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NuSiF-Solver/BasicSolver/3D-seq/src/solver.c

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Initial checkin
2023-02-05 07:34:23 +01:00
/*
* Copyright (C) 2022 NHR@FAU, University Erlangen-Nuremberg.
* All rights reserved. This file is part of nusif-solver.
* Use of this source code is governed by a MIT style
* license that can be found in the LICENSE file.
*/
#include <float.h>
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include "allocate.h"
#include "parameter.h"
#include "solver.h"
#include "util.h"
#define P(i, j, k) p[(k) * (imax + 2) * (jmax + 2) + (j) * (imax + 2) + (i)]
#define F(i, j, k) f[(k) * (imax + 2) * (jmax + 2) + (j) * (imax + 2) + (i)]
#define G(i, j, k) g[(k) * (imax + 2) * (jmax + 2) + (j) * (imax + 2) + (i)]
#define H(i, j, k) h[(k) * (imax + 2) * (jmax + 2) + (j) * (imax + 2) + (i)]
#define U(i, j, k) u[(k) * (imax + 2) * (jmax + 2) + (j) * (imax + 2) + (i)]
#define V(i, j, k) v[(k) * (imax + 2) * (jmax + 2) + (j) * (imax + 2) + (i)]
#define W(i, j, k) w[(k) * (imax + 2) * (jmax + 2) + (j) * (imax + 2) + (i)]
#define RHS(i, j, k) rhs[(k) * (imax + 2) * (jmax + 2) + (j) * (imax + 2) + (i)]
static void printConfig(Solver* s)
{
printf("Parameters for #%s#\n", s->problem);
printf("BC Left:%d Right:%d Bottom:%d Top:%d Front:%d Back:%d\n",
s->bcLeft,
s->bcRight,
s->bcBottom,
s->bcTop,
s->bcFront,
s->bcBack);
printf("\tReynolds number: %.2f\n", s->re);
printf("\tGx Gy: %.2f %.2f %.2f\n", s->gx, s->gy, s->gz);
printf("Geometry data:\n");
printf("\tDomain box size (x, y, z): %.2f, %.2f, %.2f\n",
s->grid.xlength,
s->grid.ylength,
s->grid.zlength);
printf("\tCells (x, y, z): %d, %d, %d\n", s->grid.imax, s->grid.jmax, s->grid.kmax);
printf("\tCell size (dx, dy, dz): %f, %f, %f\n", s->grid.dx, s->grid.dy, s->grid.dz);
printf("Timestep parameters:\n");
printf("\tDefault stepsize: %.2f, Final time %.2f\n", s->dt, s->te);
printf("\tdt bound: %.6f\n", s->dtBound);
printf("\tTau factor: %.2f\n", s->tau);
printf("Iterative s parameters:\n");
printf("\tMax iterations: %d\n", s->itermax);
printf("\tepsilon (stopping tolerance) : %f\n", s->eps);
printf("\tgamma factor: %f\n", s->gamma);
printf("\tomega (SOR relaxation): %f\n", s->omega);
}
void initSolver(Solver* s, Parameter* params)
{
s->problem = params->name;
s->bcLeft = params->bcLeft;
s->bcRight = params->bcRight;
s->bcBottom = params->bcBottom;
s->bcTop = params->bcTop;
s->bcFront = params->bcFront;
s->bcBack = params->bcBack;
s->grid.imax = params->imax;
s->grid.jmax = params->jmax;
s->grid.kmax = params->kmax;
s->grid.xlength = params->xlength;
s->grid.ylength = params->ylength;
