Rewrite: change cli arguments handling
This commit is contained in:
17
src/driving.c
Normal file
17
src/driving.c
Normal file
@@ -0,0 +1,17 @@
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#include "driving.h"
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#include <math.h>
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_Complex double g_test(
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int kx,
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int ky
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){
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//return sqrt(kx*kx*ky*ky)*exp(-(kx*kx+ky*ky));
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if(kx==2 && ky==-1){
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return 0.5+sqrt(3)/2*I;
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}
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else if(kx==-2 && ky==1){
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return 0.5-sqrt(3)/2*I;
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}
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return 0.;
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}
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8
src/driving.h
Normal file
8
src/driving.h
Normal file
@@ -0,0 +1,8 @@
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#ifndef DRIVING_H
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#define DRIVING_H
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#include <complex.h>
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_Complex double g_test( int kx, int ky);
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#endif
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502
src/main.c
502
src/main.c
@@ -1,43 +1,77 @@
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#define VERSION "0.0"
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#define VERSION "0.1"
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#include <math.h>
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#include <complex.h>
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#include <fftw3.h>
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#include <string.h>
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#include <stdlib.h>
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#include <stdbool.h>
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#include "navier-stokes.h"
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#include "driving.h"
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// usage message
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int print_usage();
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// read command line arguments
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int read_args(int argc, const char* argv[], ns_params* params, unsigned int* nsteps, unsigned int* computation_nr);
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// compute enstrophy as a function of time in the I-NS equation
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int enstrophy(ns_params params, unsigned int Nsteps);
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int read_args(int argc, const char* argv[], char** params, unsigned int* driving_force, unsigned int* command);
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int read_params(char* params, int* K1, int* K2, int* N1, int* N2, unsigned int* nsteps, double* nu, double* delta, unsigned int* print_freq);
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int set_parameter(char* lhs, char* rhs, int* K1, int* K2, int* N1, int* N2, unsigned int* nsteps, double* nu, double* delta, unsigned int* print_freq, bool* setN1, bool* setN2);
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#define COMPUTATION_ENSTROPHY 1
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int main (int argc, const char* argv[]){
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ns_params params;
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#define COMMAND_UK 1
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#define COMMAND_ENSTROPHY 2
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#define DRIVING_TEST 1
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int main (
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int argc,
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const char* argv[]
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){
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char* params=NULL;
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int K1,K2;
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int N1,N2;
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unsigned int nsteps;
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double nu,delta;
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_Complex double (*g)(int,int);
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int ret;
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unsigned int computation_nr;
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unsigned int driving,command;
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unsigned int print_freq;
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// default computation: phase diagram
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computation_nr=COMPUTATION_ENSTROPHY;
