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Fix eighth-order C derivative and lopsided stencils

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CGH0S7
2026-05-14 20:32:53 +08:00
parent 3b8774c1b1
commit 2bbde059db
5 changed files with 140 additions and 222 deletions
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92
AMSS_NCKU_source/lopsided_kodis_c.C
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@@ -3,7 +3,9 @@
/*
* C 版 lopsided_kodis — combined upwind advection + KO dissipation.
* Uses one shared symmetry_bd buffer (ord = ghost_width for both components).
* Uses one shared symmetry_bd buffer (ord = ghost_width for both components)
* where a stable merged stencil is available. The 8th-order path delegates to
* the separate lopsided + kodis kernels, matching the original Fortran flow.
*
* FD order selection via ghost_width:
* 2 → 2nd-order advection + r=2 KO (cof=16, sign=-)
@@ -292,92 +294,8 @@ void lopsided_kodis(const int ex[3],
}
#elif (ghost_width == 5)
{
const int ord = 5;
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;
double *fh = (double*)malloc(nx*ny*nz*sizeof(double));
if (!fh) return;
symmetry_bd(ord, ex, f, fh, SoA);
const double d840dx=ONE/F840/dX, d840dy=ONE/F840/dY, d840dz=ONE/F840/dZ;
const double d60dx=ONE/F60/dX, d60dy=ONE/F60/dY, d60dz=ONE/F60/dZ;
const double d12dx=ONE/F12/dX, d12dy=ONE/F12/dY, d12dz=ONE/F12/dZ;
const double d2dx=ONE/TWO/dX, d2dy=ONE/TWO/dY, d2dz=ONE/TWO/dZ;
/* ---- advection (8th-order lopsided) ---- */
for (int k0=0;k0<=ex3-2;++k0) { const int kF=k0+1;
for (int j0=0;j0<=ex2-2;++j0) { const int jF=j0+1;
for (int i0=0;i0<=ex1-2;++i0) { const int iF=i0+1;
const size_t p=idx_ex(i0,j0,k0,ex);
const double sfx=Sfx[p];
if (sfx>ZEO) {
if (i0<=ex1-6&&(i0-2)>=iminF) f_rhs[p]+=sfx*d840dx*(-F5*fh[idx_fh_F_ord5(iF-3,jF,kF,ex)]+F60*fh[idx_fh_F_ord5(iF-2,jF,kF,ex)]-F420*fh[idx_fh_F_ord5(iF-1,jF,kF,ex)]-F378*fh[idx_fh_F_ord5(iF,jF,kF,ex)]+F1050*fh[idx_fh_F_ord5(iF+1,jF,kF,ex)]-F420*fh[idx_fh_F_ord5(iF+2,jF,kF,ex)]+F140*fh[idx_fh_F_ord5(iF+3,jF,kF,ex)]-F30*fh[idx_fh_F_ord5(iF+4,jF,kF,ex)]+F3*fh[idx_fh_F_ord5(iF+5,jF,kF,ex)]);
