1601 lines
58 KiB
C
1601 lines
58 KiB
C
/*
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* Copyright (C) 2022 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 "parameter.h"
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#include "solver.h"
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#include "util.h"
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#define P(i, j, k) p[(k) * (imax + 2) * (jmax + 2) + (j) * (imax + 2) + (i)]
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#define F(i, j, k) f[(k) * (imax + 2) * (jmax + 2) + (j) * (imax + 2) + (i)]
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#define G(i, j, k) g[(k) * (imax + 2) * (jmax + 2) + (j) * (imax + 2) + (i)]
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#define H(i, j, k) h[(k) * (imax + 2) * (jmax + 2) + (j) * (imax + 2) + (i)]
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#define U(i, j, k) u[(k) * (imax + 2) * (jmax + 2) + (j) * (imax + 2) + (i)]
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#define V(i, j, k) v[(k) * (imax + 2) * (jmax + 2) + (j) * (imax + 2) + (i)]
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#define W(i, j, k) w[(k) * (imax + 2) * (jmax + 2) + (j) * (imax + 2) + (i)]
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#define S(i, j, k) seg[(k) * (imax + 2) * (jmax + 2) + (j) * (imax + 2) + (i)]
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#define RHS(i, j, k) rhs[(k) * (imax + 2) * (jmax + 2) + (j) * (imax + 2) + (i)]
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static double distance(
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double i, double j, double k, double iCenter, double jCenter, double kCenter)
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{
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return sqrt(pow(iCenter - i, 2) + pow(jCenter - j, 2) + pow(kCenter - k, 2) * 1.0);
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}
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void printGrid(Solver* solver, int* grid)
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{
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int imax = solver->grid.imax;
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int jmax = solver->grid.jmax;
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for (int k = 0; k < solver->grid.kmax + 2; k++) {
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printf("K : %02d:\n", k);
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for (int j = 0; j < solver->grid.jmax + 2; j++) {
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printf("J : %02d: ", j);
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for (int i = 0; i < solver->grid.imax + 2; i++) {
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switch (grid[(k) * (imax + 2) * (jmax + 2) + (j) * (imax + 2) + (i)]) {
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case FRONTFACE:
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printf("FF ");
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break;
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case BACKFACE:
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printf("BF ");
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break;
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case LEFTFACE:
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printf("LF ");
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break;
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case RIGHTFACE:
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printf("RF ");
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break;
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case TOPFACE:
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printf("TF ");
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break;
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case BOTTOMFACE:
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printf("BMF ");
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break;
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case FRONTTOPLEFTCORNER:
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printf("FTLC ");
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break;
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case FRONTTOPRIGHTCORNER:
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printf("FTRC ");
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break;
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case FRONTBOTTOMLEFTCORNER:
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printf("FBLC ");
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break;
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case FRONTBOTTOMRIGHTCORNER:
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printf("FBRC ");
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break;
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case BACKTOPLEFTCORNER:
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printf("BTLC ");
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break;
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case BACKTOPRIGHTCORNER:
