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Separate solver and discretization modules

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This commit is contained in:
Jan Eitzinger
2024-02-18 13:45:46 +01:00
parent fe57042556
commit e35aca7037
8 changed files with 595 additions and 519 deletions
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453
BasicSolver/2D-mpi/src/discretization.c Normal file
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@@ -0,0 +1,453 @@
/*
* 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 <stdlib.h>
#include <string.h>
#include "allocate.h"
#include "comm.h"
#include "discretization.h"
#include "parameter.h"
#include "util.h"
static void printConfig(Discretization* s)
{
if (commIsMaster(&s->comm)) {
printf("Parameters for #%s#\n", s->problem);
printf("BC Left:%d Right:%d Bottom:%d Top:%d\n",
s->bcLeft,
s->bcRight,
s->bcBottom,
s->bcTop);
printf("\tReynolds number: %.2f\n", s->re);
printf("\tGx Gy: %.2f %.2f\n", s->gx, s->gy);
printf("Geometry data:\n");
printf("\tDomain box size (x, y): %.2f, %.2f\n",
s->grid.xlength,
s->grid.ylength);
printf("\tCells (x, y): %d, %d\n", s->grid.imax, s->grid.jmax);
printf("\tCell size (dx, dy): %f, %f\n", s->grid.dx, s->grid.dy);
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("\tgamma factor: %f\n", s->gamma);
}
commPrintConfig(&s->comm);
}
void initDiscretiztion(Discretization* s, Parameter* params)
{
s->problem = params->name;
s->bcLeft = params->bcLeft;
s->bcRight = params->bcRight;
s->bcBottom = params->bcBottom;
s->bcTop = params->bcTop;
s->grid.imax = params->imax;
s->grid.jmax = params->jmax;
s->grid.xlength = params->xlength;
s->grid.ylength = params->ylength;
s->grid.dx = params->xlength / params->imax;
s->grid.dy = params->ylength / params->jmax;
s->re = params->re;
s->gx = params->gx;
s->gy = params->gy;
s->dt = params->dt;
s->te = params->te;
s->tau = params->tau;
s->gamma = params->gamma;
/* allocate arrays */
int imaxLocal = s->comm.imaxLocal;
int jmaxLocal = s->comm.jmaxLocal;
size_t size = (imaxLocal + 2) * (jmaxLocal + 2);
s->u = allocate(64, size * sizeof(double));
s->v = allocate(64, size * sizeof(double));
s->p = allocate(64, size * sizeof(double));
s->rhs = allocate(64, size * sizeof(double));
s->f = allocate(64, size * sizeof(double));
s->g = allocate(64, size * sizeof(double));
for (int i = 0; i < size; i++) {
s->u[i] = params->u_init;
s->v[i] = params->v_init;
s->p[i] = params->p_init;
s->rhs[i] = 0.0;
s->f[i] = 0.0;
s->g[i] = 0.0;
}
double dx = s->grid.dx;
double dy = s->grid.dy;
double invSqrSum = 1.0 / (dx * dx) + 1.0 / (dy * dy);
s->dtBound = 0.5 * s->re * 1.0 / invSqrSum;
#ifdef VERBOSE
printConfig(s);
#endif
}
void computeRHS(Discretization* s)
{
int imaxLocal = s->comm.imaxLocal;
int jmaxLocal = s->comm.jmaxLocal;
double idx = 1.0 / s->grid.dx;
double idy = 1.0 / s->grid.dy;
double idt = 1.0 / s->dt;
double* rhs = s->rhs;
double* f = s->f;
double* g = s->g;
commShift(&s->comm, f, g);
for (int j = 1; j < jmaxLocal + 1; j++) {
for (int i = 1; i < imaxLocal + 1; i++) {
RHS(i, j) = ((F(i, j) - F(i - 1, j)) * idx + (G(i, j) - G(i, j - 1)) * idy) *
idt;
}
}
}
static double maxElement(Discretization* s, double* m)
{
int imaxLocal = s->comm.imaxLocal;
int jmaxLocal = s->comm.jmaxLocal;
int size = (imaxLocal + 2) * (jmaxLocal + 2);
double maxval = DBL_MIN;
for (int i = 0; i < size; i++) {
maxval = MAX(maxval, fabs(m[i]));
}
commReduction(&maxval, MAX);
return maxval;
}
void computeTimestep(Discretization* s)
{
double dt = s->dtBound;
double dx = s->grid.dx;
double dy = s->grid.dy;
double umax = maxElement(s, s->u);