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command=0;
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driving=0;
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// read command line arguments
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ret=read_args(argc, argv, ¶ms, &nsteps, &computation_nr);
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ret=read_args(argc, argv, ¶ms, &driving, &command);
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if(ret<0){
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return(-1);
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}
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if(ret>0){
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return(0);
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// read params
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ret=read_params(params, &K1, &K2, &N1, &N2, &nsteps, &nu, &delta, &print_freq);
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if(ret<0){
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return(-1);
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}
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// set driving force
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switch(driving){
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case DRIVING_TEST:
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g=g_test;
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break;
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default:
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g=g_test;
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break;
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}
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// enstrophy
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if(computation_nr==COMPUTATION_ENSTROPHY){
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enstrophy(params, nsteps);
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// run command
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if (command==COMMAND_UK){
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uk(K1, K2, N1, N2, nsteps, nu, delta, g, print_freq);
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}
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else if(command==COMMAND_ENSTROPHY){
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enstrophy(K1, K2, N1, N2, nsteps, nu, delta, g, print_freq);
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}
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else if(command==0){
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fprintf(stderr, "error: no command specified\n");
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print_usage();
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}
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return(0);
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@@ -45,44 +79,25 @@ int main (int argc, const char* argv[]){
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// usage message
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int print_usage(){
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fprintf(stderr, "usage:\n nstrophy enstrophy [-h timestep] [-K modes] [-v] [-N nsteps]\n\n nstrophy -V [-v]\n\n");
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fprintf(stderr, "usage:\n nstrophy [-p parameters] [-g driving_force] <command>\n\n");
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return(0);
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}
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// read command line arguments
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#define CP_FLAG_TIMESTEP 1
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#define CP_FLAG_NSTEPS 2
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#define CP_FLAG_MODES 3
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#define CP_FLAG_NU 4
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int read_args(int argc, const char* argv[], ns_params* params, unsigned int* nsteps, unsigned int* computation_nr){
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#define CP_FLAG_PARAMS 1
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#define CP_FLAG_DRIVING 2
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int read_args(
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int argc,
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const char* argv[],
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char** params,
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unsigned int* driving_force,
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unsigned int* command
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){
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int i;
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int ret;
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// temporary int
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int tmp_int;
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// temporary unsigned int
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unsigned int tmp_uint;
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// temporary double
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double tmp_double;
