640 lines
21 KiB
C
640 lines
21 KiB
C
/*
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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 <string.h>
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#include "allocate.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 void printConfig(Discretization* d)
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{
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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 Front:%d Back:%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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d->bcFront,
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d->bcBack);
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printf("\tReynolds number: %.2f\n", d->re);
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printf("\tGx Gy: %.2f %.2f %.2f\n", d->gx, d->gy, d->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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d->grid.xlength,
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d->grid.ylength,
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d->grid.zlength);
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printf("\tCells (x, y, z): %d, %d, %d\n", d->grid.imax, d->grid.jmax, d->grid.kmax);
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printf("\tCell size (dx, dy, dz): %f, %f, %f\n", d->grid.dx, d->grid.dy, d->grid.dz);
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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 parameters:\n");
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printf("\tepsilon (stopping tolerance) : %f\n", d->eps);
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printf("\tgamma factor: %f\n", d->gamma);
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printf("\tomega (SOR relaxation): %f\n", d->omega);
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}
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void initDiscretization(Discretization* d, Parameter* p)
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{
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d->problem = p->name;
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d->bcLeft = p->bcLeft;
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d->bcRight = p->bcRight;
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d->bcBottom = p->bcBottom;
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d->bcTop = p->bcTop;
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d->bcFront = p->bcFront;
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d->bcBack = p->bcBack;
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d->grid.imax = p->imax;
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d->grid.jmax = p->jmax;
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d->grid.kmax = p->kmax;
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d->grid.xlength = p->xlength;
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d->grid.ylength = p->ylength;
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d->grid.zlength = p->zlength;
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d->grid.dx = p->xlength / p->imax;
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d->grid.dy = p->ylength / p->jmax;
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d->grid.dz = p->zlength / p->kmax;
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d->eps = p->eps;
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d->omega = p->omg;
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d->re = p->re;
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d->gx = p->gx;
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d->gy = p->gy;
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d->gz = p->gz;
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d->dt = p->dt;
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d->te = p->te;
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d->tau = p->tau;
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d->gamma = p->gamma;
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int imax = d->grid.imax;
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int jmax = d->grid.jmax;
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int kmax = d->grid.kmax;
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size_t bytesize = (imax + 2) * (jmax + 2) * (kmax + 2) * sizeof(double);
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d->u = allocate(64, bytesize);
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d->v = allocate(64, bytesize);
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d->w = allocate(64, bytesize);
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d->p = allocate(64, bytesize);
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d->rhs = allocate(64, bytesize);
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d->f = allocate(64, bytesize);
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d->g = allocate(64, bytesize);
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d->h = allocate(64, bytesize);
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for (int i = 0; i < (imax + 2) * (jmax + 2) * (kmax + 2); i++) {
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d->u[i] = p->u_init;
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d->v[i] = p->v_init;
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d->w[i] = p->w_init;
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d->p[i] = p->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->h[i] = 0.0;
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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 dz = d->grid.dz;
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double invSqrSum = 1.0 / (dx * dx) + 1.0 / (dy * dy) + 1.0 / (dz * dz);
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d->dtBound = 0.5 * d->re * 1.0 / invSqrSum;
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#ifdef VERBOSE
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printConfig(d);
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#endif /* VERBOSE */
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}
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void computeRHS(Discretization* d)
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{