double vmax = maxElement(s, s->v);
if (umax > 0) {
dt = (dt > dx / umax) ? dx / umax : dt;
}
if (vmax > 0) {
dt = (dt > dy / vmax) ? dy / vmax : dt;
}
s->dt = dt * s->tau;
}
void setBoundaryConditions(Discretization* s)
{
int imaxLocal = s->comm.imaxLocal;
int jmaxLocal = s->comm.jmaxLocal;
double* u = s->u;
double* v = s->v;
if (commIsBoundary(&s->comm, TOP)) {
switch (s->bcTop) {
case NOSLIP:
for (int i = 1; i < imaxLocal + 1; i++) {
V(i, jmaxLocal) = 0.0;
U(i, jmaxLocal + 1) = -U(i, jmaxLocal);
}
break;
case SLIP:
for (int i = 1; i < imaxLocal + 1; i++) {
V(i, jmaxLocal) = 0.0;
U(i, jmaxLocal + 1) = U(i, jmaxLocal);
}
break;
case OUTFLOW:
for (int i = 1; i < imaxLocal + 1; i++) {
U(i, jmaxLocal + 1) = U(i, jmaxLocal);
V(i, jmaxLocal) = V(i, jmaxLocal - 1);
}
break;
case PERIODIC:
break;
}
}
if (commIsBoundary(&s->comm, BOTTOM)) {
switch (s->bcBottom) {
case NOSLIP:
for (int i = 1; i < imaxLocal + 1; i++) {
V(i, 0) = 0.0;
U(i, 0) = -U(i, 1);
}
break;
case SLIP:
for (int i = 1; i < imaxLocal + 1; i++) {
V(i, 0) = 0.0;
U(i, 0) = U(i, 1);
}
break;
case OUTFLOW:
for (int i = 1; i < imaxLocal + 1; i++) {
U(i, 0) = U(i, 1);
V(i, 0) = V(i, 1);
}
break;
case PERIODIC:
break;
}
}
if (commIsBoundary(&s->comm, RIGHT)) {
switch (s->bcRight) {
case NOSLIP:
for (int j = 1; j < jmaxLocal + 1; j++) {
U(imaxLocal, j) = 0.0;
V(imaxLocal + 1, j) = -V(imaxLocal, j);
}
break;
case SLIP:
for (int j = 1; j < jmaxLocal + 1; j++) {
U(imaxLocal, j) = 0.0;
V(imaxLocal + 1, j) = V(imaxLocal, j);
}
break;
case OUTFLOW:
for (int j = 1; j < jmaxLocal + 1; j++) {
U(imaxLocal, j) = U(imaxLocal - 1, j);
V(imaxLocal + 1, j) = V(imaxLocal, j);
}
break;
case PERIODIC:
break;
}
}
if (commIsBoundary(&s->comm, LEFT)) {
switch (s->bcLeft) {
case NOSLIP:
for (int j = 1; j < jmaxLocal + 1; j++) {
U(0, j) = 0.0;
V(0, j) = -V(1, j);
}
break;
case SLIP:
for (int j = 1; j < jmaxLocal + 1; j++) {
U(0, j) = 0.0;
V(0, j) = V(1, j);
}
break;
case OUTFLOW:
for (int j = 1; j < jmaxLocal + 1; j++) {
U(0, j) = U(1, j);
V(0, j) = V(1, j);
}
break;
case PERIODIC:
break;
}
}
}
void setSpecialBoundaryCondition(Discretization* s)
{
int imaxLocal = s->comm.imaxLocal;
int jmaxLocal = s->comm.jmaxLocal;
double* u = s->u;
if (strcmp(s->problem, "dcavity") == 0) {
if (commIsBoundary(&s->comm, TOP)) {
for (int i = 1; i < imaxLocal + 1; i++) {
U(i, jmaxLocal + 1) = 2.0 - U(i, jmaxLocal);
}
}
} else if (strcmp(s->problem, "canal") == 0) {
if (commIsBoundary(&s->comm, LEFT)) {
double ylength = s->grid.ylength;
double dy = s->grid.dy;
int rest = s->grid.jmax % s->comm.size;
int yc = s->comm.rank * (s->grid.jmax / s->comm.size) +
MIN(rest, s->comm.rank);
double ys = dy * (yc + 0.5);
double y;
/* printf("RANK %d yc: %d ys: %f\n", solver->rank, yc, ys); */
for (int j = 1; j < jmaxLocal + 1; j++) {
y = ys + dy * (j - 0.5);
U(0, j) = y * (ylength - y) * 4.0 / (ylength * ylength);
}
}
}
/* print(solver, solver->u); */
}
void computeFG(Discretization* s)
{
double* u = s->u;
double* v = s->v;
double* f = s->f;
double* g = s->g;
int imaxLocal = s->comm.imaxLocal;
int jmaxLocal = s->comm.jmaxLocal;
double gx = s->gx;
double gy = s->gy;
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 du2dx, dv2dy, duvdx, duvdy;
double du2dx2, du2dy2, dv2dx2, dv2dy2;
commExchange(&s->comm, u);
commExchange(&s->comm, v);
for (int j = 1; j < jmaxLocal + 1; j++) {
for (int i = 1; i < imaxLocal + 1; i++) {
du2dx = inverseDx * 0.25 *
((U(i, j) + U(i + 1, j)) * (U(i, j) + U(i + 1, j)) -
(U(i, j) + U(i - 1, j)) * (U(i, j) + U(i - 1, j))) +
gamma * inverseDx * 0.25 *
(fabs(U(i, j) + U(i + 1, j)) * (U(i, j) - U(i + 1, j)) +