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// pointers
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char* ptr;
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// flag that indicates what argument is being read
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int flag=0;
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// print version and exit
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char Vflag=0;
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// defaults
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/*
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params->K=16;
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params->h=1e-3/(2*params->K+1);
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*nsteps=10000000;
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params->nu=1./1024/(2*params->K+1);
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*/
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params->K=16;
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//h=2^-13
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params->h=0.0001220703125;
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//nu=2^-11
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*nsteps=10000000;
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params->nu=0.00048828125;
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// loop over arguments
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for(i=1;i<argc;i++){
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@@ -91,24 +106,12 @@ int read_args(int argc, const char* argv[], ns_params* params, unsigned int* nst
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for(ptr=((char*)argv[i])+1;*ptr!='\0';ptr++){
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switch(*ptr){
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// timestep
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case 'h':
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flag=CP_FLAG_TIMESTEP;
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case 'p':
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flag=CP_FLAG_PARAMS;
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break;
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// nsteps
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case 'N':
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flag=CP_FLAG_NSTEPS;
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break;
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// modes
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case 'K':
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flag=CP_FLAG_MODES;
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break;
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// friction
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case 'n':
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flag=CP_FLAG_NU;
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break;
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// print version
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case 'V':
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Vflag=1;
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case 'g':
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flag=CP_FLAG_DRIVING;
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break;
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default:
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fprintf(stderr, "unrecognized option '-%c'\n", *ptr);
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@@ -118,206 +121,241 @@ int read_args(int argc, const char* argv[], ns_params* params, unsigned int* nst
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}
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}
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}
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// timestep
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else if(flag==CP_FLAG_TIMESTEP){
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ret=sscanf(argv[i],"%lf",&tmp_double);
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if(ret!=1){
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fprintf(stderr, "error: '-h' should be followed by a double\n got '%s'\n",argv[i]);
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return(-1);
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}
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params->h=tmp_double;
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// params
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else if(flag==CP_FLAG_PARAMS){
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*params=(char*)argv[i];
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flag=0;
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}
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// nsteps
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else if(flag==CP_FLAG_NSTEPS){
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ret=sscanf(argv[i],"%u",&tmp_uint);
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if(ret!=1){
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fprintf(stderr, "error: '-N' should be followed by an unsigned int\n got '%s'\n",argv[i]);
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// driving force