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printf("BTRC ");
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break;
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case BACKBOTTOMLEFTCORNER:
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printf("BBLC ");
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break;
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case BACKBOTTOMRIGHTCORNER:
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printf("BBRC ");
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break;
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case FRONTTOPLINE:
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printf("FTL ");
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break;
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case FRONTBOTTOMLINE:
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printf("FBL ");
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break;
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case FRONTLEFTLINE:
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printf("FLL ");
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break;
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case FRONTRIGHTLINE:
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printf("FRL ");
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break;
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case MIDTOPLEFTLINE:
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printf("MTLL ");
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break;
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case MIDTOPRIGHTLINE:
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printf("MTRL ");
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break;
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case MIDBOTTOMLEFTLINE:
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printf("MBTL ");
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break;
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case MIDBOTTOMRIGHTLINE:
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printf("MBRL ");
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break;
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case BACKTOPLINE:
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printf("BTL ");
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break;
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case BACKBOTTOMLINE:
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printf("BBL ");
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break;
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case BACKLEFTLINE:
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printf("BLL ");
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break;
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case BACKRIGHTLINE:
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printf("BRL ");
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break;
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case LOCAL:
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printf("L ");
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break;
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case NONE:
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printf("N ");
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break;
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}
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}
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printf("\n");
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}
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printf("\n\n");
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}
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fflush(stdout);
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}
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static void printConfig(Solver* s)
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{
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printf("Parameters for #%s#\n", s->problem);
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printf("BC Left:%d Right:%d Bottom:%d Top:%d Front:%d Back:%d\n",
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s->bcLeft,
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s->bcRight,
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s->bcBottom,
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s->bcTop,
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s->bcFront,
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s->bcBack);
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printf("\tReynolds number: %.2f\n", s->re);
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printf("\tGx Gy: %.2f %.2f %.2f\n", s->gx, s->gy, s->gz);
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printf("Geometry data:\n");
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printf("\tDomain box size (x, y, z): %.2f, %.2f, %.2f\n",
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s->grid.xlength,