fabs(U(i, j) + U(i - 1, j)) * (U(i, j) - U(i - 1, j)));
duvdy = inverseDy * 0.25 *
((V(i, j) + V(i + 1, j)) * (U(i, j) + U(i, j + 1)) -
(V(i, j - 1) + V(i + 1, j - 1)) * (U(i, j) + U(i, j - 1))) +
gamma * inverseDy * 0.25 *
(fabs(V(i, j) + V(i + 1, j)) * (U(i, j) - U(i, j + 1)) +
fabs(V(i, j - 1) + V(i + 1, j - 1)) *
(U(i, j) - U(i, j - 1)));
du2dx2 = inverseDx * inverseDx * (U(i + 1, j) - 2.0 * U(i, j) + U(i - 1, j));
du2dy2 = inverseDy * inverseDy * (U(i, j + 1) - 2.0 * U(i, j) + U(i, j - 1));
F(i, j) = U(i, j) + dt * (inverseRe * (du2dx2 + du2dy2) - du2dx - duvdy + gx);
duvdx = inverseDx * 0.25 *
((U(i, j) + U(i, j + 1)) * (V(i, j) + V(i + 1, j)) -
(U(i - 1, j) + U(i - 1, j + 1)) * (V(i, j) + V(i - 1, j))) +
gamma * inverseDx * 0.25 *
(fabs(U(i, j) + U(i, j + 1)) * (V(i, j) - V(i + 1, j)) +
fabs(U(i - 1, j) + U(i - 1, j + 1)) *
(V(i, j) - V(i - 1, j)));
dv2dy = inverseDy * 0.25 *
((V(i, j) + V(i, j + 1)) * (V(i, j) + V(i, j + 1)) -
(V(i, j) + V(i, j - 1)) * (V(i, j) + V(i, j - 1))) +
gamma * inverseDy * 0.25 *
(fabs(V(i, j) + V(i, j + 1)) * (V(i, j) - V(i, j + 1)) +
fabs(V(i, j) + V(i, j - 1)) * (V(i, j) - V(i, j - 1)));
dv2dx2 = inverseDx * inverseDx * (V(i + 1, j) - 2.0 * V(i, j) + V(i - 1, j));
dv2dy2 = inverseDy * inverseDy * (V(i, j + 1) - 2.0 * V(i, j) + V(i, j - 1));
G(i, j) = V(i, j) + dt * (inverseRe * (dv2dx2 + dv2dy2) - duvdx - dv2dy + gy);
}
}
/* ----------------------------- boundary of F --------------------------- */
if (commIsBoundary(&s->comm, LEFT)) {
for (int j = 1; j < jmaxLocal + 1; j++) {
F(0, j) = U(0, j);
}
}
if (commIsBoundary(&s->comm, RIGHT)) {
for (int j = 1; j < jmaxLocal + 1; j++) {
F(imaxLocal, j) = U(imaxLocal, j);
}
}
/* ----------------------------- boundary of G --------------------------- */
if (commIsBoundary(&s->comm, BOTTOM)) {
for (int i = 1; i < imaxLocal + 1; i++) {
G(i, 0) = V(i, 0);
}
}
if (commIsBoundary(&s->comm, TOP)) {
for (int i = 1; i < imaxLocal + 1; i++) {
G(i, jmaxLocal) = V(i, jmaxLocal);
}
}
}
void adaptUV(Discretization* s)
{
int imaxLocal = s->comm.imaxLocal;
int jmaxLocal = s->comm.jmaxLocal;
double* p = s->p;
double* u = s->u;
double* v = s->v;
double* f = s->f;
double* g = s->g;
double factorX = s->dt / s->grid.dx;
double factorY = s->dt / s->grid.dy;
for (int j = 1; j < jmaxLocal + 1; j++) {
for (int i = 1; i < imaxLocal + 1; i++) {
U(i, j) = F(i, j) - (P(i + 1, j) - P(i, j)) * factorX;
V(i, j) = G(i, j) - (P(i, j + 1) - P(i, j)) * factorY;
}
}
}
void writeResult(Discretization* s, double* u, double* v, double* p)
{
int imax = s->grid.imax;
int jmax = s->grid.jmax;
double dx = s->grid.dx;
double dy = s->grid.dy;
double x = 0.0, y = 0.0;
FILE* fp;
fp = fopen("pressure.dat", "w");
if (fp == NULL) {
printf("Error!\n");
exit(EXIT_FAILURE);
}
for (int j = 1; j <= jmax; j++) {
y = (double)(j - 0.5) * dy;
for (int i = 1; i <= imax; i++) {
x = (double)(i - 0.5) * dx;
fprintf(fp, "%.2f %.2f %f\n", x, y, p[j * (imax + 2) + i]);
}
fprintf(fp, "\n");
}
fclose(fp);
fp = fopen("velocity.dat", "w");
if (fp == NULL) {
printf("Error!\n");
exit(EXIT_FAILURE);
}
for (int j = 1; j <= jmax; j++) {
y = dy * (j - 0.5);
for (int i = 1; i <= imax; i++) {
x = dx * (i - 0.5);
double velU = (u[j * (imax + 2) + i] + u[j * (imax + 2) + (i - 1)]) / 2.0;
double velV = (v[j * (imax + 2) + i] + v[(j - 1) * (imax + 2) + i]) / 2.0;
double len = sqrt((velU * velU) + (velV * velV));
fprintf(fp, "%.2f %.2f %f %f %f\n", x, y, velU, velV, len);
}
}
fclose(fp);
}

43
BasicSolver/2D-mpi/src/discretization.h Normal file
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@@ -0,0 +1,43 @@
/*
* 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.
