/*
Copyright 2013--2018 James E. McClure, Virginia Polytechnic & State University
Copyright Equnior ASA
This file is part of the Open Porous Media project (OPM).
OPM is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
OPM is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with OPM. If not, see .
*/
/*
Copyright 2013--2018 James E. McClure, Virginia Polytechnic & State University
Copyright Equnior ASA
This file is part of the Open Porous Media project (OPM).
OPM is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
OPM is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with OPM. If not, see .
*/
#include
#include
extern "C" void ScaLBL_Gradient_Unpack(double weight, double Cqx, double Cqy,
double Cqz, int *list, int start,
int count, double *recvbuf, double *phi,
double *grad, int N) {
//....................................................................................
// unpack halo and incorporate into D3Q19 based gradient
// Distribution q matche Cqx, Cqy, Cqz
//....................................................................................
int n, idx;
double value;
for (idx = 0; idx < count; idx++) {
// Get the index from the list
n = list[start + idx];
// unpack the distribution to the proper location
if (!(n < 0)) {
// PARALLEL UPDATE MUST BE DONE ATOMICALLY
value = weight * (recvbuf[idx] - phi[n]);
grad[n] += Cqx * value;
grad[N + n] += Cqy * value;
grad[2 * N + n] += Cqz * value;
}
}
}
extern "C" void ScaLBL_DFH_Init(double *Phi, double *Den, double *Aq,
double *Bq, int start, int finish, int Np) {
for (int idx = start; idx < finish; idx++) {
double phi, nA, nB;
phi = Phi[idx];
if (phi > 0.f) {
nA = 1.0;
nB = 0.f;
} else {
nB = 1.0;
nA = 0.f;
}
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;
}
}
// LBM based on density functional hydrodynamics
extern "C" void ScaLBL_D3Q19_AAeven_DFH(
int *neighborList, double *dist, double *Aq, double *Bq, double *Den,
double *Phi, double *Gradient, double *SolidForce, double rhoA, double rhoB,
double tauA, double tauB, double alpha, double beta, double Fx, double Fy,
double Fz, int start, int finish, int Np) {
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 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;
double force_x, force_y, force_z;
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);
//...........Read the Color Gradient.................................
nx = Gradient[n];
ny = Gradient[n + Np];
nz = Gradient[n + 2 * Np];
C = sqrt(nx * nx + ny * ny + nz * nz);
if (C == 0.0)
C = 1.0;
nx = nx / C;
ny = ny / C;
nz = nz / C;
// 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) -
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);
//.......................................................................................................
// assign force with wetting BC
force_x = alpha * (nA - nB) * SolidForce[n] + Fx;
force_y = alpha * (nA - nB) * SolidForce[n + Np] + Fy;
force_z = alpha * (nA - nB) * SolidForce[n + 2 * Np] + Fz;
//.................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 * force_x;
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 * force_x;
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 * force_y;
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 * force_y;
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 * force_z;
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 * force_z;
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 * (force_x + force_y);
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 * (force_x + force_y);
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 * (force_x - force_y);
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 * (force_x - force_y);
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 * (force_x + force_z);
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 * (force_x + force_z);
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 * (force_x - force_z);
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 * (force_x - force_z);
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 * (force_y + force_z);
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 * (force_y + force_z);
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 * (force_y - force_z);
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 * (force_y - force_z);
dist[18 * Np + n] = fq;
//........................................................................
