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

640 lines
21 KiB
C

/*
* Copyright (C) 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 <string.h>
#include "allocate.h"
#include "discretization.h"
#include "parameter.h"
#include "util.h"
static void printConfig(Discretization* d)
{
printf("Parameters for #%s#\n", d->problem);
printf("BC Left:%d Right:%d Bottom:%d Top:%d Front:%d Back:%d\n",
d->bcLeft,
d->bcRight,
d->bcBottom,
d->bcTop,
d->bcFront,
d->bcBack);
printf("\tReynolds number: %.2f\n", d->re);
printf("\tGx Gy: %.2f %.2f %.2f\n", d->gx, d->gy, d->gz);
printf("Geometry data:\n");
printf("\tDomain box size (x, y, z): %.2f, %.2f, %.2f\n",
d->grid.xlength,
d->grid.ylength,
d->grid.zlength);
printf("\tCells (x, y, z): %d, %d, %d\n", d->grid.imax, d->grid.jmax, d->grid.kmax);
printf("\tCell size (dx, dy, dz): %f, %f, %f\n", d->grid.dx, d->grid.dy, d->grid.dz);
printf("Timestep parameters:\n");
printf("\tDefault stepsize: %.2f, Final time %.2f\n", d->dt, d->te);
printf("\tdt bound: %.6f\n", d->dtBound);
printf("\tTau factor: %.2f\n", d->tau);
printf("Iterative parameters:\n");
printf("\tepsilon (stopping tolerance) : %f\n", d->eps);
printf("\tgamma factor: %f\n", d->gamma);
printf("\tomega (SOR relaxation): %f\n", d->omega);
}
void initDiscretization(Discretization* d, Parameter* p)
{
d->problem = p->name;
d->bcLeft = p->bcLeft;
d->bcRight = p->bcRight;
d->bcBottom = p->bcBottom;
d->bcTop = p->bcTop;
d->bcFront = p->bcFront;
d->bcBack = p->bcBack;
d->grid.imax = p->imax;
d->grid.jmax = p->jmax;
d->grid.kmax = p->kmax;
d->grid.xlength = p->xlength;
d->grid.ylength = p->ylength;
d->grid.zlength = p->zlength;
d->grid.dx = p->xlength / p->imax;
d->grid.dy = p->ylength / p->jmax;
d->grid.dz = p->zlength / p->kmax;
d->eps = p->eps;
d->omega = p->omg;
d->re = p->re;
d->gx = p->gx;
d->gy = p->gy;
d->gz = p->gz;
d->dt = p->dt;
d->te = p->te;
d->tau = p->tau;
d->gamma = p->gamma;
int imax = d->grid.imax;
int jmax = d->grid.jmax;
int kmax = d->grid.kmax;
size_t bytesize = (imax + 2) * (jmax + 2) * (kmax + 2) * sizeof(double);
d->u = allocate(64, bytesize);
d->v = allocate(64, bytesize);
d->w = allocate(64, bytesize);
d->p = allocate(64, bytesize);
d->rhs = allocate(64, bytesize);
d->f = allocate(64, bytesize);
d->g = allocate(64, bytesize);
d->h = allocate(64, bytesize);
for (int i = 0; i < (imax + 2) * (jmax + 2) * (kmax + 2); i++) {
d->u[i] = p->u_init;
d->v[i] = p->v_init;
d->w[i] = p->w_init;
d->p[i] = p->p_init;
d->rhs[i] = 0.0;
d->f[i] = 0.0;
d->g[i] = 0.0;
d->h[i] = 0.0;
}
double dx = d->grid.dx;
double dy = d->grid.dy;
double dz = d->grid.dz;
double invSqrSum = 1.0 / (dx * dx) + 1.0 / (dy * dy) + 1.0 / (dz * dz);
d->dtBound = 0.5 * d->re * 1.0 / invSqrSum;
#ifdef VERBOSE
printConfig(d);
#endif /* VERBOSE */
}
void computeRHS(Discretization* d)
{
int imax = d->grid.imax;
int jmax = d->grid.jmax;
int kmax = d->grid.kmax;
double idx = 1.0 / d->grid.dx;
double idy = 1.0 / d->grid.dy;
double idz = 1.0 / d->grid.dz;
double idt = 1.0 / d->dt;
double* rhs = d->rhs;
double* f = d->f;
double* g = d->g;
double* h = d->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;
}
}
}
}
static double maxElement(Discretization* d, double* m)
{
int size = (d->grid.imax + 2) * (d->grid.jmax + 2) * (d->grid.kmax + 2);
double maxval = DBL_MIN;
for (int i = 0; i < size; i++) {
maxval = MAX(maxval, fabs(m[i]));
}
return maxval;
}
void normalizePressure(Discretization* d)
{
int size = (d->grid.imax + 2) * (d->grid.jmax + 2) * (d->grid.kmax + 2);
double* p = d->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(Discretization* d)
{
double dt = d->dtBound;
double dx = d->grid.dx;
double dy = d->grid.dy;
double dz = d->grid.dz;
double umax = maxElement(d, d->u);
double vmax = maxElement(d, d->v);
double wmax = maxElement(d, d->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;
}
d->dt = dt * d->tau;
}
void setBoundaryConditions(Discretization* d)
{
int imax = d->grid.imax;
int jmax = d->grid.jmax;
int kmax = d->grid.kmax;
double* u = d->u;
double* v = d->v;
double* w = d->w;
switch (d->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 (d->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 (d->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 (d->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 (d->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 (d->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(Discretization* d)
{
int imax = d->grid.imax;
int jmax = d->grid.jmax;
int kmax = d->grid.kmax;
double mDy = d->grid.dy;
double* u = d->u;
if (strcmp(d->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(d->problem, "canal") == 0) {
double ylength = d->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(Discretization* d)
{
int imax = d->grid.imax;
int jmax = d->grid.jmax;
int kmax = d->grid.kmax;
double* u = d->u;
double* v = d->v;
double* w = d->w;
double* f = d->f;
double* g = d->g;
double* h = d->h;
double gx = d->gx;
double gy = d->gy;
double gz = d->gz;
double dt = d->dt;
double gamma = d->gamma;
double inverseRe = 1.0 / d->re;
double inverseDx = 1.0 / d->grid.dx;
double inverseDy = 1.0 / d->grid.dy;
double inverseDz = 1.0 / d->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(Discretization* d)
{
int imax = d->grid.imax;
int jmax = d->grid.jmax;
int kmax = d->grid.kmax;
double* p = d->p;
double* u = d->u;
double* v = d->v;
double* w = d->w;
double* f = d->f;
double* g = d->g;
double* h = d->h;
double factorX = d->dt / d->grid.dx;
double factorY = d->dt / d->grid.dy;
double factorZ = d->dt / d->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;
}
}
}
}