Rewrite: change cli arguments handling
This commit is contained in:
@@ -1,63 +1,311 @@
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#include "navier-stokes.h"
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#include <math.h>
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#include <stdlib.h>
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#define M_PI 3.14159265358979323846
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// compute solution as a function of time
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int uk(
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int K1,
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int K2,
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int N1,
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int N2,
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unsigned int nsteps,
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double nu,
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double delta,
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_Complex double (*g)(int,int),
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unsigned int print_freq
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){
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_Complex double* u;
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_Complex double* tmp1;
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_Complex double* tmp2;
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_Complex double* tmp3;
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unsigned int t;
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fft_vect fft1;
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fft_vect fft2;
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fft_vect ifft;
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int kx,ky;
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ns_init_tmps(&u, &tmp1, &tmp2, &tmp3, &fft1, &fft2, &ifft, K1, K2, N1, N2);
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ns_init_u(u, K1, K2);
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// iterate
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for(t=0;t<nsteps;t++){
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ins_step(u, K1, K2, N1, N2, nu, delta, g, fft1, fft2, ifft, tmp1, tmp2, tmp3);
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if(t%print_freq==0){
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fprintf(stderr,"% .8e ",t*delta);
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printf("% .15e ",t*delta);
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for(kx=-K1;kx<=K1;kx++){
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for (ky=-K2;ky<=K2;ky++){
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if (kx*kx+ky*ky<=1){
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fprintf(stderr,"% .8e % .8e ",__real__ u[klookup(kx,ky,2*K1+1,2*K2+1)], __imag__ u[klookup(kx,ky,2*K1+1,2*K2+1)]);
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}
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printf("% .8e % .8e ",__real__ u[klookup(kx,ky,2*K1+1,2*K2+1)], __imag__ u[klookup(kx,ky,2*K1+1,2*K2+1)]);
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}
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}
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fprintf(stderr,"\n");
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printf("\n");
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}
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}
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ns_free_tmps(u, tmp1, tmp2, tmp3, fft1, fft2, ifft);
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return(0);
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}
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// compute enstrophy as a function of time in the I-NS equation
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int enstrophy(
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int K1,
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int K2,
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int N1,
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int N2,
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unsigned int nsteps,
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double nu,
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double delta,
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_Complex double (*g)(int,int),
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unsigned int print_freq
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){
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_Complex double* u;
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_Complex double* tmp1;
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_Complex double* tmp2;
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_Complex double* tmp3;
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_Complex double alpha;
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_Complex double avg;
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unsigned int t;
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fft_vect fft1;
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fft_vect fft2;
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fft_vect ifft;
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ns_init_tmps(&u, &tmp1, &tmp2, &tmp3, &fft1, &fft2, &ifft, K1, K2, N1, N2);
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ns_init_u(u, K1, K2);
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// init running average
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avg=0;
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// iterate
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for(t=0;t<nsteps;t++){
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ins_step(u, K1, K2, N1, N2, nu, delta, g, fft1, fft2, ifft, tmp1, tmp2, tmp3);
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alpha=compute_alpha(u, K1, K2, g);
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// running average