else if (i0<=ex1-5&&(i0-3)>=iminF) f_rhs[p]+=sfx*d840dx*(+F3*fh[idx_fh_F_ord5(iF-4,jF,kF,ex)]-F32*fh[idx_fh_F_ord5(iF-3,jF,kF,ex)]+F168*fh[idx_fh_F_ord5(iF-2,jF,kF,ex)]-F672*fh[idx_fh_F_ord5(iF-1,jF,kF,ex)]+F672*fh[idx_fh_F_ord5(iF+1,jF,kF,ex)]-F168*fh[idx_fh_F_ord5(iF+2,jF,kF,ex)]+F32*fh[idx_fh_F_ord5(iF+3,jF,kF,ex)]-F3*fh[idx_fh_F_ord5(iF+4,jF,kF,ex)]);
else if (i0<=ex1-4&&(i0-2)>=iminF) f_rhs[p]+=sfx*d60dx*(-fh[idx_fh_F_ord5(iF-3,jF,kF,ex)]+F9*fh[idx_fh_F_ord5(iF-2,jF,kF,ex)]-F45*fh[idx_fh_F_ord5(iF-1,jF,kF,ex)]+F45*fh[idx_fh_F_ord5(iF+1,jF,kF,ex)]-F9*fh[idx_fh_F_ord5(iF+2,jF,kF,ex)]+fh[idx_fh_F_ord5(iF+3,jF,kF,ex)]);
else if (i0<=ex1-3&&(i0-1)>=iminF) f_rhs[p]+=sfx*d12dx*(fh[idx_fh_F_ord5(iF-2,jF,kF,ex)]-EIT*fh[idx_fh_F_ord5(iF-1,jF,kF,ex)]+EIT*fh[idx_fh_F_ord5(iF+1,jF,kF,ex)]-fh[idx_fh_F_ord5(iF+2,jF,kF,ex)]);
else if (i0<=ex1-2&&i0>=iminF) f_rhs[p]+=sfx*d2dx*(-fh[idx_fh_F_ord5(iF-1,jF,kF,ex)]+fh[idx_fh_F_ord5(iF+1,jF,kF,ex)]);
} else if (sfx<ZEO) {
if ((i0-5)>=iminF&&i0<=ex1-2) f_rhs[p]-=sfx*d840dx*(-F5*fh[idx_fh_F_ord5(iF+3,jF,kF,ex)]+F60*fh[idx_fh_F_ord5(iF+2,jF,kF,ex)]-F420*fh[idx_fh_F_ord5(iF+1,jF,kF,ex)]-F378*fh[idx_fh_F_ord5(iF,jF,kF,ex)]+F1050*fh[idx_fh_F_ord5(iF-1,jF,kF,ex)]-F420*fh[idx_fh_F_ord5(iF-2,jF,kF,ex)]+F140*fh[idx_fh_F_ord5(iF-3,jF,kF,ex)]-F30*fh[idx_fh_F_ord5(iF-4,jF,kF,ex)]+F3*fh[idx_fh_F_ord5(iF-5,jF,kF,ex)]);
else if ((i0-4)>=iminF&&i0<=ex1-2) f_rhs[p]-=sfx*d840dx*(+F3*fh[idx_fh_F_ord5(iF-4,jF,kF,ex)]-F32*fh[idx_fh_F_ord5(iF-3,jF,kF,ex)]+F168*fh[idx_fh_F_ord5(iF-2,jF,kF,ex)]-F672*fh[idx_fh_F_ord5(iF-1,jF,kF,ex)]+F672*fh[idx_fh_F_ord5(iF+1,jF,kF,ex)]-F168*fh[idx_fh_F_ord5(iF+2,jF,kF,ex)]+F32*fh[idx_fh_F_ord5(iF+3,jF,kF,ex)]-F3*fh[idx_fh_F_ord5(iF+4,jF,kF,ex)]);
else if ((i0-3)>=iminF&&i0<=ex1-2) f_rhs[p]-=sfx*d60dx*(-fh[idx_fh_F_ord5(iF-3,jF,kF,ex)]+F9*fh[idx_fh_F_ord5(iF-2,jF,kF,ex)]-F45*fh[idx_fh_F_ord5(iF-1,jF,kF,ex)]+F45*fh[idx_fh_F_ord5(iF+1,jF,kF,ex)]-F9*fh[idx_fh_F_ord5(iF+2,jF,kF,ex)]+fh[idx_fh_F_ord5(iF+3,jF,kF,ex)]);
else if ((i0-2)>=iminF&&i0<=ex1-2) f_rhs[p]-=sfx*d12dx*(fh[idx_fh_F_ord5(iF-2,jF,kF,ex)]-EIT*fh[idx_fh_F_ord5(iF-1,jF,kF,ex)]+EIT*fh[idx_fh_F_ord5(iF+1,jF,kF,ex)]-fh[idx_fh_F_ord5(iF+2,jF,kF,ex)]);
else if ((i0-1)>=iminF&&i0<=ex1-2) f_rhs[p]-=sfx*d2dx*(-fh[idx_fh_F_ord5(iF-1,jF,kF,ex)]+fh[idx_fh_F_ord5(iF+1,jF,kF,ex)]);