s->grid.zlength = params->zlength;
s->grid.dx = params->xlength / params->imax;
s->grid.dy = params->ylength / params->jmax;
s->grid.dz = params->zlength / params->kmax;
s->eps = params->eps;
s->omega = params->omg;
s->itermax = params->itermax;
s->re = params->re;
s->gx = params->gx;
s->gy = params->gy;
s->gz = params->gz;
s->dt = params->dt;
s->te = params->te;
s->tau = params->tau;
s->gamma = params->gamma;
Completed porting, fixing bugs and testing
2023-07-05 20:38:50 +02:00
s->rho = params->rho;
Initial checkin
2023-02-05 07:34:23 +01:00
int imax = s->grid.imax;
int jmax = s->grid.jmax;
int kmax = s->grid.kmax;
size_t bytesize = (imax + 2) * (jmax + 2) * (kmax + 2) * sizeof(double);
s->u = allocate(64, bytesize);
s->v = allocate(64, bytesize);
s->w = allocate(64, bytesize);
s->p = allocate(64, bytesize);
s->rhs = allocate(64, bytesize);
s->f = allocate(64, bytesize);
s->g = allocate(64, bytesize);
s->h = allocate(64, bytesize);
for (int i = 0; i < (imax + 2) * (jmax + 2) * (kmax + 2); i++) {
s->u[i] = params->u_init;
s->v[i] = params->v_init;
s->w[i] = params->w_init;
s->p[i] = params->p_init;
s->rhs[i] = 0.0;
s->f[i] = 0.0;
s->g[i] = 0.0;
s->h[i] = 0.0;
}
double dx = s->grid.dx;
double dy = s->grid.dy;
double dz = s->grid.dz;
double invSqrSum = 1.0 / (dx * dx) + 1.0 / (dy * dy) + 1.0 / (dz * dz);
s->dtBound = 0.5 * s->re * 1.0 / invSqrSum;
#ifdef VERBOSE
printConfig(s);
#endif /* VERBOSE */
}
void computeRHS(Solver* s)
{
int imax = s->grid.imax;
int jmax = s->grid.jmax;
int kmax = s->grid.kmax;
double idx = 1.0 / s->grid.dx;
double idy = 1.0 / s->grid.dy;
double idz = 1.0 / s->grid.dz;
double idt = 1.0 / s->dt;
double* rhs = s->rhs;
double* f = s->f;
double* g = s->g;
double* h = s->h;
for (int k = 1; k < kmax + 1; k++) {
for (int j = 1; j < jmax + 1; j++) {
for (int i = 1; i < imax + 1; i++) {
RHS(i, j, k) = ((F(i, j, k) - F(i - 1, j, k)) * idx +
(G(i, j, k) - G(i, j - 1, k)) * idy +
(H(i, j, k) - H(i, j, k - 1)) * idz) *
idt;
}
}
}
}
void solve(Solver* s)
{
int imax = s->grid.imax;
int jmax = s->grid.jmax;
int kmax = s->grid.kmax;
double eps = s->eps;
int itermax = s->itermax;
double dx2 = s->grid.dx * s->grid.dx;
double dy2 = s->grid.dy * s->grid.dy;
double dz2 = s->grid.dz * s->grid.dz;
double idx2 = 1.0 / dx2;
double idy2 = 1.0 / dy2;
double idz2 = 1.0 / dz2;
double factor = s->omega * 0.5 * (dx2 * dy2 * dz2) /
(dy2 * dz2 + dx2 * dz2 + dx2 * dy2);
double* p = s->p;
double* rhs = s->rhs;
double epssq = eps * eps;
int it = 0;
double res = 1.0;
while ((res >= epssq) && (it < itermax)) {
res = 0.0;
for (int k = 1; k < kmax + 1; k++) {
for (int j = 1; j < jmax + 1; j++) {
for (int i = 1; i < imax + 1; i++) {
