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Simpler expression for fft term

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This commit is contained in:
Ian Jauslin
2018-01-12 19:20:59 +00:00
parent 7ee5507b93
commit cff1d2ee3c
3 changed files with 57 additions and 68 deletions
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70
src/navier-stokes.c
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@@ -68,7 +68,7 @@ int ins_step(_Complex double* u, ns_params params, fft_vects vects, _Complex dou
int ins_rhs(_Complex double* out, _Complex double* u, ns_params params, fft_vects vects){
int kx,ky;
// F(u/|p|)*F(q1*q2*u/|q|)
// F(px/|p|*u)*F(qy*|q|*u)
// init to 0
for(kx=0; kx<params.N*params.N; kx++){
vects.fft1[kx]=0;
@@ -79,11 +79,12 @@ int ins_rhs(_Complex double* out, _Complex double* u, ns_params params, fft_vect
for(kx=-params.K;kx<=params.K;kx++){
for(ky=-params.K;ky<=params.K;ky++){
if(kx!=0 || ky!=0){
vects.fft1[KLOOKUP(kx,ky,params.N)]=u[KLOOKUP(kx,ky,params.S)]/sqrt(kx*kx+ky*ky);
vects.fft2[KLOOKUP(kx,ky,params.N)]=kx*ky*u[KLOOKUP(kx,ky,params.S)]/sqrt(kx*kx+ky*ky);
vects.fft1[KLOOKUP(kx,ky,params.N)]=kx/sqrt(kx*kx+ky*ky)*u[KLOOKUP(kx,ky,params.S)];
vects.fft2[KLOOKUP(kx,ky,params.N)]=ky*sqrt(kx*kx+ky*ky)*u[KLOOKUP(kx,ky,params.S)];
}
}
}
// fft
fftw_execute(vects.fft1_plan);
fftw_execute(vects.fft2_plan);
@@ -93,6 +94,33 @@ int ins_rhs(_Complex double* out, _Complex double* u, ns_params params, fft_vect
vects.invfft[KLOOKUP(kx,ky,params.N)]=vects.fft1[KLOOKUP(kx,ky,params.N)]*vects.fft2[KLOOKUP(kx,ky,params.N)];
}
}
// F(py/|p|*u)*F(qx*|q|*u)
// init to 0
for(kx=0; kx<params.N*params.N; kx++){
vects.fft1[kx]=0;
vects.fft2[kx]=0;
}
// fill modes
for(kx=-params.K;kx<=params.K;kx++){
for(ky=-params.K;ky<=params.K;ky++){
if(kx!=0 || ky!=0){
vects.fft1[KLOOKUP(kx,ky,params.N)]=ky/sqrt(kx*kx+ky*ky)*u[KLOOKUP(kx,ky,params.S)];
vects.fft2[KLOOKUP(kx,ky,params.N)]=kx*sqrt(kx*kx+ky*ky)*u[KLOOKUP(kx,ky,params.S)];
}
}
}
// fft
fftw_execute(vects.fft1_plan);
fftw_execute(vects.fft2_plan);
// write to invfft
for(kx=-2*params.K;kx<=2*params.K;kx++){
for(ky=-2*params.K;ky<=2*params.K;ky++){
vects.invfft[KLOOKUP(kx,ky,params.N)]=vects.invfft[KLOOKUP(kx,ky,params.N)]-vects.fft1[KLOOKUP(kx,ky,params.N)]*vects.fft2[KLOOKUP(kx,ky,params.N)];
}
}
// inverse fft
fftw_execute(vects.invfft_plan);
@@ -103,41 +131,7 @@ int ins_rhs(_Complex double* out, _Complex double* u, ns_params params, fft_vect
for(kx=-params.K;kx<=params.K;kx++){
for(ky=-params.K;ky<=params.K;ky++){
if(kx!=0 || ky!=0){
out[KLOOKUP(kx,ky,params.S)]=-4*M_PI*M_PI*params.nu*(kx*kx+ky*ky)*u[KLOOKUP(kx,ky,params.S)]+params.g[KLOOKUP(kx,ky,params.S)]+4*M_PI*M_PI/sqrt(kx*kx+ky*ky)*vects.invfft[KLOOKUP(kx,ky,params.N)]*(kx*kx-ky*ky)/params.N/params.N;
}
}
}
// F(u/|p|)*F((q1*q1-q2*q2)*u/|q|)
// init to 0
for(kx=0; kx<params.N*params.N; kx++){
vects.fft2[kx]=0;
vects.invfft[kx]=0;
}
// fill modes
for(kx=-params.K;kx<=params.K;kx++){
for(ky=-params.K;ky<=params.K;ky++){
if(kx!=0 || ky!=0){
vects.fft2[KLOOKUP(kx,ky,params.N)]=(kx*kx-ky*ky)*u[KLOOKUP(kx,ky,params.S)]/sqrt(kx*kx+ky*ky);
}
}
}
// fft
fftw_execute(vects.fft2_plan);
// write to invfft
for(kx=-2*params.K;kx<=2*params.K;kx++){
for(ky=-2*params.K;ky<=2*params.K;ky++){
vects.invfft[KLOOKUP(kx,ky,params.N)]=vects.fft1[KLOOKUP(kx,ky,params.N)]*vects.fft2[KLOOKUP(kx,ky,params.N)];
}
}
// inverse fft
fftw_execute(vects.invfft_plan);
// write out
for(kx=-params.K;kx<=params.K;kx++){
for(ky=-params.K;ky<=params.K;ky++){
if(kx!=0 || ky!=0){
out[KLOOKUP(kx,ky,params.S)]=out[KLOOKUP(kx,ky,params.S)]-4*M_PI*M_PI/sqrt(kx*kx+ky*ky)*vects.invfft[KLOOKUP(kx,ky,params.N)]*(kx*ky)/params.N/params.N;
out[KLOOKUP(kx,ky,params.S)]=-4*M_PI*M_PI*params.nu*(kx*kx+ky*ky)*u[KLOOKUP(kx,ky,params.S)]+params.g[KLOOKUP(kx,ky,params.S)]+4*M_PI*M_PI/sqrt(kx*kx+ky*ky)*vects.invfft[KLOOKUP(kx,ky,params.N)]/params.N/params.N;
}
}
}