// write the velocity
ux = (jx + force_x) / rho0;
uy = (jy + force_y) / rho0;
uz = (jz + force_z) / rho0;
//Velocity[n] = ux;
//Velocity[Np+n] = uy;
//Velocity[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_DFH(
int *neighborList, double *dist, double *Aq, double *Bq, double *Den,
double *Phi, double *Gradient, double *SolidForce, double rhoA, double rhoB,
double tauA, double tauB, double alpha, double beta, double Fx, double Fy,
double Fz, int start, int finish, int Np) {
int nread;
int nr1, nr2, nr3, nr4, nr5, nr6;
int nr7, nr8, nr9, nr10;
int nr11, nr12, nr13, nr14;
//int nr15,nr16,nr17,nr18;
double fq;
// conserved momemnts
double rho, jx, jy, jz;
// non-conserved moments
double m1, m2, m4, m6, m8, m9, m10, m11, m12, m13, m14, m15, m16, m17, m18;
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;
double force_x, force_y, force_z;
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);
//...........Read the Color Gradient.................................
nx = Gradient[n];
ny = Gradient[n + Np];
nz = Gradient[n + 2 * Np];
C = sqrt(nx * nx + ny * ny + nz * nz);
if (C == 0.0)
C = 1.0;
nx = nx / C;
ny = ny / C;
nz = nz / C;
// q=0
fq = dist[n];
rho = fq;
m1 = -30.0 * fq;
m2 = 12.0 * fq;
// q=1
//nread = neighborList[n]; // neighbor 2
//fq = dist[nread]; // reading the f1 data into register fq
nr1 = neighborList[n];
fq = dist[nr1]; // reading the f1 data into register fq
rho += fq;
m1 -= 11.0 * fq;
m2 -= 4.0 * fq;
jx = fq;
m4 = -4.0 * fq;
m9 = 2.0 * fq;
m10 = -4.0 * fq;
// f2 = dist[10*Np+n];
//nread = neighborList[n+Np]; // neighbor 1 ( < 10Np => even part of dist)
//fq = dist[nread]; // reading the f2 data into register fq
nr2 = neighborList[n + Np]; // neighbor 1 ( < 10Np => even part of dist)
fq = dist[nr2]; // reading the f2 data into register fq
rho += fq;
m1 -= 11.0 * (fq);
m2 -= 4.0 * (fq);
jx -= fq;
m4 += 4.0 * (fq);
m9 += 2.0 * (fq);
m10 -= 4.0 * (fq);
// q=3
//nread = neighborList[n+2*Np]; // neighbor 4
//fq = dist[nread];
nr3 = neighborList[n + 2 * Np]; // neighbor 4
fq = dist[nr3];
rho += fq;
m1 -= 11.0 * fq;
m2 -= 4.0 * fq;
jy = fq;
m6 = -4.0 * fq;
m9 -= fq;
m10 += 2.0 * fq;
m11 = fq;
m12 = -2.0 * fq;
// q = 4
//nread = neighborList[n+3*Np]; // neighbor 3
//fq = dist[nread];
nr4 = neighborList[n + 3 * Np]; // neighbor 3
fq = dist[nr4];
rho += fq;
m1 -= 11.0 * fq;
m2 -= 4.0 * fq;
jy -= fq;
m6 += 4.0 * fq;
m9 -= fq;
m10 += 2.0 * fq;
m11 += fq;
m12 -= 2.0 * fq;
// q=5
//nread = neighborList[n+4*Np];