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s->grid.ylength,
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s->grid.zlength);
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printf("\tCells (x, y, z): %d, %d, %d\n", s->grid.imax, s->grid.jmax, s->grid.kmax);
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printf("\tCell size (dx, dy, dz): %f, %f, %f\n", s->grid.dx, s->grid.dy, s->grid.dz);
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printf("Timestep parameters:\n");
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printf("\tDefault stepsize: %.2f, Final time %.2f\n", s->dt, s->te);
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printf("\tdt bound: %.6f\n", s->dtBound);
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printf("\tTau factor: %.2f\n", s->tau);
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printf("Iterative s parameters:\n");
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printf("\tMax iterations: %d\n", s->itermax);
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printf("\tepsilon (stopping tolerance) : %f\n", s->eps);
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printf("\tgamma factor: %f\n", s->gamma);
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printf("\tomega (SOR relaxation): %f\n", s->omega);
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}
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void initSolver(Solver* s, Parameter* params)
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{
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s->problem = params->name;
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s->bcLeft = params->bcLeft;
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s->bcRight = params->bcRight;
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s->bcBottom = params->bcBottom;
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s->bcTop = params->bcTop;
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s->bcFront = params->bcFront;
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s->bcBack = params->bcBack;
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s->grid.imax = params->imax;
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s->grid.jmax = params->jmax;
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s->grid.kmax = params->kmax;
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s->grid.xlength = params->xlength;
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s->grid.ylength = params->ylength;
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s->grid.zlength = params->zlength;
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s->grid.dx = params->xlength / params->imax;
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s->grid.dy = params->ylength / params->jmax;
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s->grid.dz = params->zlength / params->kmax;
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s->eps = params->eps;
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s->omega = params->omg;
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s->itermax = params->itermax;
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s->re = params->re;
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s->gx = params->gx;
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s->gy = params->gy;
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s->gz = params->gz;
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s->dt = params->dt;
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s->te = params->te;
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s->tau = params->tau;
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s->gamma = params->gamma;
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s->rho = params->rho;
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int imax = s->grid.imax;
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int jmax = s->grid.jmax;
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int kmax = s->grid.kmax;
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size_t bytesize = (imax + 2) * (jmax + 2) * (kmax + 2) * sizeof(double);
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s->u = allocate(64, bytesize);
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s->v = allocate(64, bytesize);
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s->w = allocate(64, bytesize);
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s->p = allocate(64, bytesize);
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s->rhs = allocate(64, bytesize);
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s->f = allocate(64, bytesize);
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s->g = allocate(64, bytesize);
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s->h = allocate(64, bytesize);
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s->seg = allocate(64, bytesize);
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for (int i = 0; i < (imax + 2) * (jmax + 2) * (kmax + 2); i++) {
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s->u[i] = params->u_init;
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s->v[i] = params->v_init;
