forked from moebiusband/NuSiF-Solver
725 lines
23 KiB
C
725 lines
23 KiB
C
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/*
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* Copyright (C) NHR@FAU, University Erlangen-Nuremberg.
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* All rights reserved. This file is part of nusif-solver.
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* Use of this source code is governed by a MIT style
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* license that can be found in the LICENSE file.
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*/
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#include <float.h>
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#include <math.h>
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#include <stdio.h>
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#include <stdlib.h>
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#include <string.h>
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#include "allocate.h"
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#include "comm.h"
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#include "discretization.h"
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#include "parameter.h"
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#include "util.h"
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static double distance(double i, double j, double iCenter, double jCenter)
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{
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return sqrt(pow(iCenter - i, 2) + pow(jCenter - j, 2) * 1.0);
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}
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double sumOffset(double* sizes, int init, int offset, int coord)
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{
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double sum = 0;
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for (int i = init - offset; coord > 0; i -= offset, --coord) {
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sum += sizes[i];
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}
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return sum;
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}
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void print(Discretization* d, double* grid)
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{
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int imaxLocal = d->comm.imaxLocal;
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for (int i = 0; i < d->comm.size; i++) {
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if (i == d->comm.rank) {
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sleep(1 * d->comm.rank);
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printf("### RANK %d LVL "
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"###################################################### #\n ",
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d->comm.rank);
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for (int j = 0; j < d->comm.jmaxLocal + 2; j++) {
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printf("%02d: ", j);
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for (int i = 0; i < d->comm.imaxLocal + 2; i++) {
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printf("%2.2f ", grid[j * (imaxLocal + 2) + i]);
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}
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printf("\n");
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}
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fflush(stdout);
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}
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}
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}
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static void printConfig(Discretization* d)
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{
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if (commIsMaster(&d->comm)) {
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printf("Parameters for #%s#\n", d->problem);
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printf("BC Left:%d Right:%d Bottom:%d Top:%d\n",
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d->bcLeft,
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d->bcRight,
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d->bcBottom,
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d->bcTop);
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printf("\tReynolds number: %.2f\n", d->re);
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printf("\tGx Gy: %.2f %.2f\n", d->gx, d->gy);
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printf("Geometry data:\n");
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printf("\tDomain box size (x, y): %.2f, %.2f\n",
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d->grid.xlength,
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d->grid.ylength);
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printf("\tCells (x, y): %d, %d\n", d->grid.imax, d->grid.jmax);