*/
#ifndef __DISCRETIZATION_H_
#define __DISCRETIZATION_H_
#include "comm.h"
#include "grid.h"
#include "parameter.h"
enum BC { NOSLIP = 1, SLIP, OUTFLOW, PERIODIC };
typedef struct {
/* geometry and grid information */
Grid grid;
/* arrays */
double *p, *rhs;
double *f, *g;
double *u, *v;
/* parameters */
double re, tau, gamma;
double gx, gy;
/* time stepping */
double dt, te;
double dtBound;
char* problem;
int bcLeft, bcRight, bcBottom, bcTop;
/* communication */
Comm comm;
} Discretization;
void initDiscretiztion(Discretization*, Parameter*);
void computeRHS(Discretization*);
void normalizePressure(Discretization*);
void computeTimestep(Discretization*);
void setBoundaryConditions(Discretization*);
void setSpecialBoundaryCondition(Discretization*);
void computeFG(Discretization*);
void adaptUV(Discretization*);
void writeResult(Discretization* s, double* u, double* v, double* p);
#endif

16
BasicSolver/2D-mpi/src/grid.h Normal file
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@@ -0,0 +1,16 @@
/*
* 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.
*/
#ifndef __GRID_H_
#define __GRID_H_
typedef struct {
double dx, dy;
int imax, jmax;
double xlength, ylength;
} Grid;
#endif // __GRID_H_

63
BasicSolver/2D-mpi/src/main.c
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@@ -10,21 +10,22 @@
#include "allocate.h"
#include "comm.h"
#include "discretization.h"
#include "parameter.h"
#include "progress.h"
#include "solver.h"
#include "timing.h"
static void writeResults(Solver* s)
static void writeResults(Discretization* s)
{
#ifdef _MPI
size_t bytesize = (s->imax + 2) * (s->jmax + 2) * sizeof(double);
size_t bytesize = (s->grid.imax + 2) * (s->grid.jmax + 2) * sizeof(double);
double* ug = allocate(64, bytesize);
double* vg = allocate(64, bytesize);
double* pg = allocate(64, bytesize);
commCollectResult(&s->comm, ug, vg, pg, s->u, s->v, s->p, s->imax, s->jmax);
commCollectResult(&s->comm, ug, vg, pg, s->u, s->v, s->p, s->grid.imax, s->grid.jmax);
writeResult(s, ug, vg, pg);
free(ug);
@@ -40,9 +41,10 @@ int main(int argc, char** argv)
int rank;
double timeStart, timeStop;
Parameter p;
Discretization d;
Solver s;
commInit(&s.comm, argc, argv);
commInit(&d.comm, argc, argv);
initParameter(&p);
if (argc != 2) {
@@ -51,44 +53,45 @@ int main(int argc, char** argv)
}
readParameter(&p, argv[1]);
commPartition(&s.comm, p.jmax, p.imax);
if (commIsMaster(&s.comm)) {
commPartition(&d.comm, p.jmax, p.imax);
if (commIsMaster(&d.comm)) {
printParameter(&p);
}
initSolver(&s, &p);
initDiscretiztion(&d, &p);
initSolver(&s, &d, &p);
#ifdef TEST
commPrintConfig(&s.comm);
commTestInit(&s.comm, s.p, s.f, s.g);
commExchange(&s.comm, s.p);
commShift(&s.comm, s.f, s.g);
commTestWrite(&s.comm, s.p, s.f, s.g);
writeResults(&s);
commFinalize(&s.comm);
commPrintConfig(&d.comm);
commTestInit(&d.comm, d.p, d.f, d.g);
commExchange(&d.comm, d.p);
commShift(&d.comm, d.f, d.g);
commTestWrite(&d.comm, d.p, d.f, d.g);
writeResults(&d);
commFinalize(&d.comm);
exit(EXIT_SUCCESS);
#endif
#ifndef VERBOSE
initProgress(s.te);
initProgress(d.te);
#endif
double tau = s.tau;
double te = s.te;
double tau = d.tau;
double te = d.te;
double t = 0.0;
timeStart = getTimeStamp();
while (t <= te) {
if (tau > 0.0) computeTimestep(&s);
setBoundaryConditions(&s);
setSpecialBoundaryCondition(&s);
computeFG(&s);
computeRHS(&s);
solve(&s);
adaptUV(&s);
t += s.dt;
if (tau > 0.0) computeTimestep(&d);
setBoundaryConditions(&d);
setSpecialBoundaryCondition(&d);
computeFG(&d);
computeRHS(&d);
solve(&s, d.p, d.rhs);
adaptUV(&d);
t += d.dt;
#ifdef VERBOSE
if (commIsMaster(&s.comm)) {
printf("TIME %f , TIMESTEP %f\n", t, s.dt);