double r = RHS(i, j, k) -
((P(i + 1, j, k) - 2.0 * P(i, j, k) + P(i - 1, j, k)) *
idx2 +
(P(i, j + 1, k) - 2.0 * P(i, j, k) + P(i, j - 1, k)) *
idy2 +
(P(i, j, k + 1) - 2.0 * P(i, j, k) + P(i, j, k - 1)) *
idz2);
P(i, j, k) -= (factor * r);
res += (r * r);
}
}
}
for (int j = 1; j < jmax + 1; j++) {
for (int i = 1; i < imax + 1; i++) {
P(i, j, 0) = P(i, j, 1);
P(i, j, kmax + 1) = P(i, j, kmax);
}
}
for (int k = 1; k < kmax + 1; k++) {
for (int i = 1; i < imax + 1; i++) {
P(i, 0, k) = P(i, 1, k);
P(i, jmax + 1, k) = P(i, jmax, k);
}
}
for (int k = 1; k < kmax + 1; k++) {
for (int j = 1; j < jmax + 1; j++) {
P(0, j, k) = P(1, j, k);
P(imax + 1, j, k) = P(imax, j, k);
}
}
res = res / (double)(imax * jmax * kmax);
#ifdef DEBUG
printf("%d Residuum: %e\n", it, res);
#endif
it++;
}
#ifdef VERBOSE
printf("Solver took %d iterations to reach %f\n", it, sqrt(res));
#endif
}
Refactor and add red-black solver
2023-06-17 09:19:04 +02:00
void solveRB(Solver* s)
{
int imax = s->grid.imax;
int jmax = s->grid.jmax;
int kmax = s->grid.kmax;
double eps = s->eps;
int itermax = s->itermax;
double dx2 = s->grid.dx * s->grid.dx;
double dy2 = s->grid.dy * s->grid.dy;
double dz2 = s->grid.dz * s->grid.dz;
double idx2 = 1.0 / dx2;
double idy2 = 1.0 / dy2;
double idz2 = 1.0 / dz2;
double factor = s->omega * 0.5 * (dx2 * dy2 * dz2) /
(dy2 * dz2 + dx2 * dz2 + dx2 * dy2);
double* p = s->p;
double* rhs = s->rhs;
double epssq = eps * eps;
int it = 0;
double res = 1.0;
int pass, ksw, jsw, isw;
while ((res >= epssq) && (it < itermax)) {
res = 0.0;
ksw = 1;
for (pass = 0; pass < 2; pass++) {
jsw = ksw;
for (int k = 1; k < kmax + 1; k++) {
isw = jsw;
for (int j = 1; j < jmax + 1; j++) {
for (int i = isw; i < imax + 1; i += 2) {
double r =
RHS(i, j, k) -
((P(i + 1, j, k) - 2.0 * P(i, j, k) + P(i - 1, j, k)) * idx2 +
(P(i, j + 1, k) - 2.0 * P(i, j, k) + P(i, j - 1, k)) *
idy2 +
(P(i, j, k + 1) - 2.0 * P(i, j, k) + P(i, j, k - 1)) *
idz2);
P(i, j, k) -= (factor * r);
res += (r * r);
}
isw = 3 - isw;
}
jsw = 3 - jsw;
}
ksw = 3 - ksw;
}
for (int j = 1; j < jmax + 1; j++) {
for (int i = 1; i < imax + 1; i++) {
P(i, j, 0) = P(i, j, 1);
P(i, j, kmax + 1) = P(i, j, kmax);
}
}
for (int k = 1; k < kmax + 1; k++) {
for (int i = 1; i < imax + 1; i++) {
P(i, 0, k) = P(i, 1, k);
P(i, jmax + 1, k) = P(i, jmax, k);
}
}
for (int k = 1; k < kmax + 1; k++) {
for (int j = 1; j < jmax + 1; j++) {
P(0, j, k) = P(1, j, k);
P(imax + 1, j, k) = P(imax, j, k);
}
}
res = res / (double)(imax * jmax * kmax);
#ifdef DEBUG
printf("%d Residuum: %e\n", it, res);
#endif
it++;
}
#ifdef VERBOSE
printf("Solver took %d iterations to reach %f\n", it, sqrt(res));
#endif
}
Completed porting, fixing bugs and testing