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printf("\tCell size (dx, dy): %f, %f\n", d->grid.dx, d->grid.dy);
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printf("Timestep parameters:\n");
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printf("\tDefault stepsize: %.2f, Final time %.2f\n", d->dt, d->te);
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printf("\tdt bound: %.6f\n", d->dtBound);
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printf("\tTau factor: %.2f\n", d->tau);
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printf("Iterative s parameters:\n");
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printf("\tgamma factor: %f\n", d->gamma);
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}
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commPrintConfig(&d->comm);
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}
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void initDiscretiztion(Discretization* d, Parameter* params)
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{
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d->problem = params->name;
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d->bcLeft = params->bcLeft;
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d->bcRight = params->bcRight;
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d->bcBottom = params->bcBottom;
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d->bcTop = params->bcTop;
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d->grid.imax = params->imax;
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d->grid.jmax = params->jmax;
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d->grid.xlength = params->xlength;
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d->grid.ylength = params->ylength;
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d->grid.dx = params->xlength / params->imax;
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d->grid.dy = params->ylength / params->jmax;
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d->re = params->re;
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d->gx = params->gx;
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d->gy = params->gy;
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d->dt = params->dt;
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d->te = params->te;
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d->tau = params->tau;
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d->gamma = params->gamma;
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/* allocate arrays */
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int imaxLocal = d->comm.imaxLocal;
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int jmaxLocal = d->comm.jmaxLocal;
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size_t size = (imaxLocal + 2) * (jmaxLocal + 2);
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d->u = allocate(64, size * sizeof(double));
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d->v = allocate(64, size * sizeof(double));
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d->p = allocate(64, size * sizeof(double));
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d->rhs = allocate(64, size * sizeof(double));
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d->f = allocate(64, size * sizeof(double));
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d->g = allocate(64, size * sizeof(double));
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d->grid.s = allocate(64, size * sizeof(double));
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for (int i = 0; i < size; i++) {
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d->u[i] = params->u_init;
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d->v[i] = params->v_init;
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d->p[i] = params->p_init;
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d->rhs[i] = 0.0;
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d->f[i] = 0.0;
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d->g[i] = 0.0;
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d->grid.s[i] = FLUID;
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}
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double dx = d->grid.dx;
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double dy = d->grid.dy;
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double invSqrSum = 1.0 / (dx * dx) + 1.0 / (dy * dy);
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d->dtBound = 0.5 * d->re * 1.0 / invSqrSum;
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d->xLocal = d->comm.imaxLocal * d->grid.dx;
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d->yLocal = d->comm.jmaxLocal * d->grid.dy;
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double xLocal[d->comm.size];
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double yLocal[d->comm.size];
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#ifdef _MPI
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MPI_Allgather(&d->xLocal, 1, MPI_DOUBLE, xLocal, 1, MPI_DOUBLE, d->comm.comm);