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if(t>0){
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avg=avg-(avg-alpha)/t;
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}
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if(t>0 && t%print_freq==0){
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fprintf(stderr,"% .15e % .15e % .15e % .15e % .15e\n",t*delta, __real__ avg, __imag__ avg, __real__ alpha, __imag__ alpha);
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printf("% .15e % .15e % .15e % .15e % .15e\n",t*delta, __real__ avg, __imag__ avg, __real__ alpha, __imag__ alpha);
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}
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}
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ns_free_tmps(u, tmp1, tmp2, tmp3, fft1, fft2, ifft);
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return(0);
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}
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// initialize vectors for computation
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int ns_init_tmps(
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_Complex double ** u,
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_Complex double ** tmp1,
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_Complex double ** tmp2,
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_Complex double ** tmp3,
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fft_vect* fft1,
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fft_vect* fft2,
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fft_vect* ifft,
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int K1,
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int K2,
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int N1,
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int N2
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){
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// velocity field
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*u=calloc(sizeof(_Complex double),(2*K1+1)*(2*K2+1));
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// allocate tmp vectors for computation
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*tmp1=calloc(sizeof(_Complex double),(2*K1+1)*(2*K2+1));
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*tmp2=calloc(sizeof(_Complex double),(2*K1+1)*(2*K2+1));
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*tmp3=calloc(sizeof(_Complex double),(2*K1+1)*(2*K2+1));
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// prepare vectors for fft
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fft1->fft=fftw_malloc(sizeof(fftw_complex)*N1*N2);
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fft1->fft_plan=fftw_plan_dft_2d(N1,N2, fft1->fft, fft1->fft, FFTW_FORWARD, FFTW_MEASURE);
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fft2->fft=fftw_malloc(sizeof(fftw_complex)*N1*N2);
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fft2->fft_plan=fftw_plan_dft_2d(N1,N2, fft2->fft, fft2->fft, FFTW_FORWARD, FFTW_MEASURE);
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ifft->fft=fftw_malloc(sizeof(fftw_complex)*N1*N2);
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ifft->fft_plan=fftw_plan_dft_2d(N1,N2, ifft->fft, ifft->fft, FFTW_BACKWARD, FFTW_MEASURE);
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return 0;
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}
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// release vectors
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int ns_free_tmps(
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_Complex double* u,
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_Complex double* tmp1,
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_Complex double* tmp2,
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_Complex double* tmp3,
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fft_vect fft1,
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fft_vect fft2,
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fft_vect ifft
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){
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// free memory
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fftw_destroy_plan(fft1.fft_plan);
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fftw_destroy_plan(fft2.fft_plan);
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fftw_destroy_plan(ifft.fft_plan);
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fftw_free(fft1.fft);
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fftw_free(fft2.fft);
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fftw_free(ifft.fft);
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fftw_cleanup();
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free(tmp3);
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free(tmp2);
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free(tmp1);
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free(u);
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return 0;
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}
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// initial value
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int ns_init_u(
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_Complex double* u,
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int K1,
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int K2
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){
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int kx,ky;
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/*
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double rescale;
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srand(17);
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// random init (set half, then the other half are the conjugates)
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for(ky=0;ky<=K2;ky++){
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u[klookup(0,ky,2*K1+1,2*K2+1)]=(-RAND_MAX*0.5+rand())*1.0/RAND_MAX+(-RAND_MAX*0.5+rand())*1.0/RAND_MAX*I;