//fq = dist[nread];
nr5 = neighborList[n + 4 * Np];
fq = dist[nr5];
rho += fq;
m1 -= 11.0 * fq;
m2 -= 4.0 * fq;
jz = fq;
m8 = -4.0 * fq;
m9 -= fq;
m10 += 2.0 * fq;
m11 -= fq;
m12 += 2.0 * fq;
// q = 6
//nread = neighborList[n+5*Np];
//fq = dist[nread];
nr6 = neighborList[n + 5 * Np];
fq = dist[nr6];
rho += fq;
m1 -= 11.0 * fq;
m2 -= 4.0 * fq;
jz -= fq;
m8 += 4.0 * fq;
m9 -= fq;
m10 += 2.0 * fq;
m11 -= fq;
m12 += 2.0 * fq;
// q=7
//nread = neighborList[n+6*Np];
//fq = dist[nread];
nr7 = neighborList[n + 6 * Np];
fq = dist[nr7];
rho += fq;
m1 += 8.0 * fq;
m2 += fq;
jx += fq;
m4 += fq;
jy += fq;
m6 += fq;
m9 += fq;
m10 += fq;
m11 += fq;
m12 += fq;
m13 = fq;
m16 = fq;
m17 = -fq;
// q = 8
//nread = neighborList[n+7*Np];
//fq = dist[nread];
nr8 = neighborList[n + 7 * Np];
fq = dist[nr8];
rho += fq;
m1 += 8.0 * fq;
m2 += fq;
jx -= fq;
m4 -= fq;
jy -= fq;
m6 -= fq;
m9 += fq;
m10 += fq;
m11 += fq;
m12 += fq;
m13 += fq;
m16 -= fq;
m17 += fq;
// q=9
//nread = neighborList[n+8*Np];
//fq = dist[nread];
nr9 = neighborList[n + 8 * Np];
fq = dist[nr9];
rho += fq;
m1 += 8.0 * fq;
m2 += fq;
jx += fq;
m4 += fq;
jy -= fq;
m6 -= fq;
m9 += fq;
m10 += fq;
m11 += fq;
m12 += fq;
m13 -= fq;
m16 += fq;
m17 += fq;
// q = 10
//nread = neighborList[n+9*Np];
//fq = dist[nread];
nr10 = neighborList[n + 9 * Np];
fq = dist[nr10];
rho += fq;
m1 += 8.0 * fq;
m2 += fq;
jx -= fq;
m4 -= fq;
jy += fq;
m6 += fq;
m9 += fq;
m10 += fq;
m11 += fq;
m12 += fq;
m13 -= fq;
m16 -= fq;
m17 -= fq;
// q=11
//nread = neighborList[n+10*Np];
//fq = dist[nread];
nr11 = neighborList[n + 10 * Np];
fq = dist[nr11];
rho += fq;
m1 += 8.0 * fq;
m2 += fq;
jx += fq;
m4 += fq;
jz += fq;
m8 += fq;
m9 += fq;
m10 += fq;
m11 -= fq;
m12 -= fq;
m15 = fq;
m16 -= fq;
m18 = fq;
// q=12
//nread = neighborList[n+11*Np];
//fq = dist[nread];
nr12 = neighborList[n + 11 * Np];
fq = dist[nr12];
rho += fq;
m1 += 8.0 * fq;
m2 += fq;
jx -= fq;
m4 -= fq;
jz -= fq;
m8 -= fq;
m9 += fq;
m10 += fq;
m11 -= fq;
m12 -= fq;
m15 += fq;
m16 += fq;
m18 -= fq;
// q=13
//nread = neighborList[n+12*Np];
//fq = dist[nread];
nr13 = neighborList[n + 12 * Np];
fq = dist[nr13];
rho += fq;
m1 += 8.0 * fq;
m2 += fq;
jx += fq;
m4 += fq;
jz -= fq;
m8 -= fq;
m9 += fq;
m10 += fq;
m11 -= fq;
m12 -= fq;
m15 -= fq;
m16 -= fq;
m18 -= fq;
// q=14
//nread = neighborList[n+13*Np];
//fq = dist[nread];
nr14 = neighborList[n + 13 * Np];
fq = dist[nr14];
rho += fq;
m1 += 8.0 * fq;
m2 += fq;
jx -= fq;
m4 -= fq;
jz += fq;
m8 += fq;
m9 += fq;