if (commIsMaster(s.comm)) {
printf("TIME %f , TIMESTEP %f\n", t, d.dt);
}
#else
printProgress(t);
@@ -98,11 +101,11 @@ int main(int argc, char** argv)
#ifndef VERBOSE
stopProgress();
#endif
if (commIsMaster(&s.comm)) {
if (commIsMaster(s.comm)) {
printf("Solution took %.2fs\n", timeStop - timeStart);
}
writeResults(&s);
commFinalize(&s.comm);
writeResults(&d);
commFinalize(s.comm);
return EXIT_SUCCESS;
}

483
BasicSolver/2D-mpi/src/solver.c
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@@ -4,144 +4,38 @@
* 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 "comm.h"
#include "discretization.h"
#include "parameter.h"
#include "solver.h"
#include "util.h"
#define P(i, j) p[(j) * (imaxLocal + 2) + (i)]
#define F(i, j) f[(j) * (imaxLocal + 2) + (i)]
#define G(i, j) g[(j) * (imaxLocal + 2) + (i)]
#define U(i, j) u[(j) * (imaxLocal + 2) + (i)]
#define V(i, j) v[(j) * (imaxLocal + 2) + (i)]
#define RHS(i, j) rhs[(j) * (imaxLocal + 2) + (i)]
static void printConfig(Solver* s)
void initSolver(Solver* s, Discretization* d, Parameter* p)
{
if (commIsMaster(&s->comm)) {
printf("Parameters for #%s#\n", s->problem);
printf("BC Left:%d Right:%d Bottom:%d Top:%d\n",
s->bcLeft,
s->bcRight,
s->bcBottom,
s->bcTop);
printf("\tReynolds number: %.2f\n", s->re);
printf("\tGx Gy: %.2f %.2f\n", s->gx, s->gy);
printf("Geometry data:\n");
printf("\tDomain box size (x, y): %.2f, %.2f\n", s->xlength, s->ylength);
printf("\tCells (x, y): %d, %d\n", s->imax, s->jmax);
printf("\tCell size (dx, dy): %f, %f\n", s->dx, s->dy);
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);
}
commPrintConfig(&s->comm);
s->grid = &d->grid;
s->eps = p->eps;
s->omega = p->omg;
s->itermax = p->itermax;
s->comm = &d->comm;
}
void initSolver(Solver* s, Parameter* params)
void solve(Solver* s, double* p, double* rhs)
{
s->problem = params->name;
s->bcLeft = params->bcLeft;
s->bcRight = params->bcRight;
s->bcBottom = params->bcBottom;
s->bcTop = params->bcTop;
s->imax = params->imax;
s->jmax = params->jmax;
s->xlength = params->xlength;
s->ylength = params->ylength;
s->dx = params->xlength / params->imax;
s->dy = params->ylength / params->jmax;
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->dt = params->dt;
s->te = params->te;
s->tau = params->tau;
s->gamma = params->gamma;
/* allocate arrays */
int imaxLocal = s->comm.imaxLocal;
int jmaxLocal = s->comm.jmaxLocal;
size_t size = (imaxLocal + 2) * (jmaxLocal + 2);
s->u = allocate(64, size * sizeof(double));
s->v = allocate(64, size * sizeof(double));
s->p = allocate(64, size * sizeof(double));
s->rhs = allocate(64, size * sizeof(double));
s->f = allocate(64, size * sizeof(double));
s->g = allocate(64, size * sizeof(double));
for (int i = 0; i < size; i++) {
s->u[i] = params->u_init;
s->v[i] = params->v_init;
s->p[i] = params->p_init;
s->rhs[i] = 0.0;
s->f[i] = 0.0;
s->g[i] = 0.0;
}
double dx = s->dx;
double dy = s->dy;
double invSqrSum = 1.0 / (dx * dx) + 1.0 / (dy * dy);
s->dtBound = 0.5 * s->re * 1.0 / invSqrSum;
#ifdef VERBOSE
printConfig(s);
#endif
}
void computeRHS(Solver* s)
{
int imaxLocal = s->comm.imaxLocal;
int jmaxLocal = s->comm.jmaxLocal;
double idx = 1.0 / s->dx;
double idy = 1.0 / s->dy;
double idt = 1.0 / s->dt;
double* rhs = s->rhs;
double* f = s->f;
double* g = s->g;
commShift(&s->comm, f, g);
for (int j = 1; j < jmaxLocal + 1; j++) {
for (int i = 1; i < imaxLocal + 1; i++) {
RHS(i, j) = ((F(i, j) - F(i - 1, j)) * idx + (G(i, j) - G(i, j - 1)) * idy) *
idt;
}
}
}
void solve(Solver* s)
{
int imax = s->imax;
int jmax = s->jmax;
int imaxLocal = s->comm.imaxLocal;
int jmaxLocal = s->comm.jmaxLocal;
int imax = s->grid->imax;
int jmax = s->grid->jmax;