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}
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for(kx=1;kx<=K1;kx++){
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for(ky=-K2;ky<=K2;ky++){
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u[klookup(kx,ky,2*K1+1,2*K2+1)]=(-RAND_MAX*0.5+rand())*1.0/RAND_MAX+(-RAND_MAX*0.5+rand())*1.0/RAND_MAX*I;
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}
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}
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// conjugates
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for(ky=-K2;ky<=-1;ky++){
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u[klookup(0,ky,2*K1+1,2*K2+1)]=conj(u[klookup(0,-ky,2*K1+1,2*K2+1)]);
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}
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for(kx=-K1;kx<=-1;kx++){
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for(ky=-K2;ky<=K2;ky++){
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u[klookup(kx,ky,2*K1+1,2*K2+1)]=conj(u[klookup(-kx,-ky,2*K1+1,2*K2+1)]);
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}
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}
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// rescale: 1/k decay
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rescale=0;
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for(kx=-K1;kx<=K1;kx++){
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for(ky=-K2;ky<=K2;ky++){
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rescale=rescale+((__real__ u[klookup(kx,ky,2*K1+1,2*K2+1)])*(__real__ u[klookup(kx,ky,2*K1+1,2*K2+1)])+(__imag__ u[klookup(kx,ky,2*K1+1,2*K2+1)])*(__imag__ u[klookup(kx,ky,2*K1+1,2*K2+1)]))*(kx*kx+ky*ky);
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}
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}
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for(kx=-K1;kx<=K1;kx++){
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for(ky=-K2;ky<=K2;ky++){
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u[klookup(kx,ky,2*K1+1,2*K2+1)]=u[klookup(kx,ky,2*K1+1,2*K2+1)]*sqrt(155.1/rescale);
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}
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}
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*/
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/*
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// constant init
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for(kx=-K1;kx<=K1;kx++){
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for(ky=-K2;ky<=K2;ky++){
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u[klookup(kx,ky,2*K1+1,2*K2+1)]=1.;
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}
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}
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*/
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// exponentially decaying init
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for(kx=-K1;kx<=K1;kx++){
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for(ky=-K2;ky<=K2;ky++){
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u[klookup(kx,ky,2*K1+1,2*K2+1)]=exp(-sqrt(kx*kx+ky*ky));
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}
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}
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return 0;
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}
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// next time step for Irreversible Navier-Stokes equation
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int ins_step(_Complex double* u, ns_params params, fft_vects vects, _Complex double* tmp1, _Complex double* tmp2, _Complex double* tmp3){
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int ins_step(
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_Complex double* u,
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int K1,
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int K2,
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int N1,
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int N2,
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double nu,
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double delta,
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_Complex double (*g)(int,int),
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fft_vect fft1,
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fft_vect fft2,
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fft_vect ifft,
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_Complex double* tmp1,
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_Complex double* tmp2,
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_Complex double* tmp3
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){
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int kx,ky;
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// k1
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ins_rhs(tmp1, u, params, vects);
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ins_rhs(tmp1, u, K1, K2, N1, N2, nu, g, fft1, fft2, ifft);
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// add to output
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for(kx=-params.K;kx<=params.K;kx++){
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for(ky=-params.K;ky<=params.K;ky++){
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tmp3[KLOOKUP(kx,ky,params.S)]=u[KLOOKUP(kx,ky,params.S)]+params.h/6*tmp1[KLOOKUP(kx,ky,params.S)];
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for(kx=-K1;kx<=K1;kx++){
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for(ky=-K2;ky<=K2;ky++){
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tmp3[klookup(kx,ky,2*K1+1,2*K2+1)]=u[klookup(kx,ky,2*K1+1,2*K2+1)]+delta/6*tmp1[klookup(kx,ky,2*K1+1,2*K2+1)];
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}
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}
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// u+h*k1/2
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for(kx=-params.K;kx<=params.K;kx++){