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MPI_Allgather(&d->yLocal, 1, MPI_DOUBLE, yLocal, 1, MPI_DOUBLE, d->comm.comm);
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d->xOffset = sumOffset(xLocal,
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d->comm.rank,
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d->comm.dims[JDIM],
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d->comm.coords[IDIM]);
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d->yOffset = sumOffset(yLocal, d->comm.rank, 1, d->comm.coords[JDIM]);
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d->xOffsetEnd = d->xOffset + d->xLocal;
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d->yOffsetEnd = d->yOffset + d->yLocal;
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#else
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d->xOffset = 0;
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d->yOffset = 0;
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d->xOffsetEnd = d->xOffset + d->xLocal;
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d->yOffsetEnd = d->yOffset + d->yLocal;
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#endif
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printf("Rank : %d, xOffset : %.2f, yOffset : %.2f, xOffsetEnd : %.2f, yOffsetEnd : "
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"%.2f\n",
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d->comm.rank,
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d->xOffset,
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d->yOffset,
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d->xOffsetEnd,
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d->yOffsetEnd);
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double* s = d->grid.s;
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int iOffset = 0, jOffset = 0;
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double xCenter = 0, yCenter = 0, radius = 0;
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double x1 = 0, x2 = 0, y1 = 0, y2 = 0;
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switch (params->shape) {
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case NOSHAPE:
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break;
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case RECT:
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x1 = params->xCenter - params->xRectLength / 2;
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x2 = params->xCenter + params->xRectLength / 2;
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y1 = params->yCenter - params->yRectLength / 2;
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y2 = params->yCenter + params->yRectLength / 2;
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iOffset = d->xOffset / dx;
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jOffset = d->yOffset / dy;
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for (int j = 1; j < jmaxLocal + 1; ++j) {
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for (int i = 1; i < imaxLocal + 1; ++i) {
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if ((x1 <= ((i + iOffset) * dx)) && (((i + iOffset) * dx) <= x2) &&
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(y1 <= ((j + jOffset) * dy)) && (((j + jOffset) * dy) <= y2)) {
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S(i, j) = OBSTACLE;
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}
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}
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}
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break;
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case CIRCLE:
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xCenter = params->xCenter;
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yCenter = params->yCenter;
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radius = params->circleRadius;
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iOffset = d->xOffset / dx;
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jOffset = d->yOffset / dy;
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for (int j = 1; j < jmaxLocal + 1; j++) {
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for (int i = 1; i < imaxLocal + 1; i++) {
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if (distance(((i + iOffset) * dx),
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((j + jOffset) * dy),
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xCenter,
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yCenter) <= radius) {
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S(i, j) = OBSTACLE;
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}
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}
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}
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break;
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default:
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break;
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}
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#ifdef _MPI
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commExchange(&d->comm, s);