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else if(flag==CP_FLAG_DRIVING){
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if (strcmp(argv[i],"test")==0){
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*driving_force=DRIVING_TEST;
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}
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else{
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fprintf(stderr, "error: unrecognized driving force '%s'\n",argv[i]);
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return(-1);
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}
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*nsteps=tmp_uint;
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flag=0;
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}
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// modes
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else if(flag==CP_FLAG_MODES){
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ret=sscanf(argv[i],"%d",&tmp_int);
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if(ret!=1){
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fprintf(stderr, "error: '-K' should be followed by an int\n got '%s'\n",argv[i]);
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return(-1);
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}
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params->K=tmp_int;
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flag=0;
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}
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// friction
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else if(flag==CP_FLAG_TIMESTEP){
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ret=sscanf(argv[i],"%lf",&tmp_double);
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if(ret!=1){
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fprintf(stderr, "error: '-n' should be followed by a double\n got '%s'\n",argv[i]);
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return(-1);
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}
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params->nu=tmp_double;
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flag=0;
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}
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// computation to run
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else{
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if(strcmp(argv[i], "enstrophy")==0){
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*computation_nr=COMPUTATION_ENSTROPHY;
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if(strcmp(argv[i], "uk")==0){
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*command=COMMAND_UK;
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}
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else if(strcmp(argv[i], "enstrophy")==0){
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*command=COMMAND_ENSTROPHY;
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}
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else{
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fprintf(stderr, "error: unrecognized computation: '%s'\n",argv[i]);
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print_usage();
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fprintf(stderr, "error: unrecognized command: '%s'\n",argv[i]);
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return(-1);
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}
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flag=0;
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}
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}
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// print version and exit
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if(Vflag==1){
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printf("nstrophy " VERSION "\n");
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return(1);
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}
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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(ns_params params, unsigned int Nsteps){
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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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int kx,ky;
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fft_vects fft_vects;
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double rescale;
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// read parameters string
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int read_params(
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char* params,
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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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unsigned int* print_freq
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){
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int ret;
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// pointer in params
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char* ptr;
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// buffer and associated pointer
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char *buffer_lhs, *lhs_ptr;