int imaxLocal = s->comm->imaxLocal;
int jmaxLocal = s->comm->jmaxLocal;
double eps = s->eps;
int itermax = s->itermax;
double dx2 = s->dx * s->dx;
double dy2 = s->dy * s->dy;
double dx2 = s->grid->dx * s->grid->dx;
double dy2 = s->grid->dy * s->grid->dy;
double idx2 = 1.0 / dx2;
double idy2 = 1.0 / dy2;
double factor = s->omega * 0.5 * (dx2 * dy2) / (dx2 + dy2);
double* p = s->p;
double* rhs = s->rhs;
double epssq = eps * eps;
int pass, jsw, isw;
int it = 0;
@@ -151,7 +45,7 @@ void solve(Solver* s)
jsw = 1;
for (pass = 0; pass < 2; pass++) {
isw = jsw;
commExchange(&s->comm, p);
commExchange(s->comm, p);
for (int j = 1; j < jmaxLocal + 1; j++) {
for (int i = isw; i < imaxLocal + 1; i += 2) {
@@ -168,25 +62,25 @@ void solve(Solver* s)
jsw = 3 - jsw;
}
if (commIsBoundary(&s->comm, BOTTOM)) { // set bottom bc
if (commIsBoundary(s->comm, BOTTOM)) { // set bottom bc
for (int i = 1; i < imaxLocal + 1; i++) {
P(i, 0) = P(i, 1);
}
}
if (commIsBoundary(&s->comm, TOP)) { // set top bc
if (commIsBoundary(s->comm, TOP)) { // set top bc
for (int i = 1; i < imaxLocal + 1; i++) {
P(i, jmaxLocal + 1) = P(i, jmaxLocal);
}
}
if (commIsBoundary(&s->comm, LEFT)) { // set left bc
if (commIsBoundary(s->comm, LEFT)) { // set left bc
for (int j = 1; j < jmaxLocal + 1; j++) {
P(0, j) = P(1, j);
}
}
if (commIsBoundary(&s->comm, RIGHT)) { // set right bc
if (commIsBoundary(s->comm, RIGHT)) { // set right bc
for (int j = 1; j < jmaxLocal + 1; j++) {
P(imaxLocal + 1, j) = P(imaxLocal, j);
}
@@ -195,7 +89,7 @@ void solve(Solver* s)
commReduction(&res, SUM);
res = res / (double)(imax * jmax);
#ifdef DEBUG
if (commIsMaster(&s->comm)) {
if (commIsMaster(s->comm)) {
printf("%d Residuum: %e\n", it, res);
}
#endif
@@ -203,343 +97,8 @@ void solve(Solver* s)
}
#ifdef VERBOSE
if (commIsMaster(&s->comm)) {
if (commIsMaster(s->comm)) {
printf("Solver took %d iterations to reach %f\n", it, sqrt(res));
}
#endif
}
static double maxElement(Solver* s, double* m)
{
int imaxLocal = s->comm.imaxLocal;
int jmaxLocal = s->comm.jmaxLocal;
int size = (imaxLocal + 2) * (jmaxLocal + 2);
double maxval = DBL_MIN;
for (int i = 0; i < size; i++) {
maxval = MAX(maxval, fabs(m[i]));
}
commReduction(&maxval, MAX);
return maxval;
}
void computeTimestep(Solver* s)
{
double dt = s->dtBound;
double dx = s->dx;
double dy = s->dy;
double umax = maxElement(s, s->u);
double vmax = maxElement(s, s->v);
if (umax > 0) {
dt = (dt > dx / umax) ? dx / umax : dt;
}
if (vmax > 0) {
dt = (dt > dy / vmax) ? dy / vmax : dt;
}
s->dt = dt * s->tau;
}
void setBoundaryConditions(Solver* s)
{
int imaxLocal = s->comm.imaxLocal;
int jmaxLocal = s->comm.jmaxLocal;
double* u = s->u;
double* v = s->v;
if (commIsBoundary(&s->comm, TOP)) {
switch (s->bcTop) {
case NOSLIP:
for (int i = 1; i < imaxLocal + 1; i++) {
V(i, jmaxLocal) = 0.0;
U(i, jmaxLocal + 1) = -U(i, jmaxLocal);
}
break;
case SLIP:
for (int i = 1; i < imaxLocal + 1; i++) {
V(i, jmaxLocal) = 0.0;
U(i, jmaxLocal + 1) = U(i, jmaxLocal);
}
break;
case OUTFLOW:
for (int i = 1; i < imaxLocal + 1; i++) {
U(i, jmaxLocal + 1) = U(i, jmaxLocal);
V(i, jmaxLocal) = V(i, jmaxLocal - 1);
}
break;
case PERIODIC:
break;
}
}
if (commIsBoundary(&s->comm, BOTTOM)) {
switch (s->bcBottom) {
case NOSLIP:
for (int i = 1; i < imaxLocal + 1; i++) {
V(i, 0) = 0.0;
U(i, 0) = -U(i, 1);
}
break;
case SLIP:
for (int i = 1; i < imaxLocal + 1; i++) {
V(i, 0) = 0.0;
U(i, 0) = U(i, 1);
}
break;
case OUTFLOW:
for (int i = 1; i < imaxLocal + 1; i++) {
U(i, 0) = U(i, 1);
V(i, 0) = V(i, 1);
}
break;
case PERIODIC:
break;
}
}
if (commIsBoundary(&s->comm, RIGHT)) {
switch (s->bcRight) {
case NOSLIP:
for (int j = 1; j < jmaxLocal + 1; j++) {