2023-07-05 20:38:50 +02:00
void solveRBA(Solver* s)
{
int imax = s->grid.imax;
int jmax = s->grid.jmax;
int kmax = s->grid.kmax;
double eps = s->eps;
int itermax = s->itermax;
double dx2 = s->grid.dx * s->grid.dx;
double dy2 = s->grid.dy * s->grid.dy;
double dz2 = s->grid.dz * s->grid.dz;
double idx2 = 1.0 / dx2;
double idy2 = 1.0 / dy2;
double idz2 = 1.0 / dz2;
double factor = 0.5 * (dx2 * dy2 * dz2) /
(dy2 * dz2 + dx2 * dz2 + dx2 * dy2);
double* p = s->p;
double* rhs = s->rhs;
double epssq = eps * eps;
double rho = s->rho;
double omega = 1.0;
int it = 0;
double res = 1.0;
int pass, ksw, jsw, isw;
while ((res >= epssq) && (it < itermax)) {
res = 0.0;
ksw = 1;
for (pass = 0; pass < 2; pass++) {
jsw = ksw;
for (int k = 1; k < kmax + 1; k++) {
isw = jsw;
for (int j = 1; j < jmax + 1; j++) {
for (int i = isw; i < imax + 1; i += 2) {
double r =
RHS(i, j, k) -
((P(i + 1, j, k) - 2.0 * P(i, j, k) + P(i - 1, j, k)) * idx2 +
(P(i, j + 1, k) - 2.0 * P(i, j, k) + P(i, j - 1, k)) *
idy2 +
(P(i, j, k + 1) - 2.0 * P(i, j, k) + P(i, j, k - 1)) *
idz2);
P(i, j, k) -= (omega * factor * r);
res += (r * r);
}
isw = 3 - isw;
}
jsw = 3 - jsw;
}
ksw = 3 - ksw;
omega = (it == 0 && pass == 0 ? 1.0 / (1.0 - 0.5 * rho * rho)
: 1.0 / (1.0 - 0.25 * rho * rho * omega));
}
for (int j = 1; j < jmax + 1; j++) {
for (int i = 1; i < imax + 1; i++) {
P(i, j, 0) = P(i, j, 1);
P(i, j, kmax + 1) = P(i, j, kmax);
}
}
for (int k = 1; k < kmax + 1; k++) {
for (int i = 1; i < imax + 1; i++) {
P(i, 0, k) = P(i, 1, k);
P(i, jmax + 1, k) = P(i, jmax, k);
}
}
for (int k = 1; k < kmax + 1; k++) {
for (int j = 1; j < jmax + 1; j++) {
P(0, j, k) = P(1, j, k);
P(imax + 1, j, k) = P(imax, j, k);
}
}
res = res / (double)(imax * jmax * kmax);
#ifdef DEBUG
printf("%d Residuum: %e\n", it, res);
#endif
it++;
}
#ifdef VERBOSE
printf("Solver took %d iterations to reach %f\n", it, sqrt(res));
#endif
}
Initial checkin
2023-02-05 07:34:23 +01:00
static double maxElement(Solver* s, double* m)
{
int size = (s->grid.imax + 2) * (s->grid.jmax + 2) * (s->grid.kmax + 2);
double maxval = DBL_MIN;
for (int i = 0; i < size; i++) {
maxval = MAX(maxval, fabs(m[i]));
}
return maxval;
}
void normalizePressure(Solver* s)
{
int size = (s->grid.imax + 2) * (s->grid.jmax + 2) * (s->grid.kmax + 2);
double* p = s->p;
double avgP = 0.0;
for (int i = 0; i < size; i++) {
avgP += p[i];
}
avgP /= size;
for (int i = 0; i < size; i++) {
p[i] = p[i] - avgP;
}
}
void computeTimestep(Solver* s)
{
double dt = s->dtBound;
double dx = s->grid.dx;
double dy = s->grid.dy;
double dz = s->grid.dz;
double umax = maxElement(s, s->u);
double vmax = maxElement(s, s->v);
double wmax = maxElement(s, s->w);