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#endif
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for (int j = 1; j < jmaxLocal + 1; j++) {
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for (int i = 1; i < imaxLocal + 1; i++) {
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if (S(i, j - 1) == FLUID && S(i, j + 1) == OBSTACLE && S(i, j) == OBSTACLE)
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S(i, j) = BOTTOM; // BOTTOM
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if (S(i - 1, j) == FLUID && S(i + 1, j) == OBSTACLE && S(i, j) == OBSTACLE)
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S(i, j) = LEFT; // LEFT
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if (S(i + 1, j) == FLUID && S(i - 1, j) == OBSTACLE && S(i, j) == OBSTACLE)
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S(i, j) = RIGHT; // RIGHT
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if (S(i, j + 1) == FLUID && S(i, j - 1) == OBSTACLE && S(i, j) == OBSTACLE)
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S(i, j) = TOP; // TOP
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if (S(i - 1, j - 1) == FLUID && S(i, j - 1) == FLUID &&
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S(i - 1, j) == FLUID && S(i + 1, j + 1) == OBSTACLE &&
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(S(i, j) == OBSTACLE || S(i, j) == LEFT || S(i, j) == BOTTOM))
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S(i, j) = BOTTOMLEFT; // BOTTOMLEFT
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if (S(i + 1, j - 1) == FLUID && S(i, j - 1) == FLUID &&
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S(i + 1, j) == FLUID && S(i - 1, j + 1) == OBSTACLE &&
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(S(i, j) == OBSTACLE || S(i, j) == RIGHT || S(i, j) == BOTTOM))
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S(i, j) = BOTTOMRIGHT; // BOTTOMRIGHT
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if (S(i - 1, j + 1) == FLUID && S(i - 1, j) == FLUID &&
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S(i, j + 1) == FLUID && S(i + 1, j - 1) == OBSTACLE &&
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(S(i, j) == OBSTACLE || S(i, j) == LEFT || S(i, j) == TOP))
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S(i, j) = TOPLEFT; // TOPLEFT
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if (S(i + 1, j + 1) == FLUID && S(i + 1, j) == FLUID &&
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S(i, j + 1) == FLUID && S(i - 1, j - 1) == OBSTACLE &&
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(S(i, j) == OBSTACLE || S(i, j) == RIGHT || S(i, j) == TOP))
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S(i, j) = TOPRIGHT; // TOPRIGHT
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}
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}
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#ifdef VERBOSE
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printConfig(d);
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#endif
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}
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void computeRHS(Discretization* d)
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{
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int imaxLocal = d->comm.imaxLocal;
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int jmaxLocal = d->comm.jmaxLocal;
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double idx = 1.0 / d->grid.dx;
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double idy = 1.0 / d->grid.dy;
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double idt = 1.0 / d->dt;
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double* rhs = d->rhs;
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double* f = d->f;
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double* g = d->g;
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commShift(&d->comm, f, g);
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for (int j = 1; j < jmaxLocal + 1; j++) {
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for (int i = 1; i < imaxLocal + 1; i++) {
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RHS(i, j) = ((F(i, j) - F(i - 1, j)) * idx + (G(i, j) - G(i, j - 1)) * idy) *
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idt;
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}
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}
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}
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static double maxElement(Discretization* d, double* m)
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{
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int imaxLocal = d->comm.imaxLocal;
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int jmaxLocal = d->comm.jmaxLocal;
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int size = (imaxLocal + 2) * (jmaxLocal + 2);
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double maxval = DBL_MIN;
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for (int i = 0; i < size; i++) {