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int imax = d->grid.imax;
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int jmax = d->grid.jmax;
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int kmax = d->grid.kmax;
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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 idz = 1.0 / d->grid.dz;
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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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double* h = d->h;
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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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RHS(i, j, k) = ((F(i, j, k) - F(i - 1, j, k)) * idx +
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(G(i, j, k) - G(i, j - 1, k)) * idy +
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(H(i, j, k) - H(i, j, k - 1)) * idz) *
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idt;
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}
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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 size = (d->grid.imax + 2) * (d->grid.jmax + 2) * (d->grid.kmax + 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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return maxval;
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}
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void normalizePressure(Discretization* d)
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{
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int size = (d->grid.imax + 2) * (d->grid.jmax + 2) * (d->grid.kmax + 2);
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double* p = d->p;
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double avgP = 0.0;
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for (int i = 0; i < size; i++) {
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avgP += p[i];
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}
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avgP /= size;
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for (int i = 0; i < size; i++) {
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p[i] = p[i] - avgP;
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}
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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 dz = d->grid.dz;
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double umax = maxElement(d, d->u);
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double vmax = maxElement(d, d->v);
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double wmax = maxElement(d, d->w);
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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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if (wmax > 0) {
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dt = (dt > dz / wmax) ? dz / wmax : 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 imax = d->grid.imax;
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int jmax = d->grid.jmax;
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int kmax = d->grid.kmax;
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double* u = d->u;
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double* v = d->v;
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double* w = d->w;
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switch (d->bcTop) {
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case NOSLIP:
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for (int k = 1; k < kmax + 1; k++) {
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for (int i = 1; i < imax + 1; i++) {
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V(i, jmax, k) = 0.0;
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U(i, jmax + 1, k) = -U(i, jmax, k);
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W(i, jmax + 1, k) = -W(i, jmax, k);
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}
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}
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break;
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case SLIP:
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for (int k = 1; k < kmax + 1; k++) {
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for (int i = 1; i < imax + 1; i++) {
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V(i, jmax, k) = 0.0;
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U(i, jmax + 1, k) = U(i, jmax, k);
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W(i, jmax + 1, k) = W(i, jmax, k);
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}
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}
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break;
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case OUTFLOW:
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for (int k = 1; k < kmax + 1; k++) {
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for (int i = 1; i < imax + 1; i++) {
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U(i, jmax + 1, k) = U(i, jmax, k);
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V(i, jmax, k) = V(i, jmax - 1, k);
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W(i, jmax + 1, k) = W(i, jmax, k);
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}
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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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switch (d->bcBottom) {
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case NOSLIP:
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for (int k = 1; k < kmax + 1; k++) {
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for (int i = 1; i < imax + 1; i++) {
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V(i, 0, k) = 0.0;
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U(i, 0, k) = -U(i, 1, k);
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W(i, 0, k) = -W(i, 1, k);
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}
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}
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break;
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case SLIP:
