC along the x-boundary
if (!(k+1<Nz)) nn -= Nx*Ny*Nz; // Perioidic BC along the z-boundary
f13 = phi[nn]; // get neighbor for phi - 13
//........................................................................
nn = n-Nx*Ny+1; // neighbor index (get convention)
if (!(i+1<Nx)) nn -= Nx; // periodic BC along the x-boundary
if (k-1<0) nn += Nx*Ny*Nz; // Perioidic BC along the z-boundary
f14 = phi[nn]; // get neighbor for phi - 14
//........................................................................
nn = n-Nx*Ny-Nx; // neighbor index (get convention)
if (j-1<0) nn += Nx*Ny; // Perioidic BC along the y-boundary
if (k-1<0) nn += Nx*Ny*Nz; // Perioidic BC along the z-boundary
f15 = phi[nn]; // get neighbor for phi - 15
//........................................................................
nn = n+Nx*Ny+Nx; // neighbor index (get convention)
if (!(j+1<Ny)) nn -= Nx*Ny; // Perioidic BC along the y-boundary
if (!(k+1<Nz)) nn -= Nx*Ny*Nz; // Perioidic BC along the z-boundary
f16 = phi[nn]; // get neighbor for phi - 16
//........................................................................
nn = n+Nx*Ny-Nx; // neighbor index (get convention)
if (j-1<0) nn += Nx*Ny; // Perioidic BC along the y-boundary
if (!(k+1<Nz)) nn -= Nx*Ny*Nz; // Perioidic BC along the z-boundary
f17 = phi[nn]; // get neighbor for phi - 17
//........................................................................
nn = n-Nx*Ny+Nx; // neighbor index (get convention)
if (!(j+1<Ny)) nn -= Nx*Ny; // Perioidic BC along the y-boundary
if (k-1<0) nn += Nx*Ny*Nz; // Perioidic BC along the z-boundary
f18 = phi[nn]; // get neighbor for phi - 18
//............Compute the Color Gradient...................................
nx = -(f1-f2+0.5*(f7-f8+f9-f10+f11-f12+f13-f14));
ny = -(f3-f4+0.5*(f7-f8-f9+f10+f15-f16+f17-f18));
nz = -(f5-f6+0.5*(f11-f12-f13+f14+f15-f16-f17+f18));
//...............................................
//...Store the Color Gradient....................
ColorGrad[idx] = nx;
ColorGrad[Np+idx] = ny;
ColorGrad[2*Np+idx] = nz;
//...............................................
}
}
extern "C" void ScaLBL_PhaseField_Init(int *Map, double *Phi, double *Den, double *Aq, double *Bq, int start, int finish, int Np){
int idx,n;
double phi,nA,nB;
for (idx=start; idx<finish; idx++){
n = Map[idx];
phi = Phi[n];
if (phi > 1.f){
nA = 1.0; nB = 0.f;
}
else if (phi < -1.f){
nB = 1.0; nA = 0.f;
}
else{
nA=0.5*(phi+1.f);
nB=0.5*(1.f-phi);
}
Den[idx] = nA;
Den[Np+idx] = nB;
Aq[idx]=0.3333333333333333*nA;
Aq[Np+idx]=0.1111111111111111*nA;
Aq[2*Np+idx]=0.1111111111111111*nA;
Aq[3*Np+idx]=0.1111111111111111*nA;
Aq[4*Np+idx]=0.1111111111111111*nA;
Aq[5*Np+idx]=0.1111111111111111*nA;
Aq[6*Np+idx]=0.1111111111111111*nA;
Bq[idx]=0.3333333333333333*nB;
Bq[Np+idx]=0.1111111111111111*nB;
Bq[2*Np+idx]=0.1111111111111111*nB;
Bq[3*Np+idx]=0.1111111111111111*nB;
Bq[4*Np+idx]=0.1111111111111111*nB;
Bq[5*Np+idx]=0.1111111111111111*nB;
Bq[6*Np+idx]=0.1111111111111111*nB;
}
}
extern "C" void ScaLBL_CopySlice_z(double *Phi, int Nx, int Ny, int Nz, int Source, int Dest){
int n; double value;
for (n=0; n<Nx*Ny; n++){
value = Phi[Source*Nx*Ny+n];
Phi[Dest*Nx*Ny+n] = value;
}
}
Reference in New Issue View Git Blame Copy Permalink