/* * Copyright (C) 2022 NHR@FAU, University Erlangen-Nuremberg. * All rights reserved. This file is part of nusif-solver. * Use of this source code is governed by a MIT style * license that can be found in the LICENSE file. */ #include #include #include #include #include #include "allocate.h" #include "comm.h" #include "parameter.h" #include "solver.h" #include "util.h" #define P(i, j, k) \ p[(k) * (imaxLocal + 2) * (jmaxLocal + 2) + (j) * (imaxLocal + 2) + (i)] #define F(i, j, k) \ f[(k) * (imaxLocal + 2) * (jmaxLocal + 2) + (j) * (imaxLocal + 2) + (i)] #define G(i, j, k) \ g[(k) * (imaxLocal + 2) * (jmaxLocal + 2) + (j) * (imaxLocal + 2) + (i)] #define H(i, j, k) \ h[(k) * (imaxLocal + 2) * (jmaxLocal + 2) + (j) * (imaxLocal + 2) + (i)] #define U(i, j, k) \ u[(k) * (imaxLocal + 2) * (jmaxLocal + 2) + (j) * (imaxLocal + 2) + (i)] #define V(i, j, k) \ v[(k) * (imaxLocal + 2) * (jmaxLocal + 2) + (j) * (imaxLocal + 2) + (i)] #define W(i, j, k) \ w[(k) * (imaxLocal + 2) * (jmaxLocal + 2) + (j) * (imaxLocal + 2) + (i)] #define RHS(i, j, k) \ rhs[(k) * (imaxLocal + 2) * (jmaxLocal + 2) + (j) * (imaxLocal + 2) + (i)] static void printConfig(Solver* s) { if (commIsMaster(&s->comm)) { printf("Parameters for #%s#\n", s->problem); printf("BC Left:%d Right:%d Bottom:%d Top:%d Front:%d Back:%d\n", s->bcLeft, s->bcRight, s->bcBottom, s->bcTop, s->bcFront, s->bcBack); printf("\tReynolds number: %.2f\n", s->re); printf("\tGx Gy: %.2f %.2f %.2f\n", s->gx, s->gy, s->gz); printf("Geometry data:\n"); printf("\tDomain box size (x, y, z): %.2f, %.2f, %.2f\n", s->grid.xlength, s->grid.ylength, s->grid.zlength); printf("\tCells (x, y, z): %d, %d, %d\n", s->grid.imax, s->grid.jmax, s->grid.kmax); printf("\tCell size (dx, dy, dz): %f, %f, %f\n", s->grid.dx, s->grid.dy, s->grid.dz); printf("Timestep parameters:\n"); printf("\tDefault stepsize: %.2f, Final time %.2f\n", s->dt, s->te); printf("\tdt bound: %.6f\n", s->dtBound); printf("\tTau factor: %.2f\n", s->tau); printf("Iterative parameters:\n"); printf("\tMax iterations: %d\n", s->itermax); printf("\tepsilon (stopping tolerance) : %f\n", s->eps); printf("\tgamma factor: %f\n", s->gamma); printf("\tomega (SOR relaxation): %f\n", s->omega); } commPrintConfig(&s->comm); } void initSolver(Solver* s, Parameter* params) { s->problem = params->name; s->bcLeft = params->bcLeft; s->bcRight = params->bcRight; s->bcBottom = params->bcBottom; s->bcTop = params->bcTop; s->bcFront = params->bcFront; s->bcBack = params->bcBack; s->grid.imax = params->imax; s->grid.jmax = params->jmax; s->grid.kmax = params->kmax; s->grid.xlength = params->xlength; s->grid.ylength = params->ylength; s->grid.zlength = params->zlength; s->grid.dx = params->xlength / params->imax; s->grid.dy = params->ylength / params->jmax; s->grid.dz = params->zlength / params->kmax; s->eps = params->eps; s->omega = params->omg; s->itermax = params->itermax; s->re = params->re; s->gx = params->gx; s->gy = params->gy; s->gz = params->gz; s->dt = params->dt; s->te = params->te; s->tau = params->tau; s->gamma = params->gamma; s->rho = params->rho; commInit(&s->comm, s->grid.kmax, s->grid.jmax, s->grid.imax); /* allocate arrays */ int imaxLocal = s->comm.imaxLocal; int jmaxLocal = s->comm.jmaxLocal; int kmaxLocal = s->comm.kmaxLocal; size_t size = (imaxLocal + 2) * (jmaxLocal + 2) * (kmaxLocal + 2); s->u = allocate(64, size * sizeof(double)); s->v = allocate(64, size * sizeof(double)); s->w = allocate(64, size * sizeof(double)); s->p = allocate(64, size * sizeof(double)); s->rhs = allocate(64, size * sizeof(double)); s->f = allocate(64, size * sizeof(double)); s->g = allocate(64, size * sizeof(double)); s->h = allocate(64, size * sizeof(double)); for (int i = 0; i < size; i++) { s->u[i] = params->u_init; s->v[i] = params->v_init; s->w[i] = params->w_init; s->p[i] = params->p_init; s->rhs[i] = 0.0; s->f[i] = 0.0; s->g[i] = 0.0; s->h[i] = 0.0; } double dx = s->grid.dx; double dy = s->grid.dy; double dz = s->grid.dz; double invSqrSum = 1.0 / (dx * dx) + 1.0 / (dy * dy) + 1.0 / (dz * dz); s->dtBound = 0.5 * s->re * 1.0 / invSqrSum; #ifdef VERBOSE //printConfig(s); #endif /* VERBOSE */ } void computeRHS(Solver* s) { int imaxLocal = s->comm.imaxLocal; int jmaxLocal = s->comm.jmaxLocal; int kmaxLocal = s->comm.kmaxLocal; 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; commShift(&s->comm, f, g, h); for (int k = 1; k < kmaxLocal + 1; k++) { for (int j = 1; j < jmaxLocal + 1; j++) { for (int i = 1; i < imaxLocal + 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 solveRB(Solver* s) { int imaxLocal = s->comm.imaxLocal; int jmaxLocal = s->comm.jmaxLocal; int kmaxLocal = s->comm.kmaxLocal; 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; while ((res >= epssq) && (it < itermax)) { res = 0.0; ksw = 1; for (pass = 0; pass < 2; pass++) { jsw = ksw; commExchange(&s->comm, p); for (int k = 1; k < kmaxLocal + 1; k++) { isw = jsw; for (int j = 1; j < jmaxLocal + 1; j++) { for (int i = isw; i < imaxLocal + 1; i += 2) { 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; } if (commIsBoundary(&s->comm, FRONT)) { for (int j = 1; j < jmaxLocal + 1; j++) { for (int i = 1; i < imaxLocal + 1; i++) { P(i, j, 0) = P(i, j, 1); } } } if (commIsBoundary(&s->comm, BACK)) { for (int j = 1; j < jmaxLocal + 1; j++) { for (int i = 1; i < imaxLocal + 1; i++) { P(i, j, kmaxLocal + 1) = P(i, j, kmaxLocal); } } } if (commIsBoundary(&s->comm, BOTTOM)) { for (int k = 1; k < kmaxLocal + 1; k++) { for (int i = 1; i < imaxLocal + 1; i++) { P(i, 0, k) = P(i, 1, k); } } } if (commIsBoundary(&s->comm, TOP)) { for (int k = 1; k < kmaxLocal + 1; k++) { for (int i = 1; i < imaxLocal + 1; i++) { P(i, jmaxLocal + 1, k) = P(i, jmaxLocal, k); } } } if (commIsBoundary(&s->comm, LEFT)) { for (int k = 1; k < kmaxLocal + 1; k++) { for (int j = 1; j < jmaxLocal + 1; j++) { P(0, j, k) = P(1, j, k); } } } if (commIsBoundary(&s->comm, RIGHT)) { for (int k = 1; k < kmaxLocal + 1; k++) { for (int j = 1; j < jmaxLocal + 1; j++) { P(imaxLocal + 1, j, k) = P(imaxLocal, j, k); } } } commReduction(&res, SUM); res = res / (double)(imax * jmax * kmax); #ifdef DEBUG if (commIsMaster(&s->comm)) { printf("%d Residuum: %e\n", it, res); } #endif commExchange(&s->comm, p); it++; } #ifdef VERBOSE if (commIsMaster(&s->comm)) { printf("Solver took %d iterations to reach %f\n", it, sqrt(res)); } #endif } void solve(Solver* s) { int imaxLocal = s->comm.imaxLocal; int jmaxLocal = s->comm.jmaxLocal; int kmaxLocal = s->comm.kmaxLocal; 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; while ((res >= epssq) && (it < itermax)) { res = 0.0; commExchange(&s->comm, p); for (int k = 1; k < kmaxLocal + 1; k++) { for (int j = 1; j < jmaxLocal + 1; j++) { for (int i = 1; i < imaxLocal + 1; i++) { 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); } } } if (commIsBoundary(&s->comm, FRONT)) { for (int j = 1; j < jmaxLocal + 1; j++) { for (int i = 1; i < imaxLocal + 1; i++) { P(i, j, 0) = P(i, j, 1); } } } if (commIsBoundary(&s->comm, BACK)) { for (int j = 1; j < jmaxLocal + 1; j++) { for (int i = 1; i < imaxLocal + 1; i++) { P(i, j, kmaxLocal + 1) = P(i, j, kmaxLocal); } } } if (commIsBoundary(&s->comm, BOTTOM)) { for (int k = 1; k < kmaxLocal + 1; k++) { for (int i = 1; i < imaxLocal + 1; i++) { P(i, 0, k) = P(i, 1, k); } } } if (commIsBoundary(&s->comm, TOP)) { for (int k = 1; k < kmaxLocal + 1; k++) { for (int i = 1; i < imaxLocal + 1; i++) { P(i, jmaxLocal + 1, k) = P(i, jmaxLocal, k); } } } if (commIsBoundary(&s->comm, LEFT)) { for (int k = 1; k < kmaxLocal + 1; k++) { for (int j = 1; j < jmaxLocal + 1; j++) { P(0, j, k) = P(1, j, k); } } } if (commIsBoundary(&s->comm, RIGHT)) { for (int k = 1; k < kmaxLocal + 1; k++) { for (int j = 1; j < jmaxLocal + 1; j++) { P(imaxLocal + 1, j, k) = P(imaxLocal, j, k); } } } commReduction(&res, SUM); res = res / (double)(imax * jmax * kmax); #ifdef DEBUG if (commIsMaster(&s->comm)) { printf("%d Residuum: %e\n", it, res); } #endif commExchange(&s->comm, p); it++; } #ifdef VERBOSE if (commIsMaster(&s->comm)) { printf("Solver took %d iterations to reach %f\n", it, sqrt(res)); } #endif } void solveRBA(Solver* s) { int imaxLocal = s->comm.imaxLocal; int jmaxLocal = s->comm.jmaxLocal; int kmaxLocal = s->comm.kmaxLocal; 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 omega = 1.0; double rho = s->rho; int it = 0; double res = 1.0; int pass, ksw, jsw, isw; while ((res >= epssq) && (it < itermax)) { res = 0.0; ksw = 1; for (pass = 0; pass < 2; pass++) { jsw = ksw; commExchange(&s->comm, p); for (int k = 1; k < kmaxLocal + 1; k++) { isw = jsw; for (int j = 1; j < jmaxLocal + 1; j++) { for (int i = isw; i < imaxLocal + 1; i += 2) { 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)); } if (commIsBoundary(&s->comm, FRONT)) { for (int j = 1; j < jmaxLocal + 1; j++) { for (int i = 1; i < imaxLocal + 1; i++) { P(i, j, 0) = P(i, j, 1); } } } if (commIsBoundary(&s->comm, BACK)) { for (int j = 1; j < jmaxLocal + 1; j++) { for (int i = 1; i < imaxLocal + 1; i++) { P(i, j, kmaxLocal + 1) = P(i, j, kmaxLocal); } } } if (commIsBoundary(&s->comm, BOTTOM)) { for (int k = 1; k < kmaxLocal + 1; k++) { for (int i = 1; i < imaxLocal + 1; i++) { P(i, 0, k) = P(i, 1, k); } } } if (commIsBoundary(&s->comm, TOP)) { for (int k = 1; k < kmaxLocal + 1; k++) { for (int i = 1; i < imaxLocal + 1; i++) { P(i, jmaxLocal + 1, k) = P(i, jmaxLocal, k); } } } if (commIsBoundary(&s->comm, LEFT)) { for (int k = 1; k < kmaxLocal + 1; k++) { for (int j = 1; j < jmaxLocal + 1; j++) { P(0, j, k) = P(1, j, k); } } } if (commIsBoundary(&s->comm, RIGHT)) { for (int k = 1; k < kmaxLocal + 1; k++) { for (int j = 1; j < jmaxLocal + 1; j++) { P(imaxLocal + 1, j, k) = P(imaxLocal, j, k); } } } commReduction(&res, SUM); res = res / (double)(imax * jmax * kmax); #ifdef DEBUG if (commIsMaster(&s->comm)) { printf("%d Residuum: %e\n", it, res); } #endif commExchange(&s->comm, p); it++; } #ifdef VERBOSE if (commIsMaster(&s->comm)) { printf("Solver took %d iterations to reach %f\n", it, sqrt(res)); } #endif } static double maxElement(Solver* s, double* m) { int size = (s->comm.imaxLocal + 2) * (s->comm.jmaxLocal + 2) * (s->comm.kmaxLocal + 2); double maxval = DBL_MIN; for (int i = 0; i < size; i++) { maxval = MAX(maxval, fabs(m[i])); } commReduction(&maxval, MAX); return maxval; } void normalizePressure(Solver* s) { int imaxLocal = s->comm.imaxLocal; int jmaxLocal = s->comm.jmaxLocal; int kmaxLocal = s->comm.kmaxLocal; double* p = s->p; double avgP = 0.0; for (int k = 1; k < kmaxLocal + 1; k++) { for (int j = 1; j < jmaxLocal + 1; j++) { for (int i = 1; i < imaxLocal + 1; i++) { avgP += P(i, j, k); } } } commReduction(&avgP, SUM); avgP /= (s->grid.imax * s->grid.jmax * s->grid.kmax); for (int k = 1; k < kmaxLocal + 1; k++) { for (int j = 1; j < jmaxLocal + 1; j++) { for (int i = 1; i < imaxLocal + 1; i++) { P(i, j, k) = P(i, j, k) - 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 imaxLocal = s->comm.imaxLocal; int jmaxLocal = s->comm.jmaxLocal; int kmaxLocal = s->comm.kmaxLocal; double* u = s->u; double* v = s->v; double* w = s->w; if (commIsBoundary(&s->comm, TOP)) { switch (s->bcTop) { case NOSLIP: for (int k = 1; k < kmaxLocal + 1; k++) { for (int i = 1; i < imaxLocal + 1; i++) { U(i, jmaxLocal + 1, k) = -U(i, jmaxLocal, k); V(i, jmaxLocal, k) = 0.0; W(i, jmaxLocal + 1, k) = -W(i, jmaxLocal, k); } } break; case SLIP: for (int k = 1; k < kmaxLocal + 1; k++) { for (int i = 1; i < imaxLocal + 1; i++) { U(i, jmaxLocal + 1, k) = U(i, jmaxLocal, k); V(i, jmaxLocal, k) = 0.0; W(i, jmaxLocal + 1, k) = W(i, jmaxLocal, k); } } break; case OUTFLOW: for (int k = 1; k < kmaxLocal + 1; k++) { for (int i = 1; i < imaxLocal + 1; i++) { U(i, jmaxLocal + 1, k) = U(i, jmaxLocal, k); V(i, jmaxLocal, k) = V(i, jmaxLocal - 1, k); W(i, jmaxLocal + 1, k) = W(i, jmaxLocal, k); } } break; case PERIODIC: break; } } if (commIsBoundary(&s->comm, BOTTOM)) { switch (s->bcBottom) { case NOSLIP: for (int k = 1; k < kmaxLocal + 1; k++) { for (int i = 1; i < imaxLocal + 1; i++) { U(i, 0, k) = -U(i, 1, k); V(i, 0, k) = 0.0; W(i, 0, k) = -W(i, 1, k); } } break; case SLIP: for (int k = 1; k < kmaxLocal + 1; k++) { for (int i = 1; i < imaxLocal + 1; i++) { U(i, 0, k) = U(i, 1, k); V(i, 0, k) = 0.0; W(i, 0, k) = W(i, 1, k); } } break; case OUTFLOW: for (int k = 1; k < kmaxLocal + 1; k++) { for (int i = 1; i < imaxLocal + 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; } } if (commIsBoundary(&s->comm, LEFT)) { switch (s->bcLeft) { case NOSLIP: for (int k = 1; k < kmaxLocal + 1; k++) { for (int j = 1; j < jmaxLocal + 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 < kmaxLocal + 1; k++) { for (int j = 1; j < jmaxLocal + 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 < kmaxLocal + 1; k++) { for (int j = 1; j < jmaxLocal + 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; } } if (commIsBoundary(&s->comm, RIGHT)) { switch (s->bcRight) { case NOSLIP: for (int k = 1; k < kmaxLocal + 1; k++) { for (int j = 1; j < jmaxLocal + 1; j++) { U(imaxLocal, j, k) = 0.0; V(imaxLocal + 1, j, k) = -V(imaxLocal, j, k); W(imaxLocal + 1, j, k) = -W(imaxLocal, j, k); } } break; case SLIP: for (int k = 1; k < kmaxLocal + 1; k++) { for (int j = 1; j < jmaxLocal + 1; j++) { U(imaxLocal, j, k) = 0.0; V(imaxLocal + 1, j, k) = V(imaxLocal, j, k); W(imaxLocal + 1, j, k) = W(imaxLocal, j, k); } } break; case OUTFLOW: for (int k = 1; k < kmaxLocal + 1; k++) { for (int j = 1; j < jmaxLocal + 1; j++) { U(imaxLocal, j, k) = U(imaxLocal - 1, j, k); V(imaxLocal + 1, j, k) = V(imaxLocal, j, k); W(imaxLocal + 1, j, k) = W(imaxLocal, j, k); } } break; case PERIODIC: break; } } if (commIsBoundary(&s->comm, FRONT)) { switch (s->bcFront) { case NOSLIP: for (int j = 1; j < jmaxLocal + 1; j++) { for (int i = 1; i < imaxLocal + 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 < jmaxLocal + 1; j++) { for (int i = 1; i < imaxLocal + 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 < jmaxLocal + 1; j++) { for (int i = 1; i < imaxLocal + 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; } } if (commIsBoundary(&s->comm, BACK)) { switch (s->bcBack) { case NOSLIP: for (int j = 1; j < jmaxLocal + 1; j++) { for (int i = 1; i < imaxLocal + 1; i++) { U(i, j, kmaxLocal + 1) = -U(i, j, kmaxLocal); V(i, j, kmaxLocal + 1) = -V(i, j, kmaxLocal); W(i, j, kmaxLocal) = 0.0; } } break; case SLIP: for (int j = 1; j < jmaxLocal + 1; j++) { for (int i = 1; i < imaxLocal + 1; i++) { U(i, j, kmaxLocal + 1) = U(i, j, kmaxLocal); V(i, j, kmaxLocal + 1) = V(i, j, kmaxLocal); W(i, j, kmaxLocal) = 0.0; } } break; case OUTFLOW: for (int j = 1; j < jmaxLocal + 1; j++) { for (int i = 1; i < imaxLocal + 1; i++) { U(i, j, kmaxLocal + 1) = U(i, j, kmaxLocal); V(i, j, kmaxLocal + 1) = V(i, j, kmaxLocal); W(i, j, kmaxLocal) = W(i, j, kmaxLocal - 1); } } break; case PERIODIC: break; } } } void setSpecialBoundaryCondition(Solver* s) { int imaxLocal = s->comm.imaxLocal; int jmaxLocal = s->comm.jmaxLocal; int kmaxLocal = s->comm.kmaxLocal; double* u = s->u; if (strcmp(s->problem, "dcavity") == 0) { if (commIsBoundary(&s->comm, TOP)) { for (int k = 1; k < kmaxLocal; k++) { for (int i = 1; i < imaxLocal; i++) { U(i, jmaxLocal + 1, k) = 2.0 - U(i, jmaxLocal, k); } } } } else if (strcmp(s->problem, "canal") == 0) { if (commIsBoundary(&s->comm, LEFT)) { for (int k = 1; k < kmaxLocal + 1; k++) { for (int j = 1; j < jmaxLocal + 1; j++) { U(0, j, k) = 2.0; } } } } } void computeFG(Solver* s) { int imaxLocal = s->comm.imaxLocal; int jmaxLocal = s->comm.jmaxLocal; int kmaxLocal = s->comm.kmaxLocal; 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 gx = s->gx; double gy = s->gy; double gz = s->gz; double dt = s->dt; double gamma = s->gamma; 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; commExchange(&s->comm, u); commExchange(&s->comm, v); commExchange(&s->comm, w); for (int k = 1; k < kmaxLocal + 1; k++) { for (int j = 1; j < jmaxLocal + 1; j++) { for (int i = 1; i < imaxLocal + 1; i++) { du2dx = inverseDx * 0.25 * ((U(i, j, k) + U(i + 1, j, k)) * (U(i, j, k) + U(i + 1, j, k)) - (U(i, j, k) + U(i - 1, j, k)) * (U(i, j, k) + U(i - 1, j, k))) + gamma * inverseDx * 0.25 * (fabs(U(i, j, k) + U(i + 1, j, k)) * (U(i, j, k) - U(i + 