U(imaxLocal, j) = 0.0;
V(imaxLocal + 1, j) = -V(imaxLocal, j);
}
break;
case SLIP:
for (int j = 1; j < jmaxLocal + 1; j++) {
U(imaxLocal, j) = 0.0;
V(imaxLocal + 1, j) = V(imaxLocal, j);
}
break;
case OUTFLOW:
for (int j = 1; j < jmaxLocal + 1; j++) {
U(imaxLocal, j) = U(imaxLocal - 1, j);
V(imaxLocal + 1, j) = V(imaxLocal, j);
}
break;
case PERIODIC:
break;
}
}
if (commIsBoundary(&s->comm, LEFT)) {
switch (s->bcLeft) {
case NOSLIP:
for (int j = 1; j < jmaxLocal + 1; j++) {
U(0, j) = 0.0;
V(0, j) = -V(1, j);
}
break;
case SLIP:
for (int j = 1; j < jmaxLocal + 1; j++) {
U(0, j) = 0.0;
V(0, j) = V(1, j);
}
break;
case OUTFLOW:
for (int j = 1; j < jmaxLocal + 1; j++) {
U(0, j) = U(1, j);
V(0, j) = V(1, j);
}
break;
case PERIODIC:
break;
}
}
}
void setSpecialBoundaryCondition(Solver* s)
{
int imaxLocal = s->comm.imaxLocal;
int jmaxLocal = s->comm.jmaxLocal;
double* u = s->u;
if (strcmp(s->problem, "dcavity") == 0) {
if (commIsBoundary(&s->comm, TOP)) {
for (int i = 1; i < imaxLocal + 1; i++) {
U(i, jmaxLocal + 1) = 2.0 - U(i, jmaxLocal);
}
}
} else if (strcmp(s->problem, "canal") == 0) {
if (commIsBoundary(&s->comm, LEFT)) {
double ylength = s->ylength;
double dy = s->dy;
int rest = s->jmax % s->comm.size;
int yc = s->comm.rank * (s->jmax / s->comm.size) + MIN(rest, s->comm.rank);
double ys = dy * (yc + 0.5);
double y;
/* printf("RANK %d yc: %d ys: %f\n", solver->rank, yc, ys); */
for (int j = 1; j < jmaxLocal + 1; j++) {
y = ys + dy * (j - 0.5);
U(0, j) = y * (ylength - y) * 4.0 / (ylength * ylength);
}
}
}
/* print(solver, solver->u); */
}
void computeFG(Solver* s)
{
double* u = s->u;
double* v = s->v;
double* f = s->f;
double* g = s->g;
int imaxLocal = s->comm.imaxLocal;
int jmaxLocal = s->comm.jmaxLocal;
double gx = s->gx;
double gy = s->gy;
double gamma = s->gamma;
double dt = s->dt;
double inverseRe = 1.0 / s->re;
double inverseDx = 1.0 / s->dx;
double inverseDy = 1.0 / s->dy;
double du2dx, dv2dy, duvdx, duvdy;
double du2dx2, du2dy2, dv2dx2, dv2dy2;
commExchange(&s->comm, u);
commExchange(&s->comm, v);
for (int j = 1; j < jmaxLocal + 1; j++) {
for (int i = 1; i < imaxLocal + 1; i++) {
du2dx = inverseDx * 0.25 *
((U(i, j) + U(i + 1, j)) * (U(i, j) + U(i + 1, j)) -
(U(i, j) + U(i - 1, j)) * (U(i, j) + U(i - 1, j))) +
gamma * inverseDx * 0.25 *
(fabs(U(i, j) + U(i + 1, j)) * (U(i, j) - U(i + 1, j)) +
fabs(U(i, j) + U(i - 1, j)) * (U(i, j) - U(i - 1, j)));
duvdy = inverseDy * 0.25 *
((V(i, j) + V(i + 1, j)) * (U(i, j) + U(i, j + 1)) -
(V(i, j - 1) + V(i + 1, j - 1)) * (U(i, j) + U(i, j - 1))) +
gamma * inverseDy * 0.25 *
(fabs(V(i, j) + V(i + 1, j)) * (U(i, j) - U(i, j + 1)) +
fabs(V(i, j - 1) + V(i + 1, j - 1)) *
(U(i, j) - U(i, j - 1)));
du2dx2 = inverseDx * inverseDx * (U(i + 1, j) - 2.0 * U(i, j) + U(i - 1, j));
du2dy2 = inverseDy * inverseDy * (U(i, j + 1) - 2.0 * U(i, j) + U(i, j - 1));
F(i, j) = U(i, j) + dt * (inverseRe * (du2dx2 + du2dy2) - du2dx - duvdy + gx);
duvdx = inverseDx * 0.25 *
((U(i, j) + U(i, j + 1)) * (V(i, j) + V(i + 1, j)) -
(U(i - 1, j) + U(i - 1, j + 1)) * (V(i, j) + V(i - 1, j))) +
gamma * inverseDx * 0.25 *
(fabs(U(i, j) + U(i, j + 1)) * (V(i, j) - V(i + 1, j)) +
fabs(U(i - 1, j) + U(i - 1, j + 1)) *
(V(i, j) - V(i - 1, j)));
dv2dy = inverseDy * 0.25 *
((V(i, j) + V(i, j + 1)) * (V(i, j) + V(i, j + 1)) -
(V(i, j) + V(i, j - 1)) * (V(i, j) + V(i, j - 1))) +
gamma * inverseDy * 0.25 *
(fabs(V(i, j) + V(i, j + 1)) * (V(i, j) - V(i, j + 1)) +
fabs(V(i, j) + V(i, j - 1)) * (V(i, j) - V(i, j - 1)));
dv2dx2 = inverseDx * inverseDx * (V(i + 1, j) - 2.0 * V(i, j) + V(i - 1, j));
dv2dy2 = inverseDy * inverseDy * (V(i, j + 1) - 2.0 * V(i, j) + V(i, j - 1));