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s->w[i] = params->w_init;
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s->p[i] = params->p_init;
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s->rhs[i] = 0.0;
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s->f[i] = 0.0;
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s->g[i] = 0.0;
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s->h[i] = 0.0;
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s->seg[i] = NONE;
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}
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double dx = s->grid.dx;
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double dy = s->grid.dy;
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double dz = s->grid.dz;
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double invSqrSum = 1.0 / (dx * dx) + 1.0 / (dy * dy) + 1.0 / (dz * dz);
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s->dtBound = 0.5 * s->re * 1.0 / invSqrSum;
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double xCenter = 0, yCenter = 0, zCenter = 0, radius = 0;
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double x1 = 0, x2 = 0, y1 = 0, y2 = 0, z1 = 0, z2 = 0;
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int* seg = s->seg;
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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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z1 = params->zCenter - params->zRectLength / 2;
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z2 = params->zCenter + params->zRectLength / 2;
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for (int k = 1; k < kmax + 1; k++) {
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for (int j = 1; j < jmax + 1; j++) {
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for (int i = 1; i < imax + 1; i++) {
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if ((x1 <= (i * dx)) && ((i * dx) <= x2) && (y1 <= (j * dy)) &&
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((j * dy) <= y2) && ((z1 <= (k * dz)) && ((k * dz) <= z2))) {
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S(i, j, k) = LOCAL;
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}
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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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zCenter = params->zCenter;
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radius = params->circleRadius;
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for (int k = 1; k < kmax + 1; k++) {
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for (int j = 1; j < jmax + 1; j++) {
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for (int i = 1; i < imax + 1; i++) {
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if (distance((i * dx),
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(j * dy),
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(k * dz),
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xCenter,
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yCenter,
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zCenter) <= radius) {
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S(i, j, k) = LOCAL;
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}
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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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for (int k = 1; k < kmax + 1; k++) {
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for (int j = 1; j < jmax + 1; j++) {
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for (int i = 1; i < imax + 1; i++) {
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/* Assigning enum values to Corners */
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if (S(i - 1, j + 1, k - 1) == NONE && S(i - 1, j, k) == NONE &&
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S(i, j + 1, k) == NONE && S(i, j, k - 1) == NONE &&
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S(i + 1, j - 1, k + 1) == LOCAL && S(i, j, k) == LOCAL) {
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S(i, j, k) = FRONTTOPLEFTCORNER; //
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}
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if (S(i + 1, j + 1, k - 1) == NONE && S(i + 1, j, k) == NONE &&
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S(i, j + 1, k) == NONE && S(i, j, k - 1) == NONE &&
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S(i - 1, j - 1, k + 1) == LOCAL && S(i, j, k) == LOCAL) {
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S(i, j, k) = FRONTTOPRIGHTCORNER; //
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}
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if (S(i - 1, j - 1, k - 1) == NONE && S(i - 1, j, k) == NONE &&
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S(i, j - 1, k) == NONE && S(i, j, k - 1) == NONE &&
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S(i + 1, j + 1, k + 1) == LOCAL && S(i, j, k) == LOCAL) {