if (umax > 0) {
dt = (dt > dx / umax) ? dx / umax : dt;
}
if (vmax > 0) {
dt = (dt > dy / vmax) ? dy / vmax : dt;
}
if (wmax > 0) {
dt = (dt > dz / wmax) ? dz / wmax : dt;
}
s->dt = dt * s->tau;
}
void setBoundaryConditions(Solver* s)
{
int imax = s->grid.imax;
int jmax = s->grid.jmax;
int kmax = s->grid.kmax;
double* u = s->u;
double* v = s->v;
double* w = s->w;
switch (s->bcTop) {
case NOSLIP:
for (int k = 1; k < kmax + 1; k++) {
for (int i = 1; i < imax + 1; i++) {
V(i, jmax, k) = 0.0;
U(i, jmax + 1, k) = -U(i, jmax, k);
W(i, jmax + 1, k) = -W(i, jmax, k);
}
}
break;
case SLIP:
for (int k = 1; k < kmax + 1; k++) {
for (int i = 1; i < imax + 1; i++) {
V(i, jmax, k) = 0.0;
U(i, jmax + 1, k) = U(i, jmax, k);
W(i, jmax + 1, k) = W(i, jmax, k);
}
}
break;
case OUTFLOW:
for (int k = 1; k < kmax + 1; k++) {
for (int i = 1; i < imax + 1; i++) {
U(i, jmax + 1, k) = U(i, jmax, k);
V(i, jmax, k) = V(i, jmax - 1, k);
W(i, jmax + 1, k) = W(i, jmax, k);
}
}
break;
case PERIODIC:
break;
}
switch (s->bcBottom) {
case NOSLIP:
for (int k = 1; k < kmax + 1; k++) {
for (int i = 1; i < imax + 1; i++) {
V(i, 0, k) = 0.0;
U(i, 0, k) = -U(i, 1, k);
W(i, 0, k) = -W(i, 1, k);
}
}
break;
case SLIP:
for (int k = 1; k < kmax + 1; k++) {
for (int i = 1; i < imax + 1; i++) {
V(i, 0, k) = 0.0;
U(i, 0, k) = U(i, 1, k);
W(i, 0, k) = W(i, 1, k);
}
}
break;
case OUTFLOW:
for (int k = 1; k < kmax + 1; k++) {
for (int i = 1; i < imax + 1; i++) {
U(i, 0, k) = U(i, 1, k);
V(i, 0, k) = V(i, 1, k);
W(i, 0, k) = W(i, 1, k);
}
}
break;
case PERIODIC:
break;
}
switch (s->bcLeft) {
case NOSLIP:
for (int k = 1; k < kmax + 1; k++) {
for (int j = 1; j < jmax + 1; j++) {
U(0, j, k) = 0.0;
V(0, j, k) = -V(1, j, k);
W(0, j, k) = -W(1, j, k);
}
}
break;
case SLIP:
for (int k = 1; k < kmax + 1; k++) {
for (int j = 1; j < jmax + 1; j++) {
U(0, j, k) = 0.0;
V(0, j, k) = V(1, j, k);
W(0, j, k) = W(1, j, k);
}
}
break;
case OUTFLOW:
for (int k = 1; k < kmax + 1; k++) {
for (int j = 1; j < jmax + 1; j++) {
U(0, j, k) = U(1, j, k);
V(0, j, k) = V(1, j, k);
W(0, j, k) = W(1, j, k);
}
}
break;
case PERIODIC:
break;
}
switch (s->bcRight) {
case NOSLIP:
for (int k = 1; k < kmax + 1; k++) {
for (int j = 1; j < jmax + 1; j++) {
U(imax, j, k) = 0.0;
V(imax + 1, j, k) = -V(imax, j, k);
W(imax + 1, j, k) = -W(imax, j, k);
}
}
break;
case SLIP:
for (int k = 1; k < kmax + 1; k++) {
for (int j = 1; j < jmax + 1; j++) {
U(imax, j, k) = 0.0;
V(imax + 1, j, k) = V(imax, j, k);
W(imax + 1, j, k) = W(imax, j, k);
}
}
break;
case OUTFLOW:
for (int k = 1; k < kmax + 1; k++) {
for (int j = 1; j < jmax + 1; j++) {
U(imax, j, k) = U(imax - 1, j, k);
V(imax + 1, j, k) = V(imax, j, k);
