#include "macrodef.h" #include "tool.h" /* * C 版 kodis — Kreiss-Oliger numerical dissipation (Cartesian patches). * * The KO operator is (D₊D₋)^r applied to f_rhs with alternating sign (-1)^(r-1). * * FD order → r → cof=2^(2r) mapping: * ghost_width=2 (2nd) → r=2, cof=16, sign=- * ghost_width=3 (4th) → r=3, cof=64, sign=+ * ghost_width=4 (6th) → r=4, cof=256, sign=- * ghost_width=5 (8th) → r=5, cof=1024,sign=+ */ void kodis(const int ex[3], const double *X, const double *Y, const double *Z, const double *f, double *f_rhs, const double SoA[3], int Symmetry, double eps) { const double ZEO = 0.0; const int ex1 = ex[0], ex2 = ex[1], ex3 = ex[2]; const double dX = X[1] - X[0]; const double dY = Y[1] - Y[0]; const double dZ = Z[1] - Z[0]; const int imaxF = ex1, jmaxF = ex2, kmaxF = ex3; #if (ghost_width == 2) /* ---- r=2, cof=16, sign=-, 5pt stencil ----------------------------- */ { const int ord = 2; const int r = 2; const double cof = 16.0; const double F4 = 4.0, F6 = 6.0; const int NO_SYMM = 0, EQ_SYMM = 1; int iminF = 1, jminF = 1, kminF = 1; if (Symmetry > NO_SYMM && fabs(Z[0]) < dZ) kminF = -1; if (Symmetry > EQ_SYMM && fabs(X[0]) < dX) iminF = -1; if (Symmetry > EQ_SYMM && fabs(Y[0]) < dY) jminF = -1; const size_t nx = (size_t)ex1 + ord; const size_t ny = (size_t)ex2 + ord; const size_t nz = (size_t)ex3 + ord; const size_t fh_size = nx * ny * nz; double *fh = (double*)malloc(fh_size * sizeof(double)); if (!fh) return; symmetry_bd(ord, ex, f, fh, SoA); /* i±2 must be valid: i-2 >= iminF && i+2 <= imaxF C 0-based: i0 >= iminF+1, i0 <= ex1-3 */ const int i0_lo = (iminF + 1 > 0) ? (iminF + 1) : 0; const int j0_lo = (jminF + 1 > 0) ? (jminF + 1) : 0; const int k0_lo = (kminF + 1 > 0) ? (kminF + 1) : 0; const int i0_hi = imaxF - 3; const int j0_hi = jmaxF - 3; const int k0_hi = kmaxF - 3; if (!(i0_lo > i0_hi || j0_lo > j0_hi || k0_lo > k0_hi)) { for (int k0 = k0_lo; k0 <= k0_hi; ++k0) { const int kF = k0 + 1; for (int j0 = j0_lo; j0 <= j0_hi; ++j0) { const int jF = j0 + 1; for (int i0 = i0_lo; i0 <= i0_hi; ++i0) { const int iF = i0 + 1; const size_t p = idx_ex(i0, j0, k0, ex); const double Dx = ( (fh[idx_fh_F_ord2(iF - 2, jF, kF, ex)] + fh[idx_fh_F_ord2(iF + 2, jF, kF, ex)]) - F4 * (fh[idx_fh_F_ord2(iF - 1, jF, kF, ex)] + fh[idx_fh_F_ord2(iF + 1, jF, kF, ex)]) + F6 * fh[idx_fh_F_ord2(iF, jF, kF, ex)] ) / dX; const double Dy = ( (fh[idx_fh_F_ord2(iF, jF - 2, kF, ex)] + fh[idx_fh_F_ord2(iF, jF + 2, kF, ex)]) - F4 * (fh[idx_fh_F_ord2(iF, jF - 1, kF, ex)] + fh[idx_fh_F_ord2(iF, jF + 1, kF, ex)]) + F6 * fh[idx_fh_F_ord2(iF, jF, kF, ex)] ) / dY; const double Dz = ( (fh[idx_fh_F_ord2(iF, jF, kF - 2, ex)] + fh[idx_fh_F_ord2(iF, jF, kF + 2, ex)]) - F4 * (fh[idx_fh_F_ord2(iF, jF, kF - 1, ex)] + fh[idx_fh_F_ord2(iF, jF, kF + 1, ex)]) + F6 * fh[idx_fh_F_ord2(iF, jF, kF, ex)] ) / dZ; f_rhs[p] -= (eps / cof) * (Dx + Dy + Dz); /* sign=- */ } } } } free(fh); return; } #elif (ghost_width == 3) /* ---- r=3, cof=64, sign=+, 7pt stencil (current default) ---------- */ { const int ord = 3; const int r = 3; const double cof = 64.0; const double SIX = 6.0, FIT = 15.0, TWT = 20.0; const int NO_SYMM = 0, OCTANT = 2; int iminF = 1, jminF = 1, kminF = 1; if (Symmetry > NO_SYMM && fabs(Z[0]) < dZ) kminF = -2; if (Symmetry == OCTANT && fabs(X[0]) < dX) iminF = -2; if (Symmetry == OCTANT && fabs(Y[0]) < dY) jminF = -2; const size_t nx = (size_t)ex1 + ord; const size_t ny = (size_t)ex2 + ord; const size_t nz = (size_t)ex3 + ord; const size_t fh_size = nx * ny * nz; double *fh = (double*)malloc(fh_size * sizeof(double)); if (!fh) return; symmetry_bd(ord, ex, f, fh, SoA); const int i0_lo = (iminF + 2 > 0) ? iminF + 2 : 0; const int j0_lo = (jminF + 2 > 0) ? jminF + 2 : 0; const int k0_lo = (kminF + 2 > 0) ? kminF + 2 : 0; const int i0_hi = imaxF - 4; const int j0_hi = jmaxF - 4; const int k0_hi = kmaxF - 4; if (!(i0_lo > i0_hi || j0_lo > j0_hi || k0_lo > k0_hi)) { for (int k0 = k0_lo; k0 <= k0_hi; ++k0) { const int kF = k0 + 1; for (int j0 = j0_lo; j0 <= j0_hi; ++j0) { const int jF = j0 + 1; for (int i0 = i0_lo; i0 <= i0_hi; ++i0) { const int iF = i0 + 1; const size_t p = idx_ex(i0, j0, k0, ex); const double Dx = ( (fh[idx_fh_F(iF - 3, jF, kF, ex)] + fh[idx_fh_F(iF + 3, jF, kF, ex)]) - SIX * (fh[idx_fh_F(iF - 2, jF, kF, ex)] + fh[idx_fh_F(iF + 2, jF, kF, ex)]) + FIT * (fh[idx_fh_F(iF - 1, jF, kF, ex)] + fh[idx_fh_F(iF + 1, jF, kF, ex)]) - TWT * fh[idx_fh_F(iF, jF, kF, ex)] ) / dX; const double Dy = ( (fh[idx_fh_F(iF, jF - 3, kF, ex)] + fh[idx_fh_F(iF, jF + 3, kF, ex)]) - SIX * (fh[idx_fh_F(iF, jF - 2, kF, ex)] + fh[idx_fh_F(iF, jF + 2, kF, ex)]) + FIT * (fh[idx_fh_F(iF, jF - 1, kF, ex)] + fh[idx_fh_F(iF, jF + 1, kF, ex)]) - TWT * fh[idx_fh_F(iF, jF, kF, ex)] ) / dY; const double Dz = ( (fh[idx_fh_F(iF, jF, kF - 3, ex)] + fh[idx_fh_F(iF, jF, kF + 3, ex)]) - SIX * (fh[idx_fh_F(iF, jF, kF - 2, ex)] + fh[idx_fh_F(iF, jF, kF + 2, ex)]) + FIT * (fh[idx_fh_F(iF, jF, kF - 1, ex)] + fh[idx_fh_F(iF, jF, kF + 1, ex)]) - TWT * fh[idx_fh_F(iF, jF, kF, ex)] ) / dZ; f_rhs[p] += (eps / cof) * (Dx + Dy + Dz); /* sign=+ */ } } } } free(fh); return; } #elif (ghost_width == 4) /* ---- r=4, cof=256, sign=-, 9pt stencil ---------------------------- */ { const int ord = 4; const int r = 4; const double cof = 256.0; const double F8 = 8.0, F28 = 28.0, F56 = 56.0, F70 = 70.0; const int NO_SYMM = 0, EQ_SYMM = 1; int iminF = 1, jminF = 1, kminF = 1; if (Symmetry > NO_SYMM && fabs(Z[0]) < dZ) kminF = -3; if (Symmetry > EQ_SYMM && fabs(X[0]) < dX) iminF = -3; if (Symmetry > EQ_SYMM && fabs(Y[0]) < dY) jminF = -3; const size_t nx = (size_t)ex1 + ord; const size_t ny = (size_t)ex2 + ord; const size_t nz = (size_t)ex3 + ord; const size_t fh_size = nx * ny * nz; double *fh = (double*)malloc(fh_size * sizeof(double)); if (!fh) return; symmetry_bd(ord, ex, f, fh, SoA); /* i±4 valid: i-4>=iminF → i0>=iminF+3, i+4<=imaxF → i0<=ex1-5 */ const int i0_lo = (iminF + 3 > 0) ? iminF + 3 : 0; const int j0_lo = (jminF + 3 > 0) ? jminF + 3 : 0; const int k0_lo = (kminF + 3 > 0) ? kminF + 3 : 0; const int i0_hi = imaxF - 5; const int j0_hi = jmaxF - 5; const int k0_hi = kmaxF - 5; if (!(i0_lo > i0_hi || j0_lo > j0_hi || k0_lo > k0_hi)) { for (int k0 = k0_lo; k0 <= k0_hi; ++k0) { const int kF = k0 + 1; for (int j0 = j0_lo; j0 <= j0_hi; ++j0) { const int jF = j0 + 1; for (int i0 = i0_lo; i0 <= i0_hi; ++i0) { const int iF = i0 + 1; const size_t p = idx_ex(i0, j0, k0, ex); /* Stencil: [1,-8,28,-56,70,-56,28,-8,1] */ const double Dx = ( (fh[idx_fh_F_ord4(iF - 4, jF, kF, ex)] + fh[idx_fh_F_ord4(iF + 4, jF, kF, ex)]) - F8 * (fh[idx_fh_F_ord4(iF - 3, jF, kF, ex)] + fh[idx_fh_F_ord4(iF + 3, jF, kF, ex)]) + F28* (fh[idx_fh_F_ord4(iF - 2, jF, kF, ex)] + fh[idx_fh_F_ord4(iF + 2, jF, kF, ex)]) - F56* (fh[idx_fh_F_ord4(iF - 1, jF, kF, ex)] + fh[idx_fh_F_ord4(iF + 1, jF, kF, ex)]) + F70* fh[idx_fh_F_ord4(iF, jF, kF, ex)] ) / dX; const double Dy = ( (fh[idx_fh_F_ord4(iF, jF - 4, kF, ex)] + fh[idx_fh_F_ord4(iF, jF + 4, kF, ex)]) - F8 * (fh[idx_fh_F_ord4(iF, jF - 3, kF, ex)] + fh[idx_fh_F_ord4(iF, jF + 3, kF, ex)]) + F28* (fh[idx_fh_F_ord4(iF, jF - 2, kF, ex)] + fh[idx_fh_F_ord4(iF, jF + 2, kF, ex)]) - F56* (fh[idx_fh_F_ord4(iF, jF - 1, kF, ex)] + fh[idx_fh_F_ord4(iF, jF + 1, kF, ex)]) + F70* fh[idx_fh_F_ord4(iF, jF, kF, ex)] ) / dY; const double Dz = ( (fh[idx_fh_F_ord4(iF, jF, kF - 4, ex)] + fh[idx_fh_F_ord4(iF, jF, kF + 4, ex)]) - F8 * (fh[idx_fh_F_ord4(iF, jF, kF - 3, ex)] + fh[idx_fh_F_ord4(iF, jF, kF + 3, ex)]) + F28* (fh[idx_fh_F_ord4(iF, jF, kF - 2, ex)] + fh[idx_fh_F_ord4(iF, jF, kF + 2, ex)]) - F56* (fh[idx_fh_F_ord4(iF, jF, kF - 1, ex)] + fh[idx_fh_F_ord4(iF, jF, kF + 1, ex)]) + F70* fh[idx_fh_F_ord4(iF, jF, kF, ex)] ) / dZ; f_rhs[p] -= (eps / cof) * (Dx + Dy + Dz); /* sign=- */ } } } } free(fh); return; } #elif (ghost_width == 5) /* ---- r=5, cof=1024, sign=+, 11pt stencil ------------------------- */ { const int ord = 5; const int r = 5; const double cof = 1024.0; const double F10 = 10.0, F45 = 45.0, F120 = 120.0; const double F210 = 210.0, F252 = 252.0; const int NO_SYMM = 0, EQ_SYMM = 1; int iminF = 1, jminF = 1, kminF = 1; if (Symmetry > NO_SYMM && fabs(Z[0]) < dZ) kminF = -4; if (Symmetry > EQ_SYMM && fabs(X[0]) < dX) iminF = -4; if (Symmetry > EQ_SYMM && fabs(Y[0]) < dY) jminF = -4; const size_t nx = (size_t)ex1 + ord; const size_t ny = (size_t)ex2 + ord; const size_t nz = (size_t)ex3 + ord; const size_t fh_size = nx * ny * nz; double *fh = (double*)malloc(fh_size * sizeof(double)); if (!fh) return; symmetry_bd(ord, ex, f, fh, SoA); /* i±5 valid: i0>=iminF+4, i0<=ex1-6 */ const int i0_lo = (iminF + 4 > 0) ? iminF + 4 : 0; const int j0_lo = (jminF + 4 > 0) ? jminF + 4 : 0; const int k0_lo = (kminF + 4 > 0) ? kminF + 4 : 0; const int i0_hi = imaxF - 6; const int j0_hi = jmaxF - 6; const int k0_hi = kmaxF - 6; if (!(i0_lo > i0_hi || j0_lo > j0_hi || k0_lo > k0_hi)) { for (int k0 = k0_lo; k0 <= k0_hi; ++k0) { const int kF = k0 + 1; for (int j0 = j0_lo; j0 <= j0_hi; ++j0) { const int jF = j0 + 1; for (int i0 = i0_lo; i0 <= i0_hi; ++i0) { const int iF = i0 + 1; const size_t p = idx_ex(i0, j0, k0, ex); /* Stencil: [1,-10,45,-120,210,-252,210,-120,45,-10,1] */ const double Dx = ( (fh[idx_fh_F_ord5(iF - 5, jF, kF, ex)] + fh[idx_fh_F_ord5(iF + 5, jF, kF, ex)]) - F10 * (fh[idx_fh_F_ord5(iF - 4, jF, kF, ex)] + fh[idx_fh_F_ord5(iF + 4, jF, kF, ex)]) + F45 * (fh[idx_fh_F_ord5(iF - 3, jF, kF, ex)] + fh[idx_fh_F_ord5(iF + 3, jF, kF, ex)]) - F120* (fh[idx_fh_F_ord5(iF - 2, jF, kF, ex)] + fh[idx_fh_F_ord5(iF + 2, jF, kF, ex)]) + F210* (fh[idx_fh_F_ord5(iF - 1, jF, kF, ex)] + fh[idx_fh_F_ord5(iF + 1, jF, kF, ex)]) - F252* fh[idx_fh_F_ord5(iF, jF, kF, ex)] ) / dX; const double Dy = ( (fh[idx_fh_F_ord5(iF, jF - 5, kF, ex)] + fh[idx_fh_F_ord5(iF, jF + 5, kF, ex)]) - F10 * (fh[idx_fh_F_ord5(iF, jF - 4, kF, ex)] + fh[idx_fh_F_ord5(iF, jF + 4, kF, ex)]) + F45 * (fh[idx_fh_F_ord5(iF, jF - 3, kF, ex)] + fh[idx_fh_F_ord5(iF, jF + 3, kF, ex)]) - F120* (fh[idx_fh_F_ord5(iF, jF - 2, kF, ex)] + fh[idx_fh_F_ord5(iF, jF + 2, kF, ex)]) + F210* (fh[idx_fh_F_ord5(iF, jF - 1, kF, ex)] + fh[idx_fh_F_ord5(iF, jF + 1, kF, ex)]) - F252* fh[idx_fh_F_ord5(iF, jF, kF, ex)] ) / dY; const double Dz = ( (fh[idx_fh_F_ord5(iF, jF, kF - 5, ex)] + fh[idx_fh_F_ord5(iF, jF, kF + 5, ex)]) - F10 * (fh[idx_fh_F_ord5(iF, jF, kF - 4, ex)] + fh[idx_fh_F_ord5(iF, jF, kF + 4, ex)]) + F45 * (fh[idx_fh_F_ord5(iF, jF, kF - 3, ex)] + fh[idx_fh_F_ord5(iF, jF, kF + 3, ex)]) - F120* (fh[idx_fh_F_ord5(iF, jF, kF - 2, ex)] + fh[idx_fh_F_ord5(iF, jF, kF + 2, ex)]) + F210* (fh[idx_fh_F_ord5(iF, jF, kF - 1, ex)] + fh[idx_fh_F_ord5(iF, jF, kF + 1, ex)]) - F252* fh[idx_fh_F_ord5(iF, jF, kF, ex)] ) / dZ; f_rhs[p] += (eps / cof) * (Dx + Dy + Dz); /* sign=+ */ } } } } free(fh); return; } #else #error "kodiss_c.C: unsupported ghost_width (must be 2, 3, 4, or 5)" #endif }