G(i, j) = V(i, j) + dt * (inverseRe * (dv2dx2 + dv2dy2) - duvdx - dv2dy + gy);
}
}
/* ----------------------------- boundary of F --------------------------- */
if (commIsBoundary(&s->comm, LEFT)) {
for (int j = 1; j < jmaxLocal + 1; j++) {
F(0, j) = U(0, j);
}
}
if (commIsBoundary(&s->comm, RIGHT)) {
for (int j = 1; j < jmaxLocal + 1; j++) {
F(imaxLocal, j) = U(imaxLocal, j);
}
}
/* ----------------------------- boundary of G --------------------------- */
if (commIsBoundary(&s->comm, BOTTOM)) {
for (int i = 1; i < imaxLocal + 1; i++) {
G(i, 0) = V(i, 0);
}
}
if (commIsBoundary(&s->comm, TOP)) {
for (int i = 1; i < imaxLocal + 1; i++) {
G(i, jmaxLocal) = V(i, jmaxLocal);
}
}
}
void adaptUV(Solver* s)
{
int imaxLocal = s->comm.imaxLocal;
int jmaxLocal = s->comm.jmaxLocal;
double* p = s->p;
double* u = s->u;
double* v = s->v;
double* f = s->f;
double* g = s->g;
double factorX = s->dt / s->dx;
double factorY = s->dt / s->dy;
for (int j = 1; j < jmaxLocal + 1; j++) {
for (int i = 1; i < imaxLocal + 1; i++) {
U(i, j) = F(i, j) - (P(i + 1, j) - P(i, j)) * factorX;
V(i, j) = G(i, j) - (P(i, j + 1) - P(i, j)) * factorY;
}
}
}
void writeResult(Solver* s, double* u, double* v, double* p)
{
int imax = s->imax;
int jmax = s->jmax;
double dx = s->dx;
double dy = s->dy;
double x = 0.0, y = 0.0;
FILE* fp;
fp = fopen("pressure.dat", "w");
if (fp == NULL) {
printf("Error!\n");
exit(EXIT_FAILURE);
}
for (int j = 1; j <= jmax; j++) {
y = (double)(j - 0.5) * dy;
for (int i = 1; i <= imax; i++) {
x = (double)(i - 0.5) * dx;
fprintf(fp, "%.2f %.2f %f\n", x, y, p[j * (imax + 2) + i]);
}
fprintf(fp, "\n");
}
fclose(fp);
fp = fopen("velocity.dat", "w");
if (fp == NULL) {
printf("Error!\n");
exit(EXIT_FAILURE);
}
for (int j = 1; j <= jmax; j++) {
y = dy * (j - 0.5);
for (int i = 1; i <= imax; i++) {
x = dx * (i - 0.5);
double velU = (u[j * (imax + 2) + i] + u[j * (imax + 2) + (i - 1)]) / 2.0;
double velV = (v[j * (imax + 2) + i] + v[(j - 1) * (imax + 2) + i]) / 2.0;
double len = sqrt((velU * velU) + (velV * velV));
fprintf(fp, "%.2f %.2f %f %f %f\n", x, y, velU, velV, len);
}
}
fclose(fp);
}

33
BasicSolver/2D-mpi/src/solver.h
View File

@@ -7,41 +7,20 @@
#ifndef __SOLVER_H_
#define __SOLVER_H_
#include "comm.h"
#include "discretization.h"
#include "grid.h"
#include "parameter.h"
enum BC { NOSLIP = 1, SLIP, OUTFLOW, PERIODIC };
typedef struct {
/* geometry and grid information */
double dx, dy;
int imax, jmax;
double xlength, ylength;
/* arrays */
double *p, *rhs;
double *f, *g;
double *u, *v;
Grid* grid;
/* parameters */
double eps, omega;
double re, tau, gamma;
double gx, gy;
/* time stepping */
int itermax;
double dt, te;
double dtBound;
char* problem;
int bcLeft, bcRight, bcBottom, bcTop;
/* communication */
Comm comm;
Comm* comm;
} Solver;
void initSolver(Solver*, Parameter*);
void computeRHS(Solver*);
void solve(Solver*);
void normalizePressure(Solver*);
void computeTimestep(Solver*);
void setBoundaryConditions(Solver*);
void setSpecialBoundaryCondition(Solver*);
void computeFG(Solver*);
void adaptUV(Solver*);
void writeResult(Solver* s, double* u, double* v, double* p);
void initSolver(Solver*, Discretization*, Parameter*);
void solve(Solver*, double*, double*);
#endif

7
BasicSolver/2D-mpi/src/util.h
View File

@@ -19,4 +19,11 @@
#define ABS(a) ((a) >= 0 ? (a) : -(a))
#endif
#define P(i, j) p[(j) * (imaxLocal + 2) + (i)]
#define F(i, j) f[(j) * (imaxLocal + 2) + (i)]
#define G(i, j) g[(j) * (imaxLocal + 2) + (i)]
#define U(i, j) u[(j) * (imaxLocal + 2) + (i)]
#define V(i, j) v[(j) * (imaxLocal + 2) + (i)]
#define RHS(i, j) rhs[(j) * (imaxLocal + 2) + (i)]
#endif // __UTIL_H_