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S(i, j, k) = FRONTBOTTOMLEFTCORNER; //
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}
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if (S(i + 1, j - 1, k - 1) == NONE && S(i + 1, j, k) == NONE &&
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S(i, j - 1, k) == NONE && S(i, j, k - 1) == NONE &&
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S(i - 1, j + 1, k + 1) == LOCAL && S(i, j, k) == LOCAL) {
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S(i, j, k) = FRONTBOTTOMRIGHTCORNER; //
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}
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if (S(i - 1, j + 1, k + 1) == NONE && S(i - 1, j, k) == NONE &&
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S(i, j + 1, k) == NONE && S(i, j, k + 1) == NONE &&
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S(i + 1, j - 1, k - 1) == LOCAL && S(i, j, k) == LOCAL) {
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S(i, j, k) = BACKTOPLEFTCORNER; //
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}
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if (S(i + 1, j + 1, k + 1) == NONE && S(i + 1, j, k) == NONE &&
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S(i, j + 1, k) == NONE && S(i, j, k + 1) == NONE &&
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S(i - 1, j - 1, k - 1) == LOCAL && S(i, j, k) == LOCAL) {
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S(i, j, k) = BACKTOPRIGHTCORNER;
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}
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if (S(i - 1, j - 1, k + 1) == NONE && S(i - 1, j, k) == NONE &&
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S(i, j - 1, k) == NONE && S(i, j, k + 1) == NONE &&
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S(i + 1, j + 1, k - 1) == LOCAL && S(i, j, k) == LOCAL) {
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S(i, j, k) = BACKBOTTOMLEFTCORNER;
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}
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if (S(i + 1, j - 1, k + 1) == NONE && S(i + 1, j, k) == NONE &&
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S(i, j - 1, k) == NONE && S(i, j, k + 1) == NONE &&
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S(i - 1, j + 1, k - 1) == LOCAL && S(i, j, k) == LOCAL) {
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S(i, j, k) = BACKBOTTOMRIGHTCORNER;
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}
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/* Assigning enum values to Lines */
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if (S(i - 1, j, k - 1) == NONE && S(i, j, k - 1) == NONE &&
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S(i - 1, j, k) == NONE && S(i + 1, j, k + 1) == LOCAL &&
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S(i, j, k) == LOCAL) {
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S(i, j, k) = FRONTLEFTLINE;
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}
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if (S(i + 1, j, k - 1) == NONE && S(i + 1, j, k) == NONE &&
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S(i, j, k - 1) == NONE && S(i - 1, j, k + 1) == LOCAL &&
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S(i, j, k) == LOCAL) {
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S(i, j, k) = FRONTRIGHTLINE;
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}
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if (S(i, j + 1, k - 1) == NONE && S(i, j + 1, k) == NONE &&
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S(i, j, k - 1) == NONE && S(i, j - 1, k + 1) == LOCAL &&
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S(i, j, k) == LOCAL) {
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S(i, j, k) = FRONTTOPLINE;
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}
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if (S(i, j - 1, k - 1) == NONE && S(i, j, k - 1) == NONE &&
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S(i, j - 1, k) == NONE && S(i, j + 1, k + 1) == LOCAL &&
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S(i, j, k) == LOCAL) {
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S(i, j, k) = FRONTBOTTOMLINE;
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}
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if (S(i - 1, j + 1, k) == NONE && S(i, j + 1, k) == NONE &&
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S(i - 1, j, k) == NONE && S(i + 1, j - 1, k) == LOCAL &&
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S(i, j, k) == LOCAL) {
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S(i, j, k) = MIDTOPLEFTLINE;
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}
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if (S(i + 1, j + 1, k) == NONE && S(i + 1, j, k) == NONE &&
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S(i, j + 1, k) == NONE && S(i - 1, j - 1, k) == LOCAL &&
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S(i, j, k) == LOCAL) {
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S(i, j, k) = MIDTOPRIGHTLINE;