m10 += fq;
m11 -= fq;
m12 -= fq;
m15 -= fq;
m16 += fq;
m18 += fq;
// q=15
nread = neighborList[n + 14 * Np];
fq = dist[nread];
//fq = dist[17*Np+n];
rho += fq;
m1 += 8.0 * fq;
m2 += fq;
jy += fq;
m6 += fq;
jz += fq;
m8 += fq;
m9 -= 2.0 * fq;
m10 -= 2.0 * fq;
m14 = fq;
m17 += fq;
m18 -= fq;
// q=16
nread = neighborList[n + 15 * Np];
fq = dist[nread];
//fq = dist[8*Np+n];
rho += fq;
m1 += 8.0 * fq;
m2 += fq;
jy -= fq;
m6 -= fq;
jz -= fq;
m8 -= fq;
m9 -= 2.0 * fq;
m10 -= 2.0 * fq;
m14 += fq;
m17 -= fq;
m18 += fq;
// q=17
//fq = dist[18*Np+n];
nread = neighborList[n + 16 * Np];
fq = dist[nread];
rho += fq;
m1 += 8.0 * fq;
m2 += fq;
jy += fq;
m6 += fq;
jz -= fq;
m8 -= fq;
m9 -= 2.0 * fq;
m10 -= 2.0 * fq;
m14 -= fq;
m17 += fq;
m18 += fq;
// q=18
nread = neighborList[n + 17 * Np];
fq = dist[nread];
//fq = dist[9*Np+n];
rho += fq;
m1 += 8.0 * fq;
m2 += fq;
jy -= fq;
m6 -= fq;
jz += fq;
m8 += fq;
m9 -= 2.0 * fq;
m10 -= 2.0 * fq;
m14 -= fq;
m17 -= fq;
m18 -= fq;
//........................................................................
//..............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) -
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);
// assign force with wetting BC
force_x = alpha * (nA - nB) * SolidForce[n] + Fx;
force_y = alpha * (nA - nB) * SolidForce[n + Np] + Fy;
force_z = alpha * (nA - nB) * SolidForce[n + 2 * Np] + Fz;
//.................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 * force_x;
//nread = neighborList[n+Np];
dist[nr2] = fq;
// q=2
fq = mrt_V1 * rho - mrt_V4 * m1 - mrt_V5 * m2 + 0.1 * (m4 - jx) +
mrt_V6 * (m9 - m10) - 0.16666666 * force_x;
//nread = neighborList[n];
dist[nr1] = fq;
// q = 3
fq = mrt_V1 * rho - mrt_V4 * m1 - mrt_V5 * m2 + 0.1 * (jy - m6) +
mrt_V7 * (m10 - m9) + mrt_V8 * (m11 - m12) + 0.16666666 * force_y;
//nread = neighborList[n+3*Np];
dist[nr4] = fq;
// q = 4
fq = mrt_V1 * rho - mrt_V4 * m1 - mrt_V5 * m2 + 0.1 * (m6 - jy) +
mrt_V7 * (m10 - m9) + mrt_V8 * (m11 - m12) - 0.16666666 * force_y;
//nread = neighborList[n+2*Np];
dist[nr3] = fq;
// q = 5
fq = mrt_V1 * rho - mrt_V4 * m1 - mrt_V5 * m2 + 0.1 * (jz - m8) +
mrt_V7 * (m10 - m9) + mrt_V8 * (m12 - m11) + 0.16666666 * force_z;
//nread = neighborList[n+5*Np];
dist[nr6] = fq;
// q = 6
fq = mrt_V1 * rho - mrt_V4 * m1 - mrt_V5 * m2 + 0.1 * (m8 - jz) +
mrt_V7 * (m10 - m9) + mrt_V8 * (m12 - m11) - 0.16666666 * force_z;
//nread = neighborList[n+4*Np];
dist[nr5] = fq;
// q = 7