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char *buffer_rhs, *rhs_ptr;
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// whether N was set explicitly
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bool setN1=false;
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bool setN2=false;
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// whether lhs (false is rhs)
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bool lhs=true;
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// sizes
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params.S=2*params.K+1;
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params.N=4*params.K+1;
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// defaults
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*K1=16;
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*K2=*K1;
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//delta=2^-13
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*delta=0.0001220703125;
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//nu=2^-11
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*nu=0.00048828125;
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*nsteps=10000000;
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*print_freq=1000;
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// velocity field
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u=calloc(sizeof(_Complex double),params.S*params.S);
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params.g=calloc(sizeof(_Complex double),params.S*params.S);
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// allocate tmp vectors for computation
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tmp1=calloc(sizeof(_Complex double),params.S*params.S);
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tmp2=calloc(sizeof(_Complex double),params.S*params.S);
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tmp3=calloc(sizeof(_Complex double),params.S*params.S);
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if (params!=NULL){
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// init
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buffer_lhs=calloc(sizeof(char),strlen(params));
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lhs_ptr=buffer_lhs;
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*lhs_ptr='\0';
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buffer_rhs=calloc(sizeof(char),strlen(params));
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rhs_ptr=buffer_rhs;
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*rhs_ptr='\0';
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/*
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srand(17);
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// initial value
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for(ky=0;ky<=params.K;ky++){
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u[KLOOKUP(0,ky,params.S)]=(-RAND_MAX*0.5+rand())*1.0/RAND_MAX+(-RAND_MAX*0.5+rand())*1.0/RAND_MAX*I;
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for(ptr=params;*ptr!='\0';ptr++){
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switch(*ptr){
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case '=':
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// reset buffer
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rhs_ptr=buffer_rhs;
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*rhs_ptr='\0';
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lhs=false;
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break;
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case ';':
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//set parameter
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ret=set_parameter(buffer_lhs,buffer_rhs,K1,K2,N1,N2,nsteps,nu,delta,print_freq,&setN1,&setN2);
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if(ret<0){
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return ret;
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}
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for(kx=1;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)]=(-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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for(ky=-params.K;ky<=-1;ky++){
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u[KLOOKUP(0,ky,params.S)]=conj(u[KLOOKUP(0,-ky,params.S)]);
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}
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for(kx=-params.K;kx<=-1;kx++){
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for(ky=-params.K;ky<=params.K;ky++){
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u[KLOOKUP(kx,ky,params.S)]=conj(u[KLOOKUP(-kx,-ky,params.S)]);
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}
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}
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rescale=0;
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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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rescale=rescale+((__real__ u[KLOOKUP(kx,ky,params.S)])*(__real__ u[KLOOKUP(kx,ky,params.S)])+(__imag__ u[KLOOKUP(kx,ky,params.S)])*(__imag__ u[KLOOKUP(kx,ky,params.S)]))*(kx*kx+ky*ky);
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}