W(imax + 1, j, k) = W(imax, j, k);
}
}
break;
case PERIODIC:
break;
}
switch (s->bcFront) {
case NOSLIP:
for (int j = 1; j < jmax + 1; j++) {
for (int i = 1; i < imax + 1; i++) {
U(i, j, 0) = -U(i, j, 1);
V(i, j, 0) = -V(i, j, 1);
W(i, j, 0) = 0.0;
}
}
break;
case SLIP:
for (int j = 1; j < jmax + 1; j++) {
for (int i = 1; i < imax + 1; i++) {
U(i, j, 0) = U(i, j, 1);
V(i, j, 0) = V(i, j, 1);
W(i, j, 0) = 0.0;
}
}
break;
case OUTFLOW:
for (int j = 1; j < jmax + 1; j++) {
for (int i = 1; i < imax + 1; i++) {
U(i, j, 0) = U(i, j, 1);
V(i, j, 0) = V(i, j, 1);
W(i, j, 0) = W(i, j, 1);
}
}
break;
case PERIODIC:
break;
}
switch (s->bcBack) {
case NOSLIP:
for (int j = 1; j < jmax + 1; j++) {
for (int i = 1; i < imax + 1; i++) {
U(i, j, kmax + 1) = -U(i, j, kmax);
V(i, j, kmax + 1) = -V(i, j, kmax);
W(i, j, kmax + 1) = 0.0;
}
}
break;
case SLIP:
for (int j = 1; j < jmax + 1; j++) {
for (int i = 1; i < imax + 1; i++) {
U(i, j, kmax + 1) = U(i, j, kmax);
V(i, j, kmax + 1) = V(i, j, kmax);
W(i, j, kmax + 1) = 0.0;
}
}
break;
case OUTFLOW:
for (int j = 1; j < jmax + 1; j++) {
for (int i = 1; i < imax + 1; i++) {
U(i, j, kmax + 1) = U(i, j, kmax);
V(i, j, kmax + 1) = V(i, j, kmax);
W(i, j, kmax) = W(i, j, kmax - 1);
}
}
break;
case PERIODIC:
break;
}
}
void setSpecialBoundaryCondition(Solver* s)
{
int imax = s->grid.imax;
int jmax = s->grid.jmax;
int kmax = s->grid.kmax;
double mDy = s->grid.dy;
double* u = s->u;
if (strcmp(s->problem, "dcavity") == 0) {
for (int k = 1; k < kmax; k++) {
for (int i = 1; i < imax; i++) {
U(i, jmax + 1, k) = 2.0 - U(i, jmax, k);
}
}
} else if (strcmp(s->problem, "canal") == 0) {
double ylength = s->grid.ylength;
double y;
for (int k = 1; k < kmax + 1; k++) {
for (int j = 1; j < jmax + 1; j++) {
y = mDy * (j - 0.5);
U(0, j, k) = y * (ylength - y) * 4.0 / (ylength * ylength);
}
}
}
}
void computeFG(Solver* s)
{
int imax = s->grid.imax;
int jmax = s->grid.jmax;
int kmax = s->grid.kmax;
double* u = s->u;
double* v = s->v;
double* w = s->w;
double* f = s->f;
double* g = s->g;
double* h = s->h;
double gx = s->gx;
double gy = s->gy;
double gz = s->gz;
double gamma = s->gamma;
double dt = s->dt;
double inverseRe = 1.0 / s->re;
double inverseDx = 1.0 / s->grid.dx;
double inverseDy = 1.0 / s->grid.dy;
double inverseDz = 1.0 / s->grid.dz;
double du2dx, dv2dy, dw2dz;
double duvdx, duwdx, duvdy, dvwdy, duwdz, dvwdz;
double du2dx2, du2dy2, du2dz2;
double dv2dx2, dv2dy2, dv2dz2;
double dw2dx2, dw2dy2, dw2dz2;
for (int k = 1; k < kmax + 1; k++) {
for (int j = 1; j < jmax + 1; j++) {
for (int i = 1; i < imax + 1; i++) {
du2dx = inverseDx * 0.25 *
((U(i, j, k) + U(i + 1, j, k)) *
(U(i, j, k) + U(i + 1, j, k)) -