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for (int k = 1; k < kmax + 1; k++) {
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for (int i = 1; i < imax + 1; i++) {
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V(i, 0, k) = 0.0;
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U(i, 0, k) = U(i, 1, k);
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W(i, 0, k) = W(i, 1, k);
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}
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}
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break;
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case OUTFLOW:
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for (int k = 1; k < kmax + 1; k++) {
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for (int i = 1; i < imax + 1; i++) {
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U(i, 0, k) = U(i, 1, k);
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V(i, 0, k) = V(i, 1, k);
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W(i, 0, k) = W(i, 1, k);
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}
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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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switch (d->bcLeft) {
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case NOSLIP:
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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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U(0, j, k) = 0.0;
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V(0, j, k) = -V(1, j, k);
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W(0, j, k) = -W(1, j, k);
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}
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}
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break;
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case SLIP:
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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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U(0, j, k) = 0.0;
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V(0, j, k) = V(1, j, k);
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W(0, j, k) = W(1, j, k);
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}
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}
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break;
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case OUTFLOW:
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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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U(0, j, k) = U(1, j, k);
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V(0, j, k) = V(1, j, k);
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W(0, j, k) = W(1, j, k);
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}
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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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switch (d->bcRight) {
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case NOSLIP:
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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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U(imax, j, k) = 0.0;
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V(imax + 1, j, k) = -V(imax, j, k);
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W(imax + 1, j, k) = -W(imax, j, k);
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}
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}
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break;
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case SLIP:
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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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U(imax, j, k) = 0.0;
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V(imax + 1, j, k) = V(imax, j, k);
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W(imax + 1, j, k) = W(imax, j, k);
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}
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}
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break;
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case OUTFLOW:
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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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U(imax, j, k) = U(imax - 1, j, k);
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V(imax + 1, j, k) = V(imax, j, k);
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W(imax + 1, j, k) = W(imax, j, k);
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}
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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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switch (d->bcFront) {
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case NOSLIP:
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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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U(i, j, 0) = -U(i, j, 1);
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V(i, j, 0) = -V(i, j, 1);
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W(i, j, 0) = 0.0;
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}
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}
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break;
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case SLIP:
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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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U(i, j, 0) = U(i, j, 1);
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V(i, j, 0) = V(i, j, 1);
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W(i, j, 0) = 0.0;
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}
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}
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break;
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case OUTFLOW:
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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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U(i, j, 0) = U(i, j, 1);