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}
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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)]=u[KLOOKUP(kx,ky,params.S)]*sqrt(155.1/rescale);
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}
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}
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*/
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/*
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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)]=1.;
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}
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}
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*/
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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)]=exp(-sqrt(kx*kx+ky*ky));
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}
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}
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// driving force
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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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//params.g[KLOOKUP(kx,ky,params.S)]=sqrt(kx*kx*ky*ky)*exp(-(kx*kx+ky*ky));
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if(kx==2 && ky==-1){
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params.g[KLOOKUP(kx,ky,params.S)]=0.5+sqrt(3)/2*I;
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}
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else if(kx==-2 && ky==1){
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params.g[KLOOKUP(kx,ky,params.S)]=0.5-sqrt(3)/2*I;
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// reset buffer
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lhs_ptr=buffer_lhs;
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*lhs_ptr='\0';
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lhs=true;
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break;
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default:
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// add to buffer
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if (lhs){
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*lhs_ptr=*ptr;
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lhs_ptr++;
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*lhs_ptr='\0';
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}
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else{
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params.g[KLOOKUP(kx,ky,params.S)]=0;
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*rhs_ptr=*ptr;
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rhs_ptr++;
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*rhs_ptr='\0';
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}
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break;
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}
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}
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// set last param
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if (*params!='\0'){
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ret=set_parameter(buffer_lhs,buffer_rhs,K1,K2,N1,N2,nsteps,nu,delta,print_freq,&setN1,&setN2);
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if(ret<0){
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return ret;
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}
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}
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// prepare vectors for fft
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fft_vects.fft1=fftw_malloc(sizeof(fftw_complex)*params.N*params.N);
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fft_vects.fft1_plan=fftw_plan_dft_2d((int)params.N,(int)params.N, fft_vects.fft1, fft_vects.fft1, FFTW_FORWARD, FFTW_MEASURE);
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fft_vects.fft2=fftw_malloc(sizeof(fftw_complex)*params.N*params.N);
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fft_vects.fft2_plan=fftw_plan_dft_2d((int)params.N,(int)params.N, fft_vects.fft2, fft_vects.fft2, FFTW_FORWARD, FFTW_MEASURE);
|
||||
fft_vects.invfft=fftw_malloc(sizeof(fftw_complex)*params.N*params.N);
|
||||
fft_vects.invfft_plan=fftw_plan_dft_2d((int)params.N,(int)params.N, fft_vects.invfft, fft_vects.invfft, FFTW_BACKWARD, FFTW_MEASURE);
|
||||
|
||||
// init running average
|
||||
avg=0;
|
||||
|
||||
// iterate
|
||||
for(t=0;t<Nsteps;t++){
|
||||
ins_step(u, params, fft_vects, tmp1, tmp2, tmp3);
|
||||
alpha=compute_alpha(u, params);
|
||||
|
||||
/*
|
||||
// to avoid errors building up in imaginary part
|
||||
for(kx=-params.K;kx<=params.K;kx++){
|
||||
for(ky=-params.K;ky<=params.K;ky++){
|
||||
u[KLOOKUP(kx,ky,params.S)]=__real__ u[KLOOKUP(kx,ky,params.S)];
|
||||
}
|
||||
}
|
||||
*/
|
||||
|
||||
// running average
|
||||
if(t>0){
|
||||
avg=avg-(avg-alpha)/t;
|
||||
}
|
||||
|
||||
if(t>0 && t%1000==0){
|
||||
fprintf(stderr,"% .15e % .15e % .15e % .15e % .15e\n",t*params.h, __real__ avg, __imag__ avg, __real__ alpha, __imag__ alpha);
|
||||
printf("% .15e % .15e % .15e % .15e % .15e\n",t*params.h, __real__ avg, __imag__ avg, __real__ alpha, __imag__ alpha);
|
||||
}
|
||||
}
|
||||
|
||||