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maxval = MAX(maxval, fabs(m[i]));
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}
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commReduction(&maxval, MAX);
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return maxval;
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}
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void computeTimestep(Discretization* d)
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{
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double dt = d->dtBound;
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double dx = d->grid.dx;
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double dy = d->grid.dy;
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double umax = maxElement(d, d->u);
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double vmax = maxElement(d, d->v);
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if (umax > 0) {
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dt = (dt > dx / umax) ? dx / umax : dt;
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}
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if (vmax > 0) {
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dt = (dt > dy / vmax) ? dy / vmax : dt;
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}
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d->dt = dt * d->tau;
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}
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void setBoundaryConditions(Discretization* d)
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{
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int imaxLocal = d->comm.imaxLocal;
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int jmaxLocal = d->comm.jmaxLocal;
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double* u = d->u;
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double* v = d->v;
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if (commIsBoundary(&d->comm, T)) {
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switch (d->bcTop) {
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case NOSLIP:
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for (int i = 1; i < imaxLocal + 1; i++) {
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V(i, jmaxLocal) = 0.0;
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U(i, jmaxLocal + 1) = -U(i, jmaxLocal);
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}
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break;
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case SLIP:
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for (int i = 1; i < imaxLocal + 1; i++) {
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V(i, jmaxLocal) = 0.0;
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U(i, jmaxLocal + 1) = U(i, jmaxLocal);
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}
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break;
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case OUTFLOW:
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for (int i = 1; i < imaxLocal + 1; i++) {
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U(i, jmaxLocal + 1) = U(i, jmaxLocal);
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V(i, jmaxLocal) = V(i, jmaxLocal - 1);
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}
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break;
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case PERIODIC:
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break;
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}
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}
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if (commIsBoundary(&d->comm, B)) {
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||
|
|
switch (d->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(&d->comm, R)) {
|
||
|
|
switch (d->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(&d->comm, L)) {
|
||
|
|
switch (d->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* d)
|
||
|
|
{
|
||
|
|
int imaxLocal = d->comm.imaxLocal;
|
||
|
|
int jmaxLocal = d->comm.jmaxLocal;
|
||
|
|
double* u = d->u;
|
||
|
|
double* s = d->grid.s;
|
||
|
|
|
||
|
|
if (strcmp(d->problem, "dcavity") == 0) {
|
||
|
|
if (commIsBoundary(&d->comm, T)) {
|
||
|
|
for (int i = 1; i < imaxLocal + 1; i++) {
|
||
|
|
U(i, jmaxLocal + 1) = 2.0 - U(i, jmaxLocal);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
} else if (strcmp(d->problem, "canal") == 0) {
|
||
|
|
if (commIsBoundary(&d->comm, L)) {
|
||
|
|
|
||
|
|
double ylength = d->grid.ylength;
|
||
|
|
double dy = d->grid.dy;
|
||
|
|
int rest = d->grid.jmax % d->comm.dims[JDIM];
|
||
|
|
int yc = d->comm.rank * (d->grid.jmax / d->comm.dims[JDIM]) +
|
||
|
|
MIN(rest, d->comm.rank);
|
||
|
|
double ys = dy * (yc + 0.5);
|
||
|
|
double y;
|
||
|
|
|
||
|
|
// printf("RANK %d yc: %d ys: %f\n",d->comm.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);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
} else if (strcmp(d->problem, "backstep") == 0) {
|
||
|
|
for (int j = 1; j < jmaxLocal + 1; j++) {
|
||
|
|