1, j, k)) + fabs(U(i, j, k) + U(i - 1, j, k)) * (U(i, j, k) - U(i - 1, j, k))); duvdy = inverseDy * 0.25 * ((V(i, j, k) + V(i + 1, j, k)) * (U(i, j, k) + U(i, j + 1, k)) - (V(i, j - 1, k) + V(i + 1, j - 1, k)) * (U(i, j, k) + U(i, j - 1, k))) + gamma * inverseDy * 0.25 * (fabs(V(i, j, k) + V(i + 1, j, k)) * (U(i, j, k) - U(i, j + 1, k)) + fabs(V(i, j - 1, k) + V(i + 1, j - 1, k)) * (U(i, j, k) - U(i, j - 1, k))); duwdz = inverseDz * 0.25 * ((W(i, j, k) + W(i + 1, j, k)) * (U(i, j, k) + U(i, j, k + 1)) - (W(i, j, k - 1) + W(i + 1, j, k - 1)) * (U(i, j, k) + U(i, j, k - 1))) + gamma * inverseDz * 0.25 * (fabs(W(i, j, k) + W(i + 1, j, k)) * (U(i, j, k) - U(i, j, k + 1)) + fabs(W(i, j, k - 1) + W(i + 1, j, k - 1)) * (U(i, j, k) - U(i, j, k - 1))); du2dx2 = inverseDx * inverseDx * (U(i + 1, j, k) - 2.0 * U(i, j, k) + U(i - 1, j, k)); du2dy2 = inverseDy * inverseDy * (U(i, j + 1, k) - 2.0 * U(i, j, k) + U(i, j - 1, k)); du2dz2 = inverseDz * inverseDz * (U(i, j, k + 1) - 2.0 * U(i, j, k) + U(i, j, k - 1)); F(i, j, k) = U(i, j, k) + dt * (inverseRe * (du2dx2 + du2dy2 + du2dz2) - du2dx - duvdy - duwdz + gx); duvdx = inverseDx * 0.25 * ((U(i, j, k) + U(i, j + 1, k)) * (V(i, j, k) + V(i + 1, j, k)) - (U(i - 1, j, k) + U(i - 1, j + 1, k)) * (V(i, j, k) + V(i - 1, j, k))) + gamma * inverseDx * 0.25 * (fabs(U(i, j, k) + U(i, j + 1, k)) * (V(i, j, k) - V(i + 1, j, k)) + fabs(U(i - 1, j, k) + U(i - 1, j + 1, k)) * (V(i, j, k) - V(i - 1, j, k))); dv2dy = inverseDy * 0.25 * ((V(i, j, k) + V(i, j + 1, k)) * (V(i, j, k) + V(i, j + 1, k)) - (V(i, j, k) + V(i, j - 1, k)) * (V(i, j, k) + V(i, j - 1, k))) + gamma * inverseDy * 0.25 * (fabs(V(i, j, k) + V(i, j + 1, k)) * (V(i, j, k) - V(i, j + 1, k)) + fabs(V(i, j, k) + V(i, j - 1, k)) * (V(i, j, k) - V(i, j - 1, k))); dvwdz = inverseDz * 0.25 * ((W(i, j, k) + W(i, j + 1, k)) * (V(i, j, k) + V(i, j, k + 1)) - (W(i, j, k - 1) + W(i, j + 1, k - 1)) * (V(i, j, k) + V(i, j, k + 1))) + gamma * inverseDz * 0.25 * (fabs(W(i, j, k) + W(i, j + 1, k)) * (V(i, j, k) - V(i, j, k + 1)) + fabs(W(i, j, k - 1) + W(i, j + 1, k - 1)) * (V(i, j, k) - V(i, j, k + 1))); dv2dx2 = inverseDx * inverseDx * (V(i + 1, j, k) - 2.0 * V(i, j, k) + V(i - 1, j, k)); dv2dy2 = inverseDy * inverseDy * (V(i, j + 1, k) - 2.0 * V(i, j, k) + V(i, j - 1, k)); dv2dz2 = inverseDz * inverseDz * (V(i, j, k + 1) - 2.0 * V(i, j, k) + V(i, j, k - 1)); G(i, j, k) = V(i, j, k) + dt * (inverseRe * (dv2dx2 + dv2dy2 + dv2dz2) - duvdx - dv2dy - dvwdz + gy); duwdx = inverseDx * 0.25 * ((U(i, j, k) + U(i, j, k + 1)) * (W(i, j, k) + W(i + 1, j, k)) - (U(i - 1, j, k) + U(i - 1, j, k + 1)) * (W(i, j, k) + W(i - 1, j, k))) + gamma * inverseDx * 0.25 * (fabs(U(i, j, k) + U(i, j, k + 1)) * (W(i, j, k) - W(i + 1, j, k)) + fabs(U(i - 1, j, k) + U(i - 1, j, k + 1)) * (W(i, j, k) - W(i - 1, j, k))); dvwdy = inverseDy * 0.25 * ((V(i, j, k) + V(i, j, k + 1)) * (W(i, j, k) + W(i, j + 1, k)) - (V(i, j - 1, k + 1) + V(i, j - 1, k)) * (W(i, j, k) + W(i, j - 1, k))) + gamma * inverseDy * 0.25 * (fabs(V(i, j, k) + V(i, j, k + 1)) * (W(i, j, k) - W(i, j + 1, k)) + fabs(V(i, j - 1, k + 1) + V(i, j - 1, k)) * (W(i, j, k) - W(i, j - 1, k))); dw2dz = inverseDz * 0.25 * ((W(i, j, k) + W(i, j, k + 1)) * (W(i, j, k) + W(i, j, k + 1)) - (W(i, j, k) + W(i, j, k - 1)) * (W(i, j, k) + W(i, j, k - 1))) + gamma * inverseDz * 0.25 * (fabs(W(i, j, k) + W(i, j, k + 1)) * (W(i, j, k) - W(i, j, k + 1)) + fabs(W(i, j, k) + W(i, j, k - 1)) * (W(i, j, k) - W(i, j, k - 1))); dw2dx2 = inverseDx * inverseDx * (W(i + 1, j, k) - 2.0 * W(i, j, k) + W(i - 1, j, k)); dw2dy2 = inverseDy * inverseDy * (W(i, j + 1, k) - 2.0 * W(i, j, k) + W(i, j - 1, k)); dw2dz2 = inverseDz * inverseDz * (W(i, j, k + 1) - 2.0 * W(i, j, k) + W(i, j, k - 1)); H(i, j, k) = W(i, j, k) + dt * (inverseRe * (dw2dx2 + dw2dy2 + dw2dz2) - duwdx - dvwdy - dw2dz + gz); } } } /* ----------------------------- boundary of F --------------------------- */ if (commIsBoundary(&s->comm, LEFT)) { for (int k = 1; k < kmaxLocal + 1; k++) { for (int j = 1; j < jmaxLocal + 1; j++) { F(0, j, k) = U(0, j, k); } } } if (commIsBoundary(&s->comm, RIGHT)) { for (int k = 1; k < kmaxLocal + 1; k++) { for (int j = 1; j < jmaxLocal + 1; j++) { F(imaxLocal, j, k) = U(imaxLocal, j, k); } } } /* ----------------------------- boundary of G --------------------------- */ if (commIsBoundary(&s->comm, BOTTOM)) { for (int k = 1; k < kmaxLocal + 1; k++) { for (int i = 1; i < imaxLocal + 1; i++) { G(i, 0, k) = V(i, 0, k); } } } if (commIsBoundary(&s->comm, TOP)) { for (int k = 1; k < kmaxLocal + 1; k++) { for (int i = 1; i < imaxLocal + 1; i++) { G(i, jmaxLocal, k) = V(i, jmaxLocal, k); } } } /* ----------------------------- boundary of H --------------------------- */ if (commIsBoundary(&s->comm, FRONT)) { for (int j = 1; j < jmaxLocal + 1; j++) { for (int i = 1; i < imaxLocal + 1; i++) { H(i, j, 0) = W(i, j, 0); } } } if (commIsBoundary(&s->comm, BACK)) { for (int j = 1; j < jmaxLocal + 1; j++) { for (int i = 1; i < imaxLocal + 1; i++) { H(i, j, kmaxLocal) = W(i, j, kmaxLocal); } } } } void adaptUV(Solver* s) { int imaxLocal = s->comm.imaxLocal; int jmaxLocal = s->comm.jmaxLocal; int kmaxLocal = s->comm.kmaxLocal; 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 < kmaxLocal + 1; k++) { for (int j = 1; j < jmaxLocal + 1; j++) { for (int i = 1; i < imaxLocal + 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; } } } }