// free memory
|
||||
fftw_destroy_plan(fft_vects.fft1_plan);
|
||||
fftw_destroy_plan(fft_vects.fft2_plan);
|
||||
fftw_destroy_plan(fft_vects.invfft_plan);
|
||||
fftw_free(fft_vects.fft1);
|
||||
fftw_free(fft_vects.fft2);
|
||||
fftw_free(fft_vects.invfft);
|
||||
|
||||
free(tmp3);
|
||||
free(tmp2);
|
||||
free(tmp1);
|
||||
free(params.g);
|
||||
free(u);
|
||||
// free vects
|
||||
free(buffer_lhs);
|
||||
free(buffer_rhs);
|
||||
}
|
||||
|
||||
// if N not set explicitly, set it
|
||||
if (!setN1){
|
||||
*N1=4*(*K1)+1;
|
||||
}
|
||||
if (!setN2){
|
||||
*N2=4*(*K2)+1;
|
||||
}
|
||||
|
||||
return(0);
|
||||
}
|
||||
|
||||
|
||||
// set a parameter from the parameter string
|
||||
int set_parameter(
|
||||
char* lhs,
|
||||
char* rhs,
|
||||
int* K1,
|
||||
int* K2,
|
||||
int* N1,
|
||||
int* N2,
|
||||
unsigned int* nsteps,
|
||||
double* nu,
|
||||
double* delta,
|
||||
unsigned int* print_freq,
|
||||
bool* setN1,
|
||||
bool* setN2
|
||||
){
|
||||
int ret;
|
||||
|
||||
if (strcmp(lhs,"K1")==0){
|
||||
ret=sscanf(rhs,"%d",K1);
|
||||
if(ret!=1){
|
||||
fprintf(stderr, "error: parameter 'K1' should be an integer\n got '%s'\n",rhs);
|
||||
return(-1);
|
||||
}
|
||||
}
|
||||
else if (strcmp(lhs,"K2")==0){
|
||||
ret=sscanf(rhs,"%d",K2);
|
||||
if(ret!=1){
|
||||
fprintf(stderr, "error: parameter 'K2' should be an integer\n got '%s'\n",rhs);
|
||||
return(-1);
|
||||
}
|
||||
}
|
||||
else if (strcmp(lhs,"K")==0){
|
||||
ret=sscanf(rhs,"%d",K1);
|
||||
if(ret!=1){
|
||||
fprintf(stderr, "error: parameter 'K' should be an integer\n got '%s'\n",rhs);
|
||||
return(-1);
|
||||
}
|
||||
*K2=*K1;
|
||||
}
|
||||
else if (strcmp(lhs,"N1")==0){
|
||||
ret=sscanf(rhs,"%d",N1);
|
||||
if(ret!=1){
|
||||
fprintf(stderr, "error: parameter 'N1' should be an integer\n got '%s'\n",rhs);
|
||||
return(-1);
|
||||
}
|
||||
*setN1=true;
|
||||
}
|
||||
else if (strcmp(lhs,"N2")==0){
|
||||
ret=sscanf(rhs,"%d",N2);
|
||||
if(ret!=1){
|
||||
fprintf(stderr, "error: parameter 'N2' should be an integer\n got '%s'\n",rhs);
|
||||
return(-1);
|
||||
}
|
||||
*setN2=true;
|
||||
}
|
||||
else if (strcmp(lhs,"N")==0){
|
||||
ret=sscanf(rhs,"%d",N1);
|
||||
if(ret!=1){
|
||||
fprintf(stderr, "error: parameter 'N' should be an integer\n got '%s'\n",rhs);
|
||||
return(-1);
|
||||
}
|
||||
*N2=*N1;
|
||||
*setN1=true;
|
||||
*setN2=true;
|
||||
}
|
||||
else if (strcmp(lhs,"nsteps")==0){
|
||||
ret=sscanf(rhs,"%u",nsteps);
|
||||
if(ret!=1){
|
||||
fprintf(stderr, "error: parameter 'nsteps' should be an unsigned integer\n got '%s'\n",rhs);
|
||||
return(-1);
|
||||
}
|
||||
}
|
||||
else if (strcmp(lhs,"nu")==0){
|
||||
ret=sscanf(rhs,"%lf",nu);
|
||||
if(ret!=1){
|
||||
fprintf(stderr, "error: parameter 'nu' should be a double\n got '%s'\n",rhs);
|
||||
return(-1);
|
||||
}
|
||||
}
|
||||
else if (strcmp(lhs,"delta")==0){
|
||||
ret=sscanf(rhs,"%lf",delta);
|
||||
if(ret!=1){
|
||||
fprintf(stderr, "error: parameter 'delta' should be a double\n got '%s'\n",rhs);
|
||||
return(-1);
|
||||
}
|
||||
}
|
||||
else if (strcmp(lhs,"print_freq")==0){
|
||||
ret=sscanf(rhs,"%u",print_freq);
|
||||
if(ret!=1){
|
||||
fprintf(stderr, "error: parameter 'print_freq' should be an unsigned integer\n got '%s'\n",rhs);
|
||||
return(-1);
|
||||
}
|
||||
}
|
||||
else{
|
||||
fprintf(stderr, "error: unrecognized parameter '%s'\n",lhs);
|
||||
return(-1);
|
||||
}
|
||||
|
||||
return(0);
|
||||
}
|
||||
|
||||
@@ -1,63 +1,311 @@
|
||||
#include "navier-stokes.h"
|
||||
#include <math.h>
|
||||
#include <stdlib.h>
|
||||
|
||||
#define M_PI 3.14159265358979323846
|
||||
|
||||
// compute solution as a function of time
|
||||
int uk(
|
||||
int K1,
|
||||
int K2,
|
||||
int N1,
|
||||
int N2,
|
||||
unsigned int nsteps,
|
||||
double nu,
|
||||
double delta,
|
||||
_Complex double (*g)(int,int),
|
||||
unsigned int print_freq
|
||||
){
|
||||
_Complex double* u;
|
||||
_Complex double* tmp1;
|
||||
_Complex double* tmp2;
|
||||
_Complex double* tmp3;
|
||||
unsigned int t;
|
||||
fft_vect fft1;
|
||||
fft_vect fft2;
|
||||
fft_vect ifft;
|
||||
int kx,ky;
|
||||
|
||||
ns_init_tmps(&u, &tmp1, &tmp2, &tmp3, &fft1, &fft2, &ifft, K1, K2, N1, N2);
|
||||
ns_init_u(u, K1, K2);
|
||||
|
||||
// iterate
|
||||
for(t=0;t<nsteps;t++){
|
||||
ins_step(u, K1, K2, N1, N2, nu, delta, g, fft1, fft2, ifft, tmp1, tmp2, tmp3);
|
||||
|
||||
if(t%print_freq==0){
|
||||
fprintf(stderr,"% .8e ",t*delta);
|
||||
printf("% .15e ",t*delta);
|
||||
|
||||
for(kx=-K1;kx<=K1;kx++){
|
||||
for (ky=-K2;ky<=K2;ky++){
|
||||
if (kx*kx+ky*ky<=1){
|
||||
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)]);
|
||||
|
||||
}
|
||||
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)]);
|
||||
}
|
||||
}
|
||||
fprintf(stderr,"\n");
|
||||
printf("\n");
|
||||
}
|
||||
}
|
||||
|
||||
ns_free_tmps(u, tmp1, tmp2, tmp3, fft1, fft2, ifft);
|
||||
return(0);
|
||||
}
|
||||
|
||||
// compute enstrophy as a function of time in the I-NS equation
|
||||
int enstrophy(
|
||||
int K1,
|
||||
int K2,
|
||||
int N1,
|
||||
int N2,
|
||||
unsigned int nsteps,
|
||||
double nu,
|
||||
double delta,
|
||||
_Complex double (*g)(int,int),
|
||||
unsigned int print_freq
|
||||
){
|
||||
_Complex double* u;
|
||||
_Complex double* tmp1;
|
||||
_Complex double* tmp2;
|
||||
_Complex double* tmp3;
|
||||
_Complex double alpha;