if (S(0, j) == FLUID) U(0, j) = 1.0;
|
||
|
|
}
|
||
|
|
} else if (strcmp(d->problem, "karman") == 0) {
|
||
|
|
for (int j = 1; j < jmaxLocal + 1; j++) {
|
||
|
|
U(0, j) = 1.0;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
/* print(solver, solver->u); */
|
||
|
|
}
|
||
|
|
|
||
|
|
void setObjectBoundaryCondition(Discretization* d)
|
||
|
|
{
|
||
|
|
int imaxLocal = d->comm.imaxLocal;
|
||
|
|
int jmaxLocal = d->comm.jmaxLocal;
|
||
|
|
double* u = d->u;
|
||
|
|
double* v = d->v;
|
||
|
|
double* s = d->grid.s;
|
||
|
|
|
||
|
|
for (int j = 1; j < jmaxLocal + 1; j++) {
|
||
|
|
for (int i = 1; i < imaxLocal + 1; i++) {
|
||
|
|
switch ((int)S(i, j)) {
|
||
|
|
case TOP:
|
||
|
|
U(i, j) = -U(i, j + 1);
|
||
|
|
U(i - 1, j) = -U(i - 1, j + 1);
|
||
|
|
V(i, j) = 0.0;
|
||
|
|
break;
|
||
|
|
case BOTTOM:
|
||
|
|
U(i, j) = -U(i, j - 1);
|
||
|
|
U(i - 1, j) = -U(i - 1, j - 1);
|
||
|
|
V(i, j) = 0.0;
|
||
|
|
break;
|
||
|
|
case LEFT:
|
||
|
|
U(i - 1, j) = 0.0;
|
||
|
|
V(i, j) = -V(i - 1, j);
|
||
|
|
V(i, j - 1) = -V(i - 1, j - 1);
|
||
|
|
break;
|
||
|
|
case RIGHT:
|
||
|
|
U(i, j) = 0.0;
|
||
|
|
V(i, j) = -V(i + 1, j);
|
||
|
|
V(i, j - 1) = -V(i + 1, j - 1);
|
||
|
|
break;
|
||
|
|
case TOPLEFT:
|
||
|
|
U(i, j) = -U(i, j + 1);
|
||
|
|
U(i - 1, j) = 0.0;
|
||
|
|
V(i, j) = 0.0;
|
||
|
|
V(i, j - 1) = -V(i - 1, j - 1);
|
||
|
|
break;
|
||
|
|
case TOPRIGHT:
|
||
|
|
U(i, j) = 0.0;
|
||
|
|
U(i - 1, j) = -U(i - 1, j + 1);
|
||
|
|
V(i, j) = 0.0;
|
||
|
|
V(i, j - 1) = -V(i + 1, j - 1);
|
||
|
|
break;
|
||
|
|
case BOTTOMLEFT:
|
||
|
|
U(i, j) = -U(i, j - 1);
|
||
|
|
U(i - 1, j) = 0.0;
|
||
|
|
V(i, j) = -V(i - 1, j);
|
||
|
|
V(i, j - 1) = 0.0;
|
||
|
|
break;
|
||
|
|
case BOTTOMRIGHT:
|
||
|
|
U(i, j) = 0.0;
|
||
|
|
U(i - 1, j) = -U(i - 1, j - 1);
|
||
|
|
V(i, j) = -V(i, j + 1);
|
||
|
|
V(i, j - 1) = 0.0;
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
void computeFG(Discretization* d)
|
||
|
|
{
|
||
|
|
double* u = d->u;
|
||
|
|
double* v = d->v;
|
||
|
|
double* f = d->f;
|
||
|
|
double* g = d->g;
|
||
|
|
double* s = d->grid.s;
|
||
|
|
|
||
|
|
int imaxLocal = d->comm.imaxLocal;
|
||
|
|
int jmaxLocal = d->comm.jmaxLocal;
|
||
|
|
|
||
|
|
double gx = d->gx;
|
||
|
|
double gy = d->gy;
|
||
|
|
double gamma = d->gamma;
|
||
|
|
double dt = d->dt;
|
||
|
|
double inverseRe = 1.0 / d->re;
|
||
|
|
double inverseDx = 1.0 / d->grid.dx;
|
||
|
|
double inverseDy = 1.0 / d->grid.dy;
|
||
|
|
double du2dx, dv2dy, duvdx, duvdy;
|
||
|
|
double du2dx2, du2dy2, dv2dx2, dv2dy2;
|
||
|
|
|
||
|
|
commExchange(&d->comm, u);
|
||
|
|
commExchange(&d->comm, v);
|
||
|
|
|
||
|
|
for (int j = 1; j < jmaxLocal + 1; j++) {
|
||
|
|
for (int i = 1; i < imaxLocal + 1; i++) {
|
||
|
|
if (S(i, j) == FLUID) {
|
||
|
|
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);
|
||
|
|
} else {
|
||
|
|
switch ((int)S(i, j)) {
|
||
|
|
case TOP:
|
||
|
|
G(i, j) = V(i, j);
|
||
|
|
break;
|
||
|
|
case BOTTOM:
|
||
|
|
G(i, j - 1) = V(i, j - 1);
|
||
|
|
break;
|
||
|
|
case LEFT:
|
||
|
|
F(i - 1, j) = U(i - 1, j);
|
||
|
|
break;
|
||
|
|
case RIGHT:
|
||
|
|
F(i, j) = U(i, j);
|
||
|
|
break;
|
||
|
|
case TOPLEFT:
|
||
|
|
F(i - 1, j) = U(i - 1, j);
|
||
|
|
G(i, j) = V(i, j);
|
||
|
|
break;
|
||
|
|
case TOPRIGHT:
|
||
|
|
F(i, j) = U(i, j);
|
||
|
|
G(i, j) = V(i, j);
|
||
|
|
break;
|
||
|
|
case BOTTOMLEFT:
|
||
|
|
F(i - 1, j) = U(i - 1, j);
|
||
|
|
G(i, j - 1) = V(i, j - 1);
|
||
|
|
break;
|
||
|
|
case BOTTOMRIGHT:
|
||
|
|
F(i, j) = U(i, j);
|
||
|
|
G(i, j - 1) = V(i, j - 1);
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
/* ----------------------------- boundary of F --------------------------- */
|
||
|
|
if (commIsBoundary(&d->comm, L)) {
|
||
|
|
for (int j = 1; j < jmaxLocal + 1; j++) {
|
||
|
|
F(0, j) = U(0, j);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
if (commIsBoundary(&d->comm, R)) {
|
||
|
|
for (int j = 1; j < jmaxLocal + 1; j++) {
|
||
|
|
F(imaxLocal, j) = U(imaxLocal, j);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
/* ----------------------------- boundary of G --------------------------- */
|
||
|
|
if (commIsBoundary(&d->comm, B)) {
|
||
|
|
for (int i = 1; i < imaxLocal + 1; i++) {
|
||
|
|
G(i, 0) = V(i, 0);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
if (commIsBoundary(&d->comm, T)) {
|
||
|
|
for (int i = 1; i < imaxLocal + 1; i++) {
|
||
|
|
G(i, jmaxLocal) = V(i, jmaxLocal);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
void adaptUV(Discretization* d)
|
||
|
|
{
|
||
|
|
int imaxLocal = d->comm.imaxLocal;
|
||
|
|
int jmaxLocal = d->comm.jmaxLocal;
|
||
|
|
|
||
|
|
double* p = d->p;
|
||
|
|
double* u = d->u;
|
||
|
|
double* v = d->v;
|
||
|
|
double* f = d->f;
|
||
|
|
double* g = d->g;
|
||
|
|
|
||
|
|
double factorX = d->dt / d->grid.dx;
|
||
|
|
double factorY = d->dt / d->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* d, double* u, double* v, double* p)
|
||
|
|
{
|
||
|
|
int imax = d->grid.imax;
|
||
|
|
int jmax = d->grid.jmax;
|
||
|
|
double dx = d->grid.dx;
|
||
|
|
double dy = d->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);
|
||
|
|
}
|