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}
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if (S(i - 1, j - 1, k) == NONE && S(i - 1, j, k) == NONE &&
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S(i, j - 1, k) == NONE && S(i + 1, j + 1, k) == LOCAL &&
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S(i, j, k) == LOCAL) {
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S(i, j, k) = MIDBOTTOMLEFTLINE;
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}
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if (S(i + 1, j - 1, k) == NONE && S(i + 1, j, k) == NONE &&
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S(i, j - 1, k) == NONE && S(i - 1, j + 1, k) == LOCAL &&
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S(i, j, k) == LOCAL) {
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S(i, j, k) = MIDBOTTOMRIGHTLINE;
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}
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if (S(i - 1, j, k + 1) == NONE && S(i - 1, j, k) == NONE &&
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S(i, j, k + 1) == NONE && S(i + 1, j, k - 1) == LOCAL &&
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S(i, j, k) == LOCAL) {
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S(i, j, k) = BACKLEFTLINE;
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}
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if (S(i + 1, j, k + 1) == NONE && S(i + 1, j, k) == NONE &&
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S(i, j, k + 1) == NONE && S(i - 1, j, k - 1) == LOCAL &&
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S(i, j, k) == LOCAL) {
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S(i, j, k) = BACKRIGHTLINE;
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}
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if (S(i, j + 1, k + 1) == NONE && S(i, j + 1, k) == NONE &&
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S(i, j, k + 1) == NONE && S(i, j - 1, k - 1) == LOCAL &&
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S(i, j, k) == LOCAL) {
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S(i, j, k) = BACKTOPLINE;
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}
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if (S(i, j - 1, k + 1) == NONE && S(i, j - 1, k) == NONE &&
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S(i, j, k + 1) == NONE && S(i, j + 1, k - 1) == LOCAL &&
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S(i, j, k) == LOCAL) {
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S(i, j, k) = BACKBOTTOMLINE;
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}
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/* Assigning enum values to Faces */
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if (S(i, j, k - 1) == NONE && S(i, j, k + 1) == LOCAL &&
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S(i, j, k) == LOCAL) {
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S(i, j, k) = FRONTFACE; //
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}
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if (S(i, j, k + 1) == NONE && S(i, j, k - 1) == LOCAL &&
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S(i, j, k) == LOCAL) {
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S(i, j, k) = BACKFACE; //
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}
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if (S(i, j - 1, k) == NONE && S(i, j + 1, k) == LOCAL &&
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S(i, j, k) == LOCAL) {
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S(i, j, k) = BOTTOMFACE; //
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}
|
|
if (S(i, j + 1, k) == NONE && S(i, j - 1, k) == LOCAL &&
|
|
S(i, j, k) == LOCAL) {
|
|
S(i, j, k) = TOPFACE; //
|
|
}
|
|
if (S(i - 1, j, k) == NONE && S(i + 1, j, k) == LOCAL &&
|
|
S(i, j, k) == LOCAL) {
|
|
S(i, j, k) = LEFTFACE; //
|
|
}
|
|
if (S(i + 1, j, k) == NONE && S(i - 1, j, k) == LOCAL &&
|
|
S(i, j, k) == LOCAL) {
|
|
S(i, j, k) = RIGHTFACE; //
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
#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;
|
|
int* seg = s->seg;
|
|
|
|
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;
|
|
int* seg = s->seg;
|
|
|
|
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++) {
|
|
// if (S(i, j, k) == NONE) {
|
|
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);
|
|
}
|
|
}
|
|
// setObjectPBoundaryCondition(s);
|
|
|
|
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
|
|
}
|
|
|
|
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;
|
|
int* seg = s->seg;
|
|
|
|
while ((res >= epssq) && (it < itermax)) {
|
|
res = 0.0;
|
|
ksw = 1;
|
|
|
|
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);
|
|
}
|
|
}
|
|
|
|
// setObjectPBoundaryCondition(s);
|
|
|
|
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) {
|
|
// if (S(i, j, k) == NONE) {
|
|
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;
|
|
}
|
|
|
|
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
|
|
}
|
|
|
|