(U(i, j, k) + U(i - 1, j, k)) *
(U(i, j, k) + U(i - 1, j, k))) +
gamma * inverseDx * 0.25 *
(fabs(U(i, j, k) + U(i + 1, j, k)) *
(U(i, j, k) - U(i + 1, j, k)) +
fabs(U(i, j, k) + U(i - 1, j, k)) *
(U(i, j, k) - U(i - 1, j, k)));
duvdy = inverseDy * 0.25 *
((V(i, j, k) + V(i + 1, j, k)) *
(U(i, j, k) + U(i, j + 1, k)) -
(V(i, j - 1, k) + V(i + 1, j - 1, k)) *
(U(i, j, k) + U(i, j - 1, k))) +
gamma * inverseDy * 0.25 *
(fabs(V(i, j, k) + V(i + 1, j, k)) *
(U(i, j, k) - U(i, j + 1, k)) +
fabs(V(i, j - 1, k) + V(i + 1, j - 1, k)) *
(U(i, j, k) - U(i, j - 1, k)));
duwdz = inverseDz * 0.25 *
((W(i, j, k) + W(i + 1, j, k)) *
(U(i, j, k) + U(i, j, k + 1)) -
(W(i, j, k - 1) + W(i + 1, j, k - 1)) *
(U(i, j, k) + U(i, j, k - 1))) +
gamma * inverseDz * 0.25 *
(fabs(W(i, j, k) + W(i + 1, j, k)) *
(U(i, j, k) - U(i, j, k + 1)) +
fabs(W(i, j, k - 1) + W(i + 1, j, k - 1)) *
(U(i, j, k) - U(i, j, k - 1)));
du2dx2 = inverseDx * inverseDx *
(U(i + 1, j, k) - 2.0 * U(i, j, k) + U(i - 1, j, k));
du2dy2 = inverseDy * inverseDy *
(U(i, j + 1, k) - 2.0 * U(i, j, k) + U(i, j - 1, k));
du2dz2 = inverseDz * inverseDz *
(U(i, j, k + 1) - 2.0 * U(i, j, k) + U(i, j, k - 1));
F(i, j, k) = U(i, j, k) + dt * (inverseRe * (du2dx2 + du2dy2 + du2dz2) -
du2dx - duvdy - duwdz + gx);
duvdx = inverseDx * 0.25 *
((U(i, j, k) + U(i, j + 1, k)) *
(V(i, j, k) + V(i + 1, j, k)) -
(U(i - 1, j, k) + U(i - 1, j + 1, k)) *
(V(i, j, k) + V(i - 1, j, k))) +
gamma * inverseDx * 0.25 *
(fabs(U(i, j, k) + U(i, j + 1, k)) *
(V(i, j, k) - V(i + 1, j, k)) +
fabs(U(i - 1, j, k) + U(i - 1, j + 1, k)) *
(V(i, j, k) - V(i - 1, j, k)));
dv2dy = inverseDy * 0.25 *
((V(i, j, k) + V(i, j + 1, k)) *
(V(i, j, k) + V(i, j + 1, k)) -
(V(i, j, k) + V(i, j - 1, k)) *
(V(i, j, k) + V(i, j - 1, k))) +
gamma * inverseDy * 0.25 *
(fabs(V(i, j, k) + V(i, j + 1, k)) *
(V(i, j, k) - V(i, j + 1, k)) +
fabs(V(i, j, k) + V(i, j - 1, k)) *
(V(i, j, k) - V(i, j - 1, k)));
dvwdz = inverseDz * 0.25 *
((W(i, j, k) + W(i, j + 1, k)) *
(V(i, j, k) + V(i, j, k + 1)) -
(W(i, j, k - 1) + W(i, j + 1, k - 1)) *
(V(i, j, k) + V(i, j, k + 1))) +
gamma * inverseDz * 0.25 *
(fabs(W(i, j, k) + W(i, j + 1, k)) *
(V(i, j, k) - V(i, j, k + 1)) +
fabs(W(i, j, k - 1) + W(i, j + 1, k - 1)) *
(V(i, j, k) - V(i, j, k + 1)));
dv2dx2 = inverseDx * inverseDx *
(V(i + 1, j, k) - 2.0 * V(i, j, k) + V(i - 1, j, k));
dv2dy2 = inverseDy * inverseDy *
(V(i, j + 1, k) - 2.0 * V(i, j, k) + V(i, j - 1, k));
dv2dz2 = inverseDz * inverseDz *
(V(i, j, k + 1) - 2.0 * V(i, j, k) + V(i, j, k - 1));
G(i, j, k) = V(i, j, k) + dt * (inverseRe * (dv2dx2 + dv2dy2 + dv2dz2) -
duvdx - dv2dy - dvwdz + gy);
duwdx = inverseDx * 0.25 *
((U(i, j, k) + U(i, j, k + 1)) *