fq = mrt_V1 * rho + mrt_V9 * m1 + mrt_V10 * m2 + 0.1 * (jx + jy) +
0.025 * (m4 + m6) + mrt_V7 * m9 + mrt_V11 * m10 + mrt_V8 * m11 +
mrt_V12 * m12 + 0.25 * m13 + 0.125 * (m16 - m17) +
0.08333333333 * (force_x + force_y);
//nread = neighborList[n+7*Np];
dist[nr8] = fq;
// q = 8
fq = mrt_V1 * rho + mrt_V9 * m1 + mrt_V10 * m2 - 0.1 * (jx + jy) -
0.025 * (m4 + m6) + mrt_V7 * m9 + mrt_V11 * m10 + mrt_V8 * m11 +
mrt_V12 * m12 + 0.25 * m13 + 0.125 * (m17 - m16) -
0.08333333333 * (force_x + force_y);
//nread = neighborList[n+6*Np];
dist[nr7] = fq;
// q = 9
fq = mrt_V1 * rho + mrt_V9 * m1 + mrt_V10 * m2 + 0.1 * (jx - jy) +
0.025 * (m4 - m6) + mrt_V7 * m9 + mrt_V11 * m10 + mrt_V8 * m11 +
mrt_V12 * m12 - 0.25 * m13 + 0.125 * (m16 + m17) +
0.08333333333 * (force_x - force_y);
//nread = neighborList[n+9*Np];
dist[nr10] = fq;
// q = 10
fq = mrt_V1 * rho + mrt_V9 * m1 + mrt_V10 * m2 + 0.1 * (jy - jx) +
0.025 * (m6 - m4) + mrt_V7 * m9 + mrt_V11 * m10 + mrt_V8 * m11 +
mrt_V12 * m12 - 0.25 * m13 - 0.125 * (m16 + m17) -
0.08333333333 * (force_x - force_y);
//nread = neighborList[n+8*Np];
dist[nr9] = fq;
// q = 11
fq = mrt_V1 * rho + mrt_V9 * m1 + mrt_V10 * m2 + 0.1 * (jx + jz) +
0.025 * (m4 + m8) + mrt_V7 * m9 + mrt_V11 * m10 - mrt_V8 * m11 -
mrt_V12 * m12 + 0.25 * m15 + 0.125 * (m18 - m16) +
0.08333333333 * (force_x + force_z);
//nread = neighborList[n+11*Np];
dist[nr12] = fq;
// q = 12
fq = mrt_V1 * rho + mrt_V9 * m1 + mrt_V10 * m2 - 0.1 * (jx + jz) -
0.025 * (m4 + m8) + mrt_V7 * m9 + mrt_V11 * m10 - mrt_V8 * m11 -
mrt_V12 * m12 + 0.25 * m15 + 0.125 * (m16 - m18) -
0.08333333333 * (force_x + force_z);
//nread = neighborList[n+10*Np];
dist[nr11] = fq;
// q = 13
fq = mrt_V1 * rho + mrt_V9 * m1 + mrt_V10 * m2 + 0.1 * (jx - jz) +
0.025 * (m4 - m8) + mrt_V7 * m9 + mrt_V11 * m10 - mrt_V8 * m11 -
mrt_V12 * m12 - 0.25 * m15 - 0.125 * (m16 + m18) +
0.08333333333 * (force_x - force_z);
//nread = neighborList[n+13*Np];
dist[nr14] = fq;
// q= 14
fq = mrt_V1 * rho + mrt_V9 * m1 + mrt_V10 * m2 + 0.1 * (jz - jx) +
0.025 * (m8 - m4) + mrt_V7 * m9 + mrt_V11 * m10 - mrt_V8 * m11 -
mrt_V12 * m12 - 0.25 * m15 + 0.125 * (m16 + m18) -
0.08333333333 * (force_x - force_z);
//nread = neighborList[n+12*Np];
dist[nr13] = fq;
// q = 15
fq = mrt_V1 * rho + mrt_V9 * m1 + mrt_V10 * m2 + 0.1 * (jy + jz) +
0.025 * (m6 + m8) - mrt_V6 * m9 - mrt_V7 * m10 + 0.25 * m14 +
0.125 * (m17 - m18) + 0.08333333333 * (force_y + force_z);
nread = neighborList[n + 15 * Np];
dist[nread] = fq;
// q = 16