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;
|
|
int* seg = s->seg;
|
|
|
|
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) {
|
|
// if (S(i, j, k) == NONE) {
|
|
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);
|
|
}
|
|
}
|
|
// setObjectPBoundaryCondition(s);
|
|
|
|
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
|
|
}
|
|
|
|
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(1, j, k) = y * (ylength - y) * 4.0 / (ylength * ylength);
|
|
}
|
|
}
|
|
} else if (strcmp(s->problem, "karman") == 0) {
|
|
for (int k = 1; k < kmax + 1; k++) {
|
|
for (int j = 1; j < jmax + 1; j++) {
|
|
U(1, j, k) = 1.0;
|
|
}
|
|
}
|
|
} else if (strcmp(s->problem, "backstep") == 0) {
|
|
|
|
int* seg = s->seg;
|
|
for (int k = 1; k < kmax + 1; k++) {
|
|
for (int j = 1; j < jmax + 1; j++) {
|
|
if (S(1, j, k) == NONE) U(0, j, k) = 1.0;
|
|
else {
|
|
U(0, j, k) = 0.0;
|
|
U(1, j, k) = 0.0;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
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;
|
|
int* seg = s->seg;
|
|
|
|
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++) {
|
|
|
|
if (S(i, j, k) == NONE) {
|
|
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);
|
|
} else {
|
|
switch (S(i, j, k)) {
|
|
case TOPFACE:
|
|
G(i, j, k) = 0.0;
|
|
break;
|
|
case BOTTOMFACE:
|
|
G(i, j, k) = 0.0;
|
|
break;
|
|
case LEFTFACE:
|
|
F(i, j, k) = 0.0;
|
|
break;
|
|
case RIGHTFACE:
|
|
F(i, j, k) = 0.0;
|
|
break;
|
|
case FRONTFACE:
|
|
H(i, j, k) = 0.0;
|
|
break;
|
|
case BACKFACE:
|
|
H(i, j, k) = 0.0;
|
|
break;
|
|
case FRONTLEFTLINE:
|
|
F(i, j, k) = 0.0;
|
|
H(i, j, k) = 0.0;
|
|
break;
|
|
case FRONTRIGHTLINE:
|
|
F(i, j, k) = 0.0;
|
|
H(i, j, k) = 0.0;
|
|
break;
|
|
case FRONTTOPLINE:
|
|
G(i, j, k) = 0.0;
|
|
H(i, j, k) = 0.0;
|
|
break;
|
|
case FRONTBOTTOMLINE:
|
|
G(i, j, k) = 0.0;
|
|
H(i, j, k) = 0.0;
|
|
break;
|
|
case MIDTOPLEFTLINE:
|
|
F(i, j, k) = 0.0;
|
|
G(i, j, k) = 0.0;
|
|
break;
|
|
case MIDTOPRIGHTLINE:
|
|
F(i, j, k) = 0.0;
|
|
G(i, j, k) = 0.0;
|
|
break;
|
|
case MIDBOTTOMLEFTLINE:
|
|
F(i, j, k) = 0.0;
|
|
G(i, j, k) = 0.0;
|
|
break;
|
|
case MIDBOTTOMRIGHTLINE:
|
|
F(i, j, k) = 0.0;
|
|
G(i, j, k) = 0.0;
|
|
break;
|
|
case BACKLEFTLINE:
|
|
F(i, j, k) = 0.0;
|
|
H(i, j, k) = 0.0;
|
|
break;
|
|
case BACKRIGHTLINE:
|
|
F(i, j, k) = 0.0;
|
|
H(i, j, k) = 0.0;
|
|
break;
|
|
case BACKTOPLINE:
|
|
G(i, j, k) = 0.0;
|
|
H(i, j, k) = 0.0;
|
|
break;
|
|
case BACKBOTTOMLINE:
|
|
G(i, j, k) = 0.0;
|
|
H(i, j, k) = 0.0;
|
|
break;
|
|
case FRONTTOPLEFTCORNER:
|
|
F(i, j, k) = 0.0;
|
|
G(i, j, k) = 0.0;
|
|
H(i, j, k) = 0.0;
|
|
break;
|
|
case FRONTTOPRIGHTCORNER:
|
|
F(i, j, k) = 0.0;
|
|
G(i, j, k) = 0.0;
|
|
H(i, j, k) = 0.0;
|
|
break;
|
|
case FRONTBOTTOMLEFTCORNER:
|
|
F(i, j, k) = 0.0;
|
|
G(i, j, k) = 0.0;
|
|
H(i, j, k) = 0.0;
|
|
break;
|
|
case FRONTBOTTOMRIGHTCORNER:
|
|
F(i, j, k) = 0.0;
|
|
G(i, j, k) = 0.0;
|
|
H(i, j, k) = 0.0;
|
|
break;
|
|
case BACKTOPLEFTCORNER:
|
|
F(i, j, k) = 0.0;
|
|
G(i, j, k) = 0.0;
|
|
H(i, j, k) = 0.0;
|
|
break;
|
|
case BACKTOPRIGHTCORNER:
|
|
F(i, j, k) = 0.0;
|
|
G(i, j, k) = 0.0;
|
|
H(i, j, k) = 0.0;
|
|
break;
|
|
case BACKBOTTOMLEFTCORNER:
|
|
F(i, j, k) = 0.0;
|
|
G(i, j, k) = 0.0;
|
|
H(i, j, k) = 0.0;
|
|
break;
|
|
case BACKBOTTOMRIGHTCORNER:
|
|
F(i, j, k) = 0.0;
|
|
G(i, j, k) = 0.0;
|
|
H(i, j, k) = 0.0;
|
|
break;
|
|
case LOCAL:
|
|
F(i, j, k) = 0.0;
|
|
G(i, j, k) = 0.0;
|
|
H(i, j, k) = 0.0;
|
|
break;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
/* ----------------------------- 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;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
void setObjectBoundaryCondition(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;
|
|
int* seg = s->seg;
|
|
for (int k = 1; k < kmax + 1; k++) {
|
|
for (int j = 1; j < jmax + 1; j++) {
|
|
for (int i = 1; i < imax + 1; i++) {
|
|
switch (S(i, j, k)) {
|
|
case TOPFACE:
|
|
U(i, j, k) = -U(i, j + 1, k);
|
|
V(i, j, k) = 0.0;
|
|
W(i, j, k) = -W(i, j + 1, k);
|
|
|
|
break;
|
|
case BOTTOMFACE:
|
|
U(i, j, k) = -U(i, j - 1, k);
|
|
V(i, j, k) = 0.0;
|
|
W(i, j, k) = -W(i, j - 1, k);
|
|
break;
|
|
case LEFTFACE:
|
|
U(i, j, k) = 0.0;
|
|
V(i, j, k) = -V(i - 1, j, k);
|
|
W(i, j, k) = -W(i - 1, j, k);
|
|
break;
|
|
case RIGHTFACE:
|
|
U(i, j, k) = 0.0;
|
|
V(i, j, k) = -V(i + 1, j, k);
|
|
W(i, j, k) = -W(i + 1, j, k);
|
|
break;
|
|
case FRONTFACE:
|
|
U(i, j, k) = -U(i, j, k - 1);
|
|
V(i, j, k) = -V(i, j, k - 1);
|
|
W(i, j, k) = 0.0;
|
|
break;
|
|
case BACKFACE:
|
|
U(i, j, k) = -U(i, j, k + 1);
|
|
V(i, j, k) = -V(i, j, k + 1);
|
|
W(i, j, k) = 0.0;
|
|
break;
|
|
case FRONTLEFTLINE:
|
|
U(i, j, k) = 0.0;
|
|
V(i, j, k) = -V(i, j, k - 1);
|
|
W(i, j, k) = -W(i - 1, j, k);
|
|
break;
|
|
case FRONTRIGHTLINE:
|
|
U(i, j, k) = 0.0;
|
|
V(i, j, k) = -V(i, j, k - 1);
|
|
W(i, j, k) = -W(i + 1, j, k);
|
|
break;
|
|
case FRONTTOPLINE:
|
|
U(i, j, k) = -U(i, j, k - 1);
|
|
V(i, j, k) = 0.0;
|
|
W(i, j, k) = -W(i, j + 1, k);
|
|
break;
|
|
case FRONTBOTTOMLINE:
|
|
U(i, j, k) = -U(i, j, k - 1);
|
|
V(i, j, k) = 0.0;
|
|
W(i, j, k) = -W(i, j - 1, k);
|
|
break;
|
|