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V(i, j, 0) = V(i, j, 1);
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W(i, j, 0) = W(i, j, 1);
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}
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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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switch (d->bcBack) {
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case NOSLIP:
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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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U(i, j, kmax + 1) = -U(i, j, kmax);
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V(i, j, kmax + 1) = -V(i, j, kmax);
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W(i, j, kmax + 1) = 0.0;
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}
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}
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break;
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case SLIP:
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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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U(i, j, kmax + 1) = U(i, j, kmax);
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V(i, j, kmax + 1) = V(i, j, kmax);
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W(i, j, kmax + 1) = 0.0;
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}
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}
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break;
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case OUTFLOW:
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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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U(i, j, kmax + 1) = U(i, j, kmax);
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V(i, j, kmax + 1) = V(i, j, kmax);
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W(i, j, kmax) = W(i, j, kmax - 1);
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}
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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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void setSpecialBoundaryCondition(Discretization* d)
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{
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int imax = d->grid.imax;
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int jmax = d->grid.jmax;
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int kmax = d->grid.kmax;
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double mDy = d->grid.dy;
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double* u = d->u;
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if (strcmp(d->problem, "dcavity") == 0) {
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for (int k = 1; k < kmax; k++) {
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for (int i = 1; i < imax; i++) {
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U(i, jmax + 1, k) = 2.0 - U(i, jmax, k);
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}
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}
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} else if (strcmp(d->problem, "canal") == 0) {
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double ylength = d->grid.ylength;
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double y;
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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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y = mDy * (j - 0.5);
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U(0, j, k) = y * (ylength - y) * 4.0 / (ylength * ylength);
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}
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}
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}
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}
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void computeFG(Discretization* d)
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{
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int imax = d->grid.imax;
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int jmax = d->grid.jmax;
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int kmax = d->grid.kmax;
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double* u = d->u;
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double* v = d->v;
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double* w = d->w;
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double* f = d->f;
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double* g = d->g;
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double* h = d->h;
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double gx = d->gx;
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double gy = d->gy;
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double gz = d->gz;
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double dt = d->dt;
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double gamma = d->gamma;
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double inverseRe = 1.0 / d->re;
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double inverseDx = 1.0 / d->grid.dx;
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double inverseDy = 1.0 / d->grid.dy;
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double inverseDz = 1.0 / d->grid.dz;
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double du2dx, dv2dy, dw2dz;
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double duvdx, duwdx, duvdy, dvwdy, duwdz, dvwdz;
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double du2dx2, du2dy2, du2dz2;
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double dv2dx2, dv2dy2, dv2dz2;
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double dw2dx2, dw2dy2, dw2dz2;
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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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du2dx = inverseDx * 0.25 *
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((U(i, j, k) + U(i + 1, j, k)) *
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(U(i, j, k) + U(i + 1, j, k)) -
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(U(i, j, k) + U(i - 1, j, k)) *