}
const double sfy=Sfy[p];
if (sfy>ZEO) {
if (j0<=ex2-6&&(j0-2)>=jminF) f_rhs[p]+=sfy*d840dy*(-F5*fh[idx_fh_F_ord5(iF,jF-3,kF,ex)]+F60*fh[idx_fh_F_ord5(iF,jF-2,kF,ex)]-F420*fh[idx_fh_F_ord5(iF,jF-1,kF,ex)]-F378*fh[idx_fh_F_ord5(iF,jF,kF,ex)]+F1050*fh[idx_fh_F_ord5(iF,jF+1,kF,ex)]-F420*fh[idx_fh_F_ord5(iF,jF+2,kF,ex)]+F140*fh[idx_fh_F_ord5(iF,jF+3,kF,ex)]-F30*fh[idx_fh_F_ord5(iF,jF+4,kF,ex)]+F3*fh[idx_fh_F_ord5(iF,jF+5,kF,ex)]);
else if (j0<=ex2-5&&(j0-3)>=jminF) f_rhs[p]+=sfy*d840dy*(+F3*fh[idx_fh_F_ord5(iF,jF-4,kF,ex)]-F32*fh[idx_fh_F_ord5(iF,jF-3,kF,ex)]+F168*fh[idx_fh_F_ord5(iF,jF-2,kF,ex)]-F672*fh[idx_fh_F_ord5(iF,jF-1,kF,ex)]+F672*fh[idx_fh_F_ord5(iF,jF+1,kF,ex)]-F168*fh[idx_fh_F_ord5(iF,jF+2,kF,ex)]+F32*fh[idx_fh_F_ord5(iF,jF+3,kF,ex)]-F3*fh[idx_fh_F_ord5(iF,jF+4,kF,ex)]);
else if (j0<=ex2-4&&(j0-2)>=jminF) f_rhs[p]+=sfy*d60dy*(-fh[idx_fh_F_ord5(iF,jF-3,kF,ex)]+F9*fh[idx_fh_F_ord5(iF,jF-2,kF,ex)]-F45*fh[idx_fh_F_ord5(iF,jF-1,kF,ex)]+F45*fh[idx_fh_F_ord5(iF,jF+1,kF,ex)]-F9*fh[idx_fh_F_ord5(iF,jF+2,kF,ex)]+fh[idx_fh_F_ord5(iF,jF+3,kF,ex)]);
else if (j0<=ex2-3&&(j0-1)>=jminF) f_rhs[p]+=sfy*d12dy*(fh[idx_fh_F_ord5(iF,jF-2,kF,ex)]-EIT*fh[idx_fh_F_ord5(iF,jF-1,kF,ex)]+EIT*fh[idx_fh_F_ord5(iF,jF+1,kF,ex)]-fh[idx_fh_F_ord5(iF,jF+2,kF,ex)]);
else if (j0<=ex2-2&&j0>=jminF) f_rhs[p]+=sfy*d2dy*(-fh[idx_fh_F_ord5(iF,jF-1,kF,ex)]+fh[idx_fh_F_ord5(iF,jF+1,kF,ex)]);
} else if (sfy<ZEO) {
if ((j0-5)>=jminF&&j0<=ex2-2) f_rhs[p]-=sfy*d840dy*(-F5*fh[idx_fh_F_ord5(iF,jF+3,kF,ex)]+F60*fh[idx_fh_F_ord5(iF,jF+2,kF,ex)]-F420*fh[idx_fh_F_ord5(iF,jF+1,kF,ex)]-F378*fh[idx_fh_F_ord5(iF,jF,kF,ex)]+F1050*fh[idx_fh_F_ord5(iF,jF-1,kF,ex)]-F420*fh[idx_fh_F_ord5(iF,jF-2,kF,ex)]+F140*fh[idx_fh_F_ord5(iF,jF-3,kF,ex)]-F30*fh[idx_fh_F_ord5(iF,jF-4,kF,ex)]+F3*fh[idx_fh_F_ord5(iF,jF-5,kF,ex)]);
else if ((j0-4)>=jminF&&j0<=ex2-2) f_rhs[p]-=sfy*d840dy*(+F3*fh[idx_fh_F_ord5(iF,jF-4,kF,ex)]-F32*fh[idx_fh_F_ord5(iF,jF-3,kF,ex)]+F168*fh[idx_fh_F_ord5(iF,jF-2,kF,ex)]-F672*fh[idx_fh_F_ord5(iF,jF-1,kF,ex)]+F672*fh[idx_fh_F_ord5(iF,jF+1,kF,ex)]-F168*fh[idx_fh_F_ord5(iF,jF+2,kF,ex)]+F32*fh[idx_fh_F_ord5(iF,jF+3,kF,ex)]-F3*fh[idx_fh_F_ord5(iF,jF+4,kF,ex)]);