case MIDTOPLEFTLINE:
|
|
U(i, j, k) = -U(i, j + 1, k);
|
|
V(i, j, k) = -V(i - 1, j, k);
|
|
W(i, j, k) = 0.0;
|
|
break;
|
|
case MIDTOPRIGHTLINE:
|
|
U(i, j, k) = 0.0;
|
|
V(i, j, k) = 0.0;
|
|
U(i - 1, j, k) = -U(i - 1, j + 1, k);
|
|
V(i, j - 1, k) = -V(i + 1, j - 1, k);
|
|
W(i, j, k) = 0.0;
|
|
break;
|
|
case MIDBOTTOMLEFTLINE:
|
|
U(i, j, k) = -U(i, j - 1, k);
|
|
V(i, j, k) = -V(i - 1, j, k);
|
|
W(i, j, k) = 0.0;
|
|
break;
|
|
case MIDBOTTOMRIGHTLINE:
|
|
U(i, j, k) = -U(i, j - 1, k);
|
|
V(i, j, k) = -V(i + 1, j, k);
|
|
W(i, j, k) = 0.0;
|
|
break;
|
|
case BACKLEFTLINE:
|
|
U(i, j, k) = 0.0;
|
|
V(i, j, k) = -V(i, j, k + 1);
|
|
W(i, j, k) = -W(i - 1, j, k);
|
|
break;
|
|
case BACKRIGHTLINE:
|
|
U(i, j, k) = 0.0;
|
|
V(i, j, k) = -V(i, j, k + 1);
|
|
W(i, j, k) = -W(i + 1, j, k);
|
|
break;
|
|
case BACKTOPLINE:
|
|
U(i, j, k) = -U(i, j, k + 1);
|
|
V(i, j, k) = 0.0;
|
|
W(i, j, k) = -W(i, j + 1, k);
|
|
break;
|
|
case BACKBOTTOMLINE:
|
|
U(i, j, k) = -U(i, j, k + 1);
|
|
V(i, j, k) = 0.0;
|
|
W(i, j, k) = -W(i, j - 1, k);
|
|
break;
|
|
case FRONTTOPLEFTCORNER:
|
|
U(i, j, k) = -U(i, j, k - 1);
|
|
V(i, j, k) = -V(i - 1, j, k);
|
|
W(i, j, k) = -W(i, j + 1, k);
|
|
break;
|
|
case FRONTTOPRIGHTCORNER:
|
|
U(i, j, k) = -U(i, j, k - 1);
|
|
V(i, j, k) = -V(i + 1, j, k);
|
|
W(i, j, k) = -W(i, j + 1, k);
|
|
break;
|
|
case FRONTBOTTOMLEFTCORNER:
|
|
U(i, j, k) = -U(i, j, k - 1);
|
|
V(i, j, k) = -V(i - 1, j, k);
|
|
W(i, j, k) = -W(i, j - 1, k);
|
|
break;
|
|
case FRONTBOTTOMRIGHTCORNER:
|
|
U(i, j, k) = -U(i, j, k - 1);
|
|
V(i, j, k) = -V(i + 1, j, k);
|
|
W(i, j, k) = -W(i, j - 1, k);
|
|
break;
|
|
case BACKTOPLEFTCORNER:
|
|
U(i, j, k) = -U(i, j, k + 1);
|
|
V(i, j, k) = -V(i - 1, j, k);
|
|
W(i, j, k) = -W(i, j + 1, k);
|
|
break;
|
|
case BACKTOPRIGHTCORNER:
|
|
U(i, j, k) = -U(i, j, k + 1);
|
|
V(i, j, k) = -V(i + 1, j, k);
|
|
W(i, j, k) = -W(i, j + 1, k);
|
|
break;
|
|
case BACKBOTTOMLEFTCORNER:
|
|
U(i, j, k) = -U(i, j, k + 1);
|
|
V(i, j, k) = -V(i - 1, j, k);
|
|
W(i, j, k) = -W(i, j - 1, k);
|
|
break;
|
|
case BACKBOTTOMRIGHTCORNER:
|
|
U(i, j, k) = -U(i, j, k + 1);
|
|
V(i, j, k) = -V(i + 1, j, k);
|
|
W(i, j, k) = -W(i, j - 1, k);
|
|
break;
|
|
case LOCAL:
|
|
U(i, j, k) = 0.0;
|
|
V(i, j, k) = 0.0;
|
|
W(i, j, k) = 0.0;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
void setObjectPBoundaryCondition(Solver* s)
|
|
{
|
|
int imax = s->grid.imax;
|
|
int jmax = s->grid.jmax;
|
|
int kmax = s->grid.kmax;
|
|
double* p = s->p;
|
|
int* seg = s->seg;
|
|
for (int k = 1; k < kmax + 1; k++) {
|
|
for (int j = 1; j < jmax + 1; j++) {
|
|
for (int i = 1; i < imax + 1; i++) {
|
|
switch (S(i, j, k)) {
|
|
case TOPFACE:
|
|
P(i, j, k) = P(i, j + 1, k);
|
|
break;
|
|
case BOTTOMFACE:
|
|
P(i, j, k) = P(i, j - 1, k);
|
|
break;
|
|
case LEFTFACE:
|
|
P(i, j, k) = P(i - 1, j, k);
|
|
break;
|
|
case RIGHTFACE:
|
|
P(i, j, k) = P(i + 1, j, k);
|
|
break;
|
|
case FRONTFACE:
|
|
P(i, j, k) = P(i, j, k - 1);
|
|
break;
|
|
case BACKFACE:
|
|
P(i, j, k) = P(i, j, k + 1);
|
|
break;
|
|
case FRONTLEFTLINE:
|
|
P(i, j, k) = (P(i, j, k - 1) + P(i - 1, j, k)) / 2;
|
|
break;
|
|
case FRONTRIGHTLINE:
|
|
P(i, j, k) = (P(i, j, k - 1) + P(i + 1, j, k)) / 2;
|
|
break;
|
|
case FRONTTOPLINE:
|
|
P(i, j, k) = (P(i, j, k - 1) + P(i, j + 1, k)) / 2;
|
|
break;
|
|
case FRONTBOTTOMLINE:
|
|
P(i, j, k) = (P(i, j, k - 1) + P(i, j - 1, k)) / 2;
|
|
break;
|
|
case MIDTOPLEFTLINE:
|
|
P(i, j, k) = (P(i - 1, j, k) + P(i, j + 1, k)) / 2;
|
|
break;
|
|
case MIDTOPRIGHTLINE:
|
|
P(i, j, k) = (P(i + 1, j, k) + P(i, j + 1, k)) / 2;
|
|
break;
|
|
case MIDBOTTOMLEFTLINE:
|
|
P(i, j, k) = (P(i - 1, j, k) + P(i, j - 1, k)) / 2;
|
|
break;
|
|
case MIDBOTTOMRIGHTLINE:
|
|
P(i, j, k) = (P(i + 1, j, k) + P(i, j - 1, k)) / 2;
|
|
break;
|
|
case BACKLEFTLINE:
|
|
P(i, j, k) = (P(i, j, k + 1) + P(i - 1, j, k)) / 2;
|
|
break;
|
|
case BACKRIGHTLINE:
|
|
P(i, j, k) = (P(i, j, k + 1) + P(i + 1, j, k)) / 2;
|
|
break;
|
|
case BACKTOPLINE:
|
|
P(i, j, k) = (P(i, j, k + 1) + P(i, j + 1, k)) / 2;
|
|
break;
|
|
case BACKBOTTOMLINE:
|
|
P(i, j, k) = (P(i, j, k + 1) + P(i, j - 1, k)) / 2;
|
|
break;
|
|
case FRONTTOPLEFTCORNER:
|
|
P(i, j, k) = (P(i, j, k - 1) + P(i - 1, j, k) + P(i, j + 1, k)) / 3;
|
|
break;
|
|
case FRONTTOPRIGHTCORNER:
|
|
P(i, j, k) = (P(i, j, k - 1) + P(i + 1, j, k) + P(i, j + 1, k)) / 3;
|
|
break;
|
|
case FRONTBOTTOMLEFTCORNER:
|
|
P(i, j, k) = (P(i, j, k - 1) + P(i - 1, j, k) + P(i, j - 1, k)) / 3;
|
|
break;
|
|
case FRONTBOTTOMRIGHTCORNER:
|
|
P(i, j, k) = (P(i, j, k - 1) + P(i + 1, j, k) + P(i, j - 1, k)) / 3;
|
|
break;
|
|
case BACKTOPLEFTCORNER:
|
|
P(i, j, k) = (P(i, j, k + 1) + P(i - 1, j, k) + P(i, j + 1, k)) / 3;
|
|
break;
|
|
case BACKTOPRIGHTCORNER:
|
|
P(i, j, k) = (P(i, j, k + 1) + P(i + 1, j, k) + P(i, j + 1, k)) / 3;
|
|
break;
|
|
case BACKBOTTOMLEFTCORNER:
|
|
P(i, j, k) = (P(i, j, k + 1) + P(i - 1, j, k) + P(i, j - 1, k)) / 3;
|
|
break;
|
|
case BACKBOTTOMRIGHTCORNER:
|
|
P(i, j, k) = (P(i, j, k + 1) + P(i + 1, j, k) + P(i, j - 1, k)) / 3;
|
|
break;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
} |