fq = mrt_V1 * rho + mrt_V9 * m1 + mrt_V10 * m2 - 0.1 * (jy + jz) -
0.025 * (m6 + m8) - mrt_V6 * m9 - mrt_V7 * m10 + 0.25 * m14 +
0.125 * (m18 - m17) - 0.08333333333 * (force_y + force_z);
nread = neighborList[n + 14 * Np];
dist[nread] = fq;
// q = 17
fq = mrt_V1 * rho + mrt_V9 * m1 + mrt_V10 * m2 + 0.1 * (jy - jz) +
0.025 * (m6 - m8) - mrt_V6 * m9 - mrt_V7 * m10 - 0.25 * m14 +
0.125 * (m17 + m18) + 0.08333333333 * (force_y - force_z);
nread = neighborList[n + 17 * Np];
dist[nread] = fq;
// q = 18
fq = mrt_V1 * rho + mrt_V9 * m1 + mrt_V10 * m2 + 0.1 * (jz - jy) +
0.025 * (m8 - m6) - mrt_V6 * m9 - mrt_V7 * m10 - 0.25 * m14 -
0.125 * (m17 + m18) - 0.08333333333 * (force_y - force_z);
nread = neighborList[n + 16 * Np];
dist[nread] = fq;
// write the velocity
ux = (jx + force_x) / rho0;
uy = (jy + force_y) / rho0;
uz = (jz + force_z) / rho0;
//Velocity[n] = ux;
//Velocity[Np+n] = uy;
//Velocity[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;
// q = 1
//nread = neighborList[n+Np];
Aq[nr2] = a1;
Bq[nr2] = b1;
// q=2
//nread = neighborList[n];
Aq[nr1] = a2;
Bq[nr1] = b2;
//...............................................
// Cq = {0,1,0}
delta = beta * nA * nB * nAB * 0.1111111111111111 * ny;
if (!(nA * nB * nAB > 0))
delta = 0;
a1 = nA * (0.1111111111111111 * (1 + 4.5 * uy)) + delta;
b1 = nB * (0.1111111111111111 * (1 + 4.5 * uy)) - delta;
a2 = nA * (0.1111111111111111 * (1 - 4.5 * uy)) - delta;
b2 = nB * (0.1111111111111111 * (1 - 4.5 * uy)) + delta;
// q = 3
//nread = neighborList[n+3*Np];
Aq[nr4] = a1;
Bq[nr4] = b1;
// q = 4
//nread = neighborList[n+2*Np];
Aq[nr3] = a2;
Bq[nr3] = b2;
//...............................................
// q = 4
// Cq = {0,0,1}
delta = beta * nA * nB * nAB * 0.1111111111111111 * nz;
if (!(nA * nB * nAB > 0))
delta = 0;
a1 = nA * (0.1111111111111111 * (1 + 4.5 * uz)) + delta;
b1 = nB * (0.1111111111111111 * (1 + 4.5 * uz)) - delta;
a2 = nA * (0.1111111111111111 * (1 - 4.5 * uz)) - delta;
b2 = nB * (0.1111111111111111 * (1 - 4.5 * uz)) + delta;
// q = 5
//nread = neighborList[n+5*Np];
Aq[nr6] = a1;
Bq[nr6] = b1;
// q = 6
//nread = neighborList[n+4*Np];
Aq[nr5] = a2;
Bq[nr5] = b2;
//...............................................
}
}
extern "C" void ScaLBL_D3Q7_AAodd_DFH(int *neighborList, double *Aq, double *Bq,
double *Den, double *Phi, int start,
int finish, int Np) {
for (int n = start; n < finish; n++) {
int nread;
double fq, nA, nB;
//..........Compute the number density for component A............