else if ((j0-3)>=jminF&&j0<=ex2-2) f_rhs[p]-=sfy*d60dy*(-fh[idx_fh_F_ord5(iF,jF-3,kF,ex)]+F9*fh[idx_fh_F_ord5(iF,jF-2,kF,ex)]-F45*fh[idx_fh_F_ord5(iF,jF-1,kF,ex)]+F45*fh[idx_fh_F_ord5(iF,jF+1,kF,ex)]-F9*fh[idx_fh_F_ord5(iF,jF+2,kF,ex)]+fh[idx_fh_F_ord5(iF,jF+3,kF,ex)]);
else if ((j0-2)>=jminF&&j0<=ex2-2) f_rhs[p]-=sfy*d12dy*(fh[idx_fh_F_ord5(iF,jF-2,kF,ex)]-EIT*fh[idx_fh_F_ord5(iF,jF-1,kF,ex)]+EIT*fh[idx_fh_F_ord5(iF,jF+1,kF,ex)]-fh[idx_fh_F_ord5(iF,jF+2,kF,ex)]);
else if ((j0-1)>=jminF&&j0<=ex2-2) f_rhs[p]-=sfy*d2dy*(-fh[idx_fh_F_ord5(iF,jF-1,kF,ex)]+fh[idx_fh_F_ord5(iF,jF+1,kF,ex)]);
}
const double sfz=Sfz[p];
if (sfz>ZEO) {
if (k0<=ex3-6&&(k0-2)>=kminF) f_rhs[p]+=sfz*d840dz*(-F5*fh[idx_fh_F_ord5(iF,jF,kF-3,ex)]+F60*fh[idx_fh_F_ord5(iF,jF,kF-2,ex)]-F420*fh[idx_fh_F_ord5(iF,jF,kF-1,ex)]-F378*fh[idx_fh_F_ord5(iF,jF,kF,ex)]+F1050*fh[idx_fh_F_ord5(iF,jF,kF+1,ex)]-F420*fh[idx_fh_F_ord5(iF,jF,kF+2,ex)]+F140*fh[idx_fh_F_ord5(iF,jF,kF+3,ex)]-F30*fh[idx_fh_F_ord5(iF,jF,kF+4,ex)]+F3*fh[idx_fh_F_ord5(iF,jF,kF+5,ex)]);
else if (k0<=ex3-5&&(k0-3)>=kminF) f_rhs[p]+=sfz*d840dz*(+F3*fh[idx_fh_F_ord5(iF,jF,kF-4,ex)]-F32*fh[idx_fh_F_ord5(iF,jF,kF-3,ex)]+F168*fh[idx_fh_F_ord5(iF,jF,kF-2,ex)]-F672*fh[idx_fh_F_ord5(iF,jF,kF-1,ex)]+F672*fh[idx_fh_F_ord5(iF,jF,kF+1,ex)]-F168*fh[idx_fh_F_ord5(iF,jF,kF+2,ex)]+F32*fh[idx_fh_F_ord5(iF,jF,kF+3,ex)]-F3*fh[idx_fh_F_ord5(iF,jF,kF+4,ex)]);
else if (k0<=ex3-4&&(k0-2)>=kminF) f_rhs[p]+=sfz*d60dz*(-fh[idx_fh_F_ord5(iF,jF,kF-3,ex)]+F9*fh[idx_fh_F_ord5(iF,jF,kF-2,ex)]-F45*fh[idx_fh_F_ord5(iF,jF,kF-1,ex)]+F45*fh[idx_fh_F_ord5(iF,jF,kF+1,ex)]-F9*fh[idx_fh_F_ord5(iF,jF,kF+2,ex)]+fh[idx_fh_F_ord5(iF,jF,kF+3,ex)]);
else if (k0<=ex3-3&&(k0-1)>=kminF) f_rhs[p]+=sfz*d12dz*(fh[idx_fh_F_ord5(iF,jF,kF-2,ex)]-EIT*fh[idx_fh_F_ord5(iF,jF,kF-1,ex)]+EIT*fh[idx_fh_F_ord5(iF,jF,kF+1,ex)]-fh[idx_fh_F_ord5(iF,jF,kF+2,ex)]);
else if (k0<=ex3-2&&k0>=kminF) f_rhs[p]+=sfz*d2dz*(-fh[idx_fh_F_ord5(iF,jF,kF-1,ex)]+fh[idx_fh_F_ord5(iF,jF,kF+1,ex)]);
} else if (sfz<ZEO) {