(W(i, j, k) + W(i + 1, j, k)) -
(U(i - 1, j, k) + U(i - 1, j, k + 1)) *
(W(i, j, k) + W(i - 1, j, k))) +
gamma * inverseDx * 0.25 *
(fabs(U(i, j, k) + U(i, j, k + 1)) *
(W(i, j, k) - W(i + 1, j, k)) +
fabs(U(i - 1, j, k) + U(i - 1, j, k + 1)) *
(W(i, j, k) - W(i - 1, j, k)));
dvwdy = inverseDy * 0.25 *
((V(i, j, k) + V(i, j, k + 1)) *
(W(i, j, k) + W(i, j + 1, k)) -
(V(i, j - 1, k + 1) + V(i, j - 1, k)) *
(W(i, j, k) + W(i, j - 1, k))) +
gamma * inverseDy * 0.25 *
(fabs(V(i, j, k) + V(i, j, k + 1)) *
(W(i, j, k) - W(i, j + 1, k)) +
fabs(V(i, j - 1, k + 1) + V(i, j - 1, k)) *
(W(i, j, k) - W(i, j - 1, k)));
dw2dz = inverseDz * 0.25 *
((W(i, j, k) + W(i, j, k + 1)) *
(W(i, j, k) + W(i, j, k + 1)) -
(W(i, j, k) + W(i, j, k - 1)) *
(W(i, j, k) + W(i, j, k - 1))) +
gamma * inverseDz * 0.25 *
(fabs(W(i, j, k) + W(i, j, k + 1)) *
(W(i, j, k) - W(i, j, k + 1)) +
fabs(W(i, j, k) + W(i, j, k - 1)) *
(W(i, j, k) - W(i, j, k - 1)));
dw2dx2 = inverseDx * inverseDx *
(W(i + 1, j, k) - 2.0 * W(i, j, k) + W(i - 1, j, k));
dw2dy2 = inverseDy * inverseDy *
(W(i, j + 1, k) - 2.0 * W(i, j, k) + W(i, j - 1, k));
dw2dz2 = inverseDz * inverseDz *
(W(i, j, k + 1) - 2.0 * W(i, j, k) + W(i, j, k - 1));
H(i, j, k) = W(i, j, k) + dt * (inverseRe * (dw2dx2 + dw2dy2 + dw2dz2) -
duwdx - dvwdy - dw2dz + gz);
}
}
}
/* ----------------------------- boundary of F ---------------------------
*/
for (int k = 1; k < kmax + 1; k++) {
for (int j = 1; j < jmax + 1; j++) {
F(0, j, k) = U(0, j, k);
F(imax, j, k) = U(imax, j, k);
}
}
/* ----------------------------- boundary of G ---------------------------
*/
for (int k = 1; k < kmax + 1; k++) {
for (int i = 1; i < imax + 1; i++) {
G(i, 0, k) = V(i, 0, k);
G(i, jmax, k) = V(i, jmax, k);
}
}
/* ----------------------------- boundary of G ---------------------------
*/
for (int j = 1; j < jmax + 1; j++) {
for (int i = 1; i < imax + 1; i++) {
H(i, j, 0) = W(i, j, 0);
H(i, j, kmax) = W(i, j, kmax);
}
}
}
void adaptUV(Solver* s)
{
int imax = s->grid.imax;
int jmax = s->grid.jmax;
int kmax = s->grid.kmax;
double* p = s->p;
double* u = s->u;
double* v = s->v;
double* w = s->w;
double* f = s->f;
double* g = s->g;
double* h = s->h;
double factorX = s->dt / s->grid.dx;
double factorY = s->dt / s->grid.dy;
double factorZ = s->dt / s->grid.dz;
for (int k = 1; k < kmax + 1; k++) {
for (int j = 1; j < jmax + 1; j++) {
for (int i = 1; i < imax + 1; i++) {
U(i, j, k) = F(i, j, k) - (P(i + 1, j, k) - P(i, j, k)) * factorX;
V(i, j, k) = G(i, j, k) - (P(i, j + 1, k) - P(i, j, k)) * factorY;
W(i, j, k) = H(i, j, k) - (P(i, j, k + 1) - P(i, j, k)) * factorZ;
}
}
}
}
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