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for(ky=-params.K;ky<=params.K;ky++){
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tmp2[KLOOKUP(kx,ky,params.S)]=u[KLOOKUP(kx,ky,params.S)]+params.h/2*tmp1[KLOOKUP(kx,ky,params.S)];
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for(kx=-K1;kx<=K1;kx++){
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for(ky=-K2;ky<=K2;ky++){
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tmp2[klookup(kx,ky,2*K1+1,2*K2+1)]=u[klookup(kx,ky,2*K1+1,2*K2+1)]+delta/2*tmp1[klookup(kx,ky,2*K1+1,2*K2+1)];
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}
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}
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// k2
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ins_rhs(tmp1, tmp2, params, vects);
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ins_rhs(tmp1, tmp2, K1, K2, N1, N2, nu, g, fft1, fft2, ifft);
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// add to output
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for(kx=-params.K;kx<=params.K;kx++){
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for(ky=-params.K;ky<=params.K;ky++){
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tmp3[KLOOKUP(kx,ky,params.S)]+=params.h/3*tmp1[KLOOKUP(kx,ky,params.S)];
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for(kx=-K1;kx<=K1;kx++){
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for(ky=-K2;ky<=K2;ky++){
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tmp3[klookup(kx,ky,2*K1+1,2*K2+1)]+=delta/3*tmp1[klookup(kx,ky,2*K1+1,2*K2+1)];
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}
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}
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// u+h*k2/2
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for(kx=-params.K;kx<=params.K;kx++){
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for(ky=-params.K;ky<=params.K;ky++){
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tmp2[KLOOKUP(kx,ky,params.S)]=u[KLOOKUP(kx,ky,params.S)]+params.h/2*tmp1[KLOOKUP(kx,ky,params.S)];
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for(kx=-K1;kx<=K1;kx++){
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for(ky=-K2;ky<=K2;ky++){
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tmp2[klookup(kx,ky,2*K1+1,2*K2+1)]=u[klookup(kx,ky,2*K1+1,2*K2+1)]+delta/2*tmp1[klookup(kx,ky,2*K1+1,2*K2+1)];
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}
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}
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// k3
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ins_rhs(tmp1, tmp2, params, vects);
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ins_rhs(tmp1, tmp2, K1, K2, N1, N2, nu, g, fft1, fft2, ifft);
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// add to output
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for(kx=-params.K;kx<=params.K;kx++){
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for(ky=-params.K;ky<=params.K;ky++){
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tmp3[KLOOKUP(kx,ky,params.S)]+=params.h/3*tmp1[KLOOKUP(kx,ky,params.S)];
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for(kx=-K1;kx<=K1;kx++){
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for(ky=-K2;ky<=K2;ky++){
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tmp3[klookup(kx,ky,2*K1+1,2*K2+1)]+=delta/3*tmp1[klookup(kx,ky,2*K1+1,2*K2+1)];
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}
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}
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// u+h*k3
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for(kx=-params.K;kx<=params.K;kx++){
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for(ky=-params.K;ky<=params.K;ky++){
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tmp2[KLOOKUP(kx,ky,params.S)]=u[KLOOKUP(kx,ky,params.S)]+params.h*tmp1[KLOOKUP(kx,ky,params.S)];
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for(kx=-K1;kx<=K1;kx++){
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for(ky=-K2;ky<=K2;ky++){
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tmp2[klookup(kx,ky,2*K1+1,2*K2+1)]=u[klookup(kx,ky,2*K1+1,2*K2+1)]+delta*tmp1[klookup(kx,ky,2*K1+1,2*K2+1)];
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}
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}
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// k4
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ins_rhs(tmp1, tmp2, params, vects);
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ins_rhs(tmp1, tmp2, K1, K2, N1, N2, nu, g, fft1, fft2, ifft);
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// add to output
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for(kx=-params.K;kx<=params.K;kx++){
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for(ky=-params.K;ky<=params.K;ky++){
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u[KLOOKUP(kx,ky,params.S)]=tmp3[KLOOKUP(kx,ky,params.S)]+params.h/6*tmp1[KLOOKUP(kx,ky,params.S)];
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for(kx=-K1;kx<=K1;kx++){
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for(ky=-K2;ky<=K2;ky++){
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u[klookup(kx,ky,2*K1+1,2*K2+1)]=tmp3[klookup(kx,ky,2*K1+1,2*K2+1)]+delta/6*tmp1[klookup(kx,ky,2*K1+1,2*K2+1)];
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}
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}
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@@ -65,74 +313,82 @@ int ins_step(_Complex double* u, ns_params params, fft_vects vects, _Complex dou
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}
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// right side of Irreversible Navier-Stokes equation
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int ins_rhs(_Complex double* out, _Complex double* u, ns_params params, fft_vects vects){
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int ins_rhs(
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_Complex double* out,
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_Complex double* u,