if ((k0-5)>=kminF&&k0<=ex3-2) f_rhs[p]-=sfz*d840dz*(-F5*fh[idx_fh_F_ord5(iF,jF,kF+3,ex)]+F60*fh[idx_fh_F_ord5(iF,jF,kF+2,ex)]-F420*fh[idx_fh_F_ord5(iF,jF,kF+1,ex)]-F378*fh[idx_fh_F_ord5(iF,jF,kF,ex)]+F1050*fh[idx_fh_F_ord5(iF,jF,kF-1,ex)]-F420*fh[idx_fh_F_ord5(iF,jF,kF-2,ex)]+F140*fh[idx_fh_F_ord5(iF,jF,kF-3,ex)]-F30*fh[idx_fh_F_ord5(iF,jF,kF-4,ex)]+F3*fh[idx_fh_F_ord5(iF,jF,kF-5,ex)]);
else if ((k0-4)>=kminF&&k0<=ex3-2) f_rhs[p]-=sfz*d840dz*(+F3*fh[idx_fh_F_ord5(iF,jF,kF-4,ex)]-F32*fh[idx_fh_F_ord5(iF,jF,kF-3,ex)]+F168*fh[idx_fh_F_ord5(iF,jF,kF-2,ex)]-F672*fh[idx_fh_F_ord5(iF,jF,kF-1,ex)]+F672*fh[idx_fh_F_ord5(iF,jF,kF+1,ex)]-F168*fh[idx_fh_F_ord5(iF,jF,kF+2,ex)]+F32*fh[idx_fh_F_ord5(iF,jF,kF+3,ex)]-F3*fh[idx_fh_F_ord5(iF,jF,kF+4,ex)]);
else if ((k0-3)>=kminF&&k0<=ex3-2) f_rhs[p]-=sfz*d60dz*(-fh[idx_fh_F_ord5(iF,jF,kF-3,ex)]+F9*fh[idx_fh_F_ord5(iF,jF,kF-2,ex)]-F45*fh[idx_fh_F_ord5(iF,jF,kF-1,ex)]+F45*fh[idx_fh_F_ord5(iF,jF,kF+1,ex)]-F9*fh[idx_fh_F_ord5(iF,jF,kF+2,ex)]+fh[idx_fh_F_ord5(iF,jF,kF+3,ex)]);
else if ((k0-2)>=kminF&&k0<=ex3-2) f_rhs[p]-=sfz*d12dz*(fh[idx_fh_F_ord5(iF,jF,kF-2,ex)]-EIT*fh[idx_fh_F_ord5(iF,jF,kF-1,ex)]+EIT*fh[idx_fh_F_ord5(iF,jF,kF+1,ex)]-fh[idx_fh_F_ord5(iF,jF,kF+2,ex)]);
else if ((k0-1)>=kminF&&k0<=ex3-2) f_rhs[p]-=sfz*d2dz*(-fh[idx_fh_F_ord5(iF,jF,kF-1,ex)]+fh[idx_fh_F_ord5(iF,jF,kF+1,ex)]);
}
}}}
/* ---- KO dissipation (r=5, cof=1024, sign=+) ---- */
if (eps > ZEO) {
const double cof = 1024.0;
const double F10k=10.0, F45k=45.0, F120=120.0, F210=210.0, F252=252.0;
const int i0_lo=(iminF+4>0)?iminF+4:0, j0_lo=(jminF+4>0)?jminF+4:0, k0_lo=(kminF+4>0)?kminF+4:0;
const int i0_hi=imaxF-6, j0_hi=jmaxF-6, 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);
const double Dx=((fh[idx_fh_F_ord5(iF-5,jF,kF,ex)]+fh[idx_fh_F_ord5(iF+5,jF,kF,ex)])-F10k*(fh[idx_fh_F_ord5(iF-4,jF,kF,ex)]+fh[idx_fh_F_ord5(iF+4,jF,kF,ex)])+F45k*(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)])-F10k*(fh[idx_fh_F_ord5(iF,jF-4,kF,ex)]+fh[idx_fh_F_ord5(iF,jF+4,kF,ex)])+F45k*(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)])-F10k*(fh[idx_fh_F_ord5(iF,jF,kF-4,ex)]+fh[idx_fh_F_ord5(iF,jF,kF+4,ex)])+F45k*(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);
}}}
}
}
free(fh);
lopsided(ex, X, Y, Z, f, f_rhs, Sfx, Sfy, Sfz, Symmetry, SoA);
if (eps > ZEO) kodis(ex, X, Y, Z, f, f_rhs, SoA, Symmetry, eps);
return;
}
#else