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(U(i, j, k) + U(i - 1, j, k))) +
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gamma * inverseDx * 0.25 *
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(fabs(U(i, j, k) + U(i + 1, j, k)) *
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(U(i, j, k) - U(i + 1, j, k)) +
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fabs(U(i, j, k) + U(i - 1, j, k)) *
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(U(i, j, k) - U(i - 1, j, k)));
|
|
|
|
duvdy = inverseDy * 0.25 *
|
|
((V(i, j, k) + V(i + 1, j, k)) *
|
|
(U(i, j, k) + U(i, j + 1, k)) -
|
|
(V(i, j - 1, k) + V(i + 1, j - 1, k)) *
|
|
(U(i, j, k) + U(i, j - 1, k))) +
|
|
gamma * inverseDy * 0.25 *
|
|
(fabs(V(i, j, k) + V(i + 1, j, k)) *
|
|
(U(i, j, k) - U(i, j + 1, k)) +
|
|
fabs(V(i, j - 1, k) + V(i + 1, j - 1, k)) *
|
|
(U(i, j, k) - U(i, j - 1, k)));
|
|
|
|
duwdz = inverseDz * 0.25 *
|
|
((W(i, j, k) + W(i + 1, j, k)) *
|
|
(U(i, j, k) + U(i, j, k + 1)) -
|
|
(W(i, j, k - 1) + W(i + 1, j, k - 1)) *
|
|
(U(i, j, k) + U(i, j, k - 1))) +
|
|
gamma * inverseDz * 0.25 *
|
|
(fabs(W(i, j, k) + W(i + 1, j, k)) *
|
|
(U(i, j, k) - U(i, j, k + 1)) +
|
|
fabs(W(i, j, k - 1) + W(i + 1, j, k - 1)) *
|
|
(U(i, j, k) - U(i, j, k - 1)));
|
|
|
|
du2dx2 = inverseDx * inverseDx *
|
|
(U(i + 1, j, k) - 2.0 * U(i, j, k) + U(i - 1, j, k));
|
|
du2dy2 = inverseDy * inverseDy *
|
|
(U(i, j + 1, k) - 2.0 * U(i, j, k) + U(i, j - 1, k));
|
|
du2dz2 = inverseDz * inverseDz *
|
|
(U(i, j, k + 1) - 2.0 * U(i, j, k) + U(i, j, k - 1));
|
|
F(i, j, k) = U(i, j, k) + dt * (inverseRe * (du2dx2 + du2dy2 + du2dz2) -
|
|
du2dx - duvdy - duwdz + gx);
|
|
|
|
duvdx = inverseDx * 0.25 *
|
|
((U(i, j, k) + U(i, j + 1, k)) *
|
|
(V(i, j, k) + V(i + 1, j, k)) -
|
|
(U(i - 1, j, k) + U(i - 1, j + 1, k)) *
|
|
(V(i, j, k) + V(i - 1, j, k))) +
|
|
gamma * inverseDx * 0.25 *
|
|
(fabs(U(i, j, k) + U(i, j + 1, k)) *
|
|
(V(i, j, k) - V(i + 1, j, k)) +
|
|
fabs(U(i - 1, j, k) + U(i - 1, j + 1, k)) *
|
|
(V(i, j, k) - V(i - 1, j, k)));
|
|
|
|
dv2dy = inverseDy * 0.25 *
|
|
((V(i, j, k) + V(i, j + 1, k)) *
|
|
(V(i, j, k) + V(i, j + 1, k)) -
|
|
(V(i, j, k) + V(i, j - 1, k)) *
|
|
(V(i, j, k) + V(i, j - 1, k))) +
|
|
gamma * inverseDy * 0.25 *
|
|
(fabs(V(i, j, k) + V(i, j + 1, k)) *
|
|
(V(i, j, k) - V(i, j + 1, k)) +
|
|
fabs(V(i, j, k) + V(i, j - 1, k)) *
|
|
(V(i, j, k) - V(i, j - 1, k)));
|
|
|
|
dvwdz = inverseDz * 0.25 *
|
|
((W(i, j, k) + W(i, j + 1, k)) *
|
|
(V(i, j, k) + V(i, j, k + 1)) -
|
|
(W(i, j, k - 1) + W(i, j + 1, k - 1)) *
|
|
(V(i, j, k) + V(i, j, k + 1))) +
|
|
gamma * inverseDz * 0.25 *
|
|
(fabs(W(i, j, k) + W(i, j + 1, k)) *
|
|
(V(i, j, k) - V(i, j, k + 1)) +
|
|
fabs(W(i, j, k - 1) + W(i, j + 1, k - 1)) *
|
|
(V(i, j, k) - V(i, j, k + 1)));
|
|
|
|
dv2dx2 = inverseDx * inverseDx *
|
|
(V(i + 1, j, k) - 2.0 * V(i, j, k) + V(i - 1, j, k));
|
|
dv2dy2 = inverseDy * inverseDy *
|
|
(V(i, j + 1, k) - 2.0 * V(i, j, k) + V(i, j - 1, k));
|
|
dv2dz2 = inverseDz * inverseDz *
|
|
(V(i, j, k + 1) - 2.0 * V(i, j, k) + V(i, j, k - 1));
|
|
G(i, j, k) = V(i, j, k) + dt * (inverseRe * (dv2dx2 + dv2dy2 + dv2dz2) -
|
|
duvdx - dv2dy - dvwdz + gy);
|
|
|
|
duwdx = inverseDx * 0.25 *
|
|
((U(i, j, k) + U(i, j, k + 1)) *
|
|
(W(i, j, k) + W(i + 1, j, k)) -
|
|
(U(i - 1, j, k) + U(i - 1, j, k + 1)) *
|
|
(W(i, j, k) + W(i - 1, j, k))) +
|
|
gamma * inverseDx * 0.25 *
|
|
(fabs(U(i, j, k) + U(i, j, k + 1)) *
|
|
(W(i, j, k) - W(i + 1, j, k)) +
|
|
fabs(U(i - 1, j, k) + U(i - 1, j, k + 1)) *
|
|
(W(i, j, k) - W(i - 1, j, k)));
|
|
|
|
dvwdy = inverseDy * 0.25 *
|
|
((V(i, j, k) + V(i, j, k + 1)) *
|
|
(W(i, j, k) + W(i, j + 1, k)) -
|
|
(V(i, j - 1, k + 1) + V(i, j - 1, k)) *
|
|
(W(i, j, k) + W(i, j - 1, k))) +
|
|
gamma * inverseDy * 0.25 *
|
|
(fabs(V(i, j, k) + V(i, j, k + 1)) *
|
|
(W(i, j, k) - W(i, j + 1, k)) +
|
|
fabs(V(i, j - 1, k + 1) + V(i, j - 1, k)) *
|
|
(W(i, j, k) - W(i, j - 1, k)));
|
|
|
|
dw2dz = inverseDz * 0.25 *
|
|
((W(i, j, k) + W(i, j, k + 1)) *
|
|
(W(i, j, k) + W(i, j, k + 1)) -
|
|
(W(i, j, k) + W(i, j, k - 1)) *
|
|
(W(i, j, k) + W(i, j, k - 1))) +
|
|
gamma * inverseDz * 0.25 *
|
|
(fabs(W(i, j, k) + W(i, j, k + 1)) *
|
|
(W(i, j, k) - W(i, j, k + 1)) +
|
|
fabs(W(i, j, k) + W(i, j, k - 1)) *
|
|
(W(i, j, k) - W(i, j, k - 1)));
|
|
|
|
dw2dx2 = inverseDx * inverseDx *
|
|
(W(i + 1, j, k) - 2.0 * W(i, j, k) + W(i - 1, j, k));
|
|
dw2dy2 = inverseDy * inverseDy *
|
|
(W(i, j + 1, k) - 2.0 * W(i, j, k) + W(i, j - 1, k));
|
|
dw2dz2 = inverseDz * inverseDz *
|
|
(W(i, j, k + 1) - 2.0 * W(i, j, k) + W(i, j, k - 1));
|
|
H(i, j, k) = W(i, j, k) + dt * (inverseRe * (dw2dx2 + dw2dy2 + dw2dz2) -
|
|
duwdx - dvwdy - dw2dz + gz);
|
|
}
|
|
}
|
|
}
|
|
|
|
/* ----------------------------- boundary of F ---------------------------
|
|
*/
|
|
for (int k = 1; k < kmax + 1; k++) {
|
|
for (int j = 1; j < jmax + 1; j++) {
|
|
F(0, j, k) = U(0, j, k);
|
|
F(imax, j, k) = U(imax, j, k);
|
|
}
|
|
}
|
|
|
|
/* ----------------------------- boundary of G ---------------------------
|
|
*/
|
|
for (int k = 1; k < kmax + 1; k++) {
|
|
for (int i = 1; i < imax + 1; i++) {
|
|
G(i, 0, k) = V(i, 0, k);
|
|
G(i, jmax, k) = V(i, jmax, k);
|
|
}
|
|
}
|
|
|
|
/* ----------------------------- boundary of G ---------------------------
|
|
*/
|
|
for (int j = 1; j < jmax + 1; j++) {
|
|
for (int i = 1; i < imax + 1; i++) {
|
|
H(i, j, 0) = W(i, j, 0);
|
|
H(i, j, kmax) = W(i, j, kmax);
|
|
}
|
|
}
|
|
}
|
|
|
|
void adaptUV(Discretization* d)
|
|
{
|
|
int imax = d->grid.imax;
|
|
int jmax = d->grid.jmax;
|
|
int kmax = d->grid.kmax;
|
|
|
|
double* p = d->p;
|
|
double* u = d->u;
|
|
double* v = d->v;
|
|
double* w = d->w;
|
|
double* f = d->f;
|
|
double* g = d->g;
|
|
double* h = d->h;
|
|
|
|
double factorX = d->dt / d->grid.dx;
|
|
double factorY = d->dt / d->grid.dy;
|
|
double factorZ = d->dt / d->grid.dz;
|
|
|
|
for (int k = 1; k < kmax + 1; k++) {
|
|
for (int j = 1; j < jmax + 1; j++) {
|
|
for (int i = 1; i < imax + 1; i++) {
|
|
U(i, j, k) = F(i, j, k) - (P(i + 1, j, k) - P(i, j, k)) * factorX;
|
|
V(i, j, k) = G(i, j, k) - (P(i, j + 1, k) - P(i, j, k)) * factorY;
|
|
W(i, j, k) = H(i, j, k) - (P(i, j, k + 1) - P(i, j, k)) * factorZ;
|
|
}
|
|
}
|
|
}
|
|
}
|