// q=0
fq = Aq[n];
nA = fq;
// q=1
nread = neighborList[n];
fq = Aq[nread];
nA += fq;
// q=2
nread = neighborList[n + Np];
fq = Aq[nread];
nA += fq;
// q=3
nread = neighborList[n + 2 * Np];
fq = Aq[nread];
nA += fq;
// q = 4
nread = neighborList[n + 3 * Np];
fq = Aq[nread];
nA += fq;
// q=5
nread = neighborList[n + 4 * Np];
fq = Aq[nread];
nA += fq;
// q = 6
nread = neighborList[n + 5 * Np];
fq = Aq[nread];
nA += fq;
//..........Compute the number density for component B............
// q=0
fq = Bq[n];
nB = fq;
// q=1
nread = neighborList[n];
fq = Bq[nread];
nB += fq;
// q=2
nread = neighborList[n + Np];
fq = Bq[nread];
nB += fq;
// q=3
nread = neighborList[n + 2 * Np];
fq = Bq[nread];
nB += fq;
// q = 4
nread = neighborList[n + 3 * Np];
fq = Bq[nread];
nB += fq;
// q=5
nread = neighborList[n + 4 * Np];
fq = Bq[nread];
nB += fq;
// q = 6
nread = neighborList[n + 5 * Np];
fq = Bq[nread];
nB += fq;
// save the number densities
Den[n] = nA;
Den[Np + n] = nB;
// save the phase indicator field
//idx = Map[n];
Phi[n] = (nA - nB) / (nA + nB);
}
}
extern "C" void ScaLBL_D3Q7_AAeven_DFH(double *Aq, double *Bq, double *Den,
double *Phi, int start, int finish,
int Np) {
for (int n = start; n < finish; n++) {
double fq, nA, nB;
// 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[n] = (nA - nB) / (nA + nB);
}
}
extern "C" void ScaLBL_D3Q19_Gradient_DFH(int *neighborList, double *Phi,
double *ColorGrad, int start,
int finish, int Np) {
int n, nn;
// distributions
double m1, m2, m4, m6, m8, m9, m10, m11, m12, m13, m14, m15, m16, m17, m18;
double m3, m5, m7;
double nx, ny, nz;
// non-conserved moments
// additional variables needed for computations
for (n = start; n < finish; n++) {
nn = neighborList[n + Np] % Np;
m1 = Phi[nn];
nn = neighborList[n] % Np;
m2 = Phi[nn];
nn = neighborList[n + 3 * Np] % Np;
m3 = Phi[nn];
nn = neighborList[n + 2 * Np] % Np;
m4 = Phi[nn];
nn = neighborList[n + 5 * Np] % Np;
m5 = Phi[nn];
nn = neighborList[n + 4 * Np] % Np;
m6 = Phi[nn];
nn = neighborList[n + 7 * Np] % Np;
m7 = Phi[nn];
nn = neighborList[n + 6 * Np] % Np;
m8 = Phi[nn];
nn = neighborList[n + 9 * Np] % Np;
m9 = Phi[nn];
nn = neighborList[n + 8 * Np] % Np;
m10 = Phi[nn];
nn = neighborList[n + 11 * Np] % Np;
m11 = Phi[nn];
nn = neighborList[n + 10 * Np] % Np;
m12 = Phi[nn];
nn = neighborList[n + 13 * Np] % Np;
m13 = Phi[nn];
nn = neighborList[n + 12 * Np] % Np;
m14 = Phi[nn];
nn = neighborList[n + 15 * Np] % Np;
m15 = Phi[nn];
nn = neighborList[n + 14 * Np] % Np;
m16 = Phi[nn];
nn = neighborList[n + 17 * Np] % Np;
m17 = Phi[nn];
nn = neighborList[n + 16 * Np] % Np;
m18 = Phi[nn];
//............Compute the Color Gradient...................................
//............Compute the wn fluid 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));
/* // .... read the solid potential gradient.....................
m1 = SolidPotential[n];
m2 = SolidPotential[n+Np];
m3 = SolidPotential[n+2*Np];
nx += m1;
ny += m2;
nz += m3;
*/
//...........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[Np + n] = ny;
ColorGrad[2 * Np + n] = nz;
//...............................................
}
}