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int K1,
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int K2,
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int N1,
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int N2,
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double nu,
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_Complex double (*g)(int,int),
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fft_vect fft1,
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fft_vect fft2,
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fft_vect ifft
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){
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int kx,ky;
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int i;
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// F(px/|p|*u)*F(qy*|q|*u)
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// init to 0
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for(kx=0; kx<params.N*params.N; kx++){
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vects.fft1[kx]=0;
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vects.fft2[kx]=0;
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vects.invfft[kx]=0;
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for(i=0; i<N1*N2; i++){
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fft1.fft[i]=0;
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fft2.fft[i]=0;
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ifft.fft[i]=0;
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}
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// fill modes
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for(kx=-params.K;kx<=params.K;kx++){
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for(ky=-params.K;ky<=params.K;ky++){
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for(kx=-K1;kx<=K1;kx++){
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for(ky=-K2;ky<=K2;ky++){
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if(kx!=0 || ky!=0){
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vects.fft1[KLOOKUP(kx,ky,params.N)]=kx/sqrt(kx*kx+ky*ky)*u[KLOOKUP(kx,ky,params.S)];
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vects.fft2[KLOOKUP(kx,ky,params.N)]=ky*sqrt(kx*kx+ky*ky)*u[KLOOKUP(kx,ky,params.S)];
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fft1.fft[klookup(kx,ky,N1,N2)]=kx/sqrt(kx*kx+ky*ky)*u[klookup(kx,ky,2*K1+1,2*K2+1)];
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fft2.fft[klookup(kx,ky,N1,N2)]=ky*sqrt(kx*kx+ky*ky)*u[klookup(kx,ky,2*K1+1,2*K2+1)];
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}
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}
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}
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|
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// 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.fft1[KLOOKUP(kx,ky,params.N)]*vects.fft2[KLOOKUP(kx,ky,params.N)];
|
||||
}
|
||||
fftw_execute(fft1.fft_plan);
|
||||
fftw_execute(fft2.fft_plan);
|
||||
// write to ifft
|
||||
for(i=0;i<N1*N2;i++){
|
||||
ifft.fft[i]=fft1.fft[i]*fft2.fft[i];
|
||||
}
|
||||
|
||||
// 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;
|
||||
for(i=0; i<N1*N2; i++){
|
||||
fft1.fft[i]=0;
|
||||
fft2.fft[i]=0;
|
||||
}
|
||||
// fill modes
|
||||
for(kx=-params.K;kx<=params.K;kx++){
|
||||
for(ky=-params.K;ky<=params.K;ky++){
|
||||
for(kx=-K1;kx<=K1;kx++){
|
||||
for(ky=-K2;ky<=K2;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)];
|
||||
fft1.fft[klookup(kx,ky,N1,N2)]=ky/sqrt(kx*kx+ky*ky)*u[klookup(kx,ky,2*K1+1,2*K2+1)];
|
||||
fft2.fft[klookup(kx,ky,N1,N2)]=kx*sqrt(kx*kx+ky*ky)*u[klookup(kx,ky,2*K1+1,2*K2+1)];
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// 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)];
|
||||
}
|
||||
fftw_execute(fft1.fft_plan);
|
||||
fftw_execute(fft2.fft_plan);
|
||||
// write to ifft
|
||||
for(i=0;i<N1*N2;i++){
|
||||
ifft.fft[i]=ifft.fft[i]-fft1.fft[i]*fft2.fft[i];
|
||||
}
|
||||
|
||||
// inverse fft
|
||||
fftw_execute(vects.invfft_plan);
|
||||
fftw_execute(ifft.fft_plan);
|
||||
|
||||
// write out
|
||||
for(kx=0; kx<params.S*params.S; kx++){
|
||||
out[kx]=0;
|
||||
for(i=0; i<(2*K1+1)*(2*K2+1); i++){
|
||||
out[i]=0;
|
||||
}
|
||||
for(kx=-params.K;kx<=params.K;kx++){
|
||||
for(ky=-params.K;ky<=params.K;ky++){
|
||||
for(kx=-K1;kx<=K1;kx++){
|
||||
for(ky=-K2;ky<=K2;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)]/params.N/params.N;
|
||||
out[klookup(kx,ky,2*K1+1,2*K2+1)]=-4*M_PI*M_PI*nu*(kx*kx+ky*ky)*u[klookup(kx,ky,2*K1+1,2*K2+1)]+(*g)(kx,ky)+4*M_PI*M_PI/sqrt(kx*kx+ky*ky)*ifft.fft[klookup(kx,ky,N1,N2)]/N1/N2;
|
||||
}
|
||||
}
|
||||
}
|
||||
@@ -142,17 +398,33 @@ int ins_rhs(_Complex double* out, _Complex double* u, ns_params params, fft_vect
|
||||
|
||||
|
||||
// compute alpha
|
||||
_Complex double compute_alpha(_Complex double* u, ns_params params){
|
||||
_Complex double compute_alpha(
|
||||
_Complex double* u,
|
||||
int K1,
|
||||
int K2,
|
||||
_Complex double (*g)(int,int)
|
||||
){
|
||||
_Complex double num=0;
|
||||
_Complex double denom=0;
|
||||
int kx,ky;
|
||||
|
||||
for(kx=-params.K;kx<=params.K;kx++){
|
||||
for(ky=-params.K;ky<=params.K;ky++){
|
||||
denom+=(kx*kx+ky*ky)*(kx*kx+ky*ky)*u[KLOOKUP(kx,ky,params.S)]*conj(u[KLOOKUP(kx,ky,params.S)])*(1+(ky!=0?kx*kx/ky/ky:0));
|
||||
num+=(kx*kx+ky*ky)*u[KLOOKUP(kx,ky,params.S)]*conj(params.g[KLOOKUP(kx,ky,params.S)])*(1+(ky!=0?kx*kx/ky/ky:0));
|
||||
for(kx=-K1;kx<=K1;kx++){
|
||||
for(ky=-K2;ky<=K2;ky++){
|
||||
denom+=(kx*kx+ky*ky)*(kx*kx+ky*ky)*u[klookup(kx,ky,2*K1+1,2*K2+1)]*conj(u[klookup(kx,ky,2*K1+1,2*K2+1)])*(1+(ky!=0?kx*kx/ky/ky:0));
|
||||
num+=(kx*kx+ky*ky)*u[klookup(kx,ky,2*K1+1,2*K2+1)]*conj((*g)(kx,ky))*(1+(ky!=0?kx*kx/ky/ky:0));
|
||||
}
|
||||
}
|
||||
|
||||
return(num/denom);
|
||||
}
|
||||
|
||||
|
||||
// get index for kx,ky in array of size S
|
||||
int klookup(
|
||||
int kx,
|
||||
int ky,
|
||||
int S1,
|
||||
int S2
|
||||
){
|
||||
return (kx>=0 ? kx : S1+kx)*S2 + (ky>=0 ? ky : S2+ky);
|
||||
}
|
||||
|
||||
Reference in New Issue
Block a user