|
||||
_Complex double avg;
|
||||
unsigned int t;
|
||||
fft_vect fft1;
|
||||
fft_vect fft2;
|
||||
fft_vect ifft;
|
||||
|
||||
ns_init_tmps(&u, &tmp1, &tmp2, &tmp3, &fft1, &fft2, &ifft, K1, K2, N1, N2);
|
||||
ns_init_u(u, K1, K2);
|
||||
|
||||
|
||||
// init running average
|
||||
avg=0;
|
||||
|
||||
// iterate
|
||||
for(t=0;t<nsteps;t++){
|
||||
ins_step(u, K1, K2, N1, N2, nu, delta, g, fft1, fft2, ifft, tmp1, tmp2, tmp3);
|
||||
alpha=compute_alpha(u, K1, K2, g);
|
||||
|
||||
// running average
|
||||
if(t>0){
|
||||
avg=avg-(avg-alpha)/t;
|
||||
}
|
||||
|
||||
if(t>0 && t%print_freq==0){
|
||||
fprintf(stderr,"% .15e % .15e % .15e % .15e % .15e\n",t*delta, __real__ avg, __imag__ avg, __real__ alpha, __imag__ alpha);
|
||||
printf("% .15e % .15e % .15e % .15e % .15e\n",t*delta, __real__ avg, __imag__ avg, __real__ alpha, __imag__ alpha);
|
||||
}
|
||||
}
|
||||
|
||||
ns_free_tmps(u, tmp1, tmp2, tmp3, fft1, fft2, ifft);
|
||||
return(0);
|
||||
}
|
||||
|
||||
|
||||
// initialize vectors for computation
|
||||
int ns_init_tmps(
|
||||
_Complex double ** u,
|
||||
_Complex double ** tmp1,
|
||||
_Complex double ** tmp2,
|
||||
_Complex double ** tmp3,
|
||||
fft_vect* fft1,
|
||||
fft_vect* fft2,
|
||||
fft_vect* ifft,
|
||||
int K1,
|
||||
int K2,
|
||||
int N1,
|
||||
int N2
|
||||
){
|
||||
// velocity field
|
||||
*u=calloc(sizeof(_Complex double),(2*K1+1)*(2*K2+1));
|
||||
|
||||
// allocate tmp vectors for computation
|
||||
*tmp1=calloc(sizeof(_Complex double),(2*K1+1)*(2*K2+1));
|
||||
*tmp2=calloc(sizeof(_Complex double),(2*K1+1)*(2*K2+1));
|
||||
*tmp3=calloc(sizeof(_Complex double),(2*K1+1)*(2*K2+1));
|
||||
|
||||
// prepare vectors for fft
|
||||
fft1->fft=fftw_malloc(sizeof(fftw_complex)*N1*N2);
|
||||
fft1->fft_plan=fftw_plan_dft_2d(N1,N2, fft1->fft, fft1->fft, FFTW_FORWARD, FFTW_MEASURE);
|
||||
fft2->fft=fftw_malloc(sizeof(fftw_complex)*N1*N2);
|
||||
fft2->fft_plan=fftw_plan_dft_2d(N1,N2, fft2->fft, fft2->fft, FFTW_FORWARD, FFTW_MEASURE);
|
||||
ifft->fft=fftw_malloc(sizeof(fftw_complex)*N1*N2);
|
||||
ifft->fft_plan=fftw_plan_dft_2d(N1,N2, ifft->fft, ifft->fft, FFTW_BACKWARD, FFTW_MEASURE);
|
||||
|
||||
return 0;
|
||||
}
|
||||
|
||||
// release vectors
|
||||
int ns_free_tmps(
|
||||
_Complex double* u,
|
||||
_Complex double* tmp1,
|
||||
_Complex double* tmp2,
|
||||
_Complex double* tmp3,
|
||||
fft_vect fft1,
|
||||
fft_vect fft2,
|
||||
fft_vect ifft
|
||||
){
|
||||
// free memory
|
||||
fftw_destroy_plan(fft1.fft_plan);
|
||||
fftw_destroy_plan(fft2.fft_plan);
|
||||
fftw_destroy_plan(ifft.fft_plan);
|
||||
fftw_free(fft1.fft);
|
||||
fftw_free(fft2.fft);
|
||||
fftw_free(ifft.fft);
|
||||
|
||||
fftw_cleanup();
|
||||
|
||||
free(tmp3);
|
||||
free(tmp2);
|
||||
free(tmp1);
|
||||
|
||||
free(u);
|
||||
|
||||
return 0;
|
||||
}
|
||||
|
||||
|
||||
|
||||
// initial value
|
||||
int ns_init_u(
|
||||
_Complex double* u,
|
||||
int K1,
|
||||
int K2
|
||||
){
|
||||
int kx,ky;
|
||||
/*
|
||||
double rescale;
|
||||
|
||||
srand(17);
|
||||
|
||||
// random init (set half, then the other half are the conjugates)
|
||||
for(ky=0;ky<=K2;ky++){
|
||||
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;
|
||||
}
|
||||
for(kx=1;kx<=K1;kx++){
|
||||
for(ky=-K2;ky<=K2;ky++){
|
||||
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;
|
||||
}
|
||||
}
|
||||
// conjugates
|
||||
for(ky=-K2;ky<=-1;ky++){
|
||||
u[klookup(0,ky,2*K1+1,2*K2+1)]=conj(u[klookup(0,-ky,2*K1+1,2*K2+1)]);
|
||||
}
|
||||
for(kx=-K1;kx<=-1;kx++){
|
||||
for(ky=-K2;ky<=K2;ky++){
|
||||
u[klookup(kx,ky,2*K1+1,2*K2+1)]=conj(u[klookup(-kx,-ky,2*K1+1,2*K2+1)]);
|
||||
}
|
||||
}
|
||||
|
||||
// rescale: 1/k decay
|
||||
rescale=0;
|
||||
for(kx=-K1;kx<=K1;kx++){
|
||||
for(ky=-K2;ky<=K2;ky++){
|
||||
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);
|
||||
}
|
||||
}
|
||||
for(kx=-K1;kx<=K1;kx++){
|
||||
for(ky=-K2;ky<=K2;ky++){
|
||||
u[klookup(kx,ky,2*K1+1,2*K2+1)]=u[klookup(kx,ky,2*K1+1,2*K2+1)]*sqrt(155.1/rescale);
|
||||
}
|
||||
}
|
||||
*/
|
||||
|
||||
|
||||
/*
|
||||
// constant init
|
||||
for(kx=-K1;kx<=K1;kx++){
|
||||
for(ky=-K2;ky<=K2;ky++){
|
||||
u[klookup(kx,ky,2*K1+1,2*K2+1)]=1.;
|
||||
}
|
||||
}
|
||||
*/
|
||||
|
||||
// exponentially decaying init
|
||||
for(kx=-K1;kx<=K1;kx++){
|
||||
for(ky=-K2;ky<=K2;ky++){
|
||||
u[klookup(kx,ky,2*K1+1,2*K2+1)]=exp(-sqrt(kx*kx+ky*ky));
|
||||
}
|
||||
}
|
||||
|
||||
return 0;
|
||||
}
|
||||
|
||||
|
||||
// next time step for Irreversible Navier-Stokes equation
|
||||
int ins_step(_Complex double* u, ns_params params, fft_vects vects, _Complex double* tmp1, _Complex double* tmp2, _Complex double* tmp3){
|
||||
int ins_step(
|
||||
_Complex double* u,
|
||||
int K1,
|
||||
int K2,
|
||||
int N1,
|
||||
int N2,
|
||||
double nu,
|
||||
double delta,
|
||||
_Complex double (*g)(int,int),
|
||||
fft_vect fft1,
|
||||
fft_vect fft2,
|
||||
fft_vect ifft,
|
||||
_Complex double* tmp1,
|
||||
_Complex double* tmp2,
|
||||
_Complex double* tmp3
|
||||
){
|
||||
int kx,ky;
|
||||
|
||||
// k1
|
||||
ins_rhs(tmp1, u, params, vects);
|
||||
ins_rhs(tmp1, u, K1, K2, N1, N2, nu, g, fft1, fft2, ifft);
|
||||
// add to output
|
||||
for(kx=-params.K;kx<=params.K;kx++){
|
||||
for(ky=-params.K;ky<=params.K;ky++){
|
||||
tmp3[KLOOKUP(kx,ky,params.S)]=u[KLOOKUP(kx,ky,params.S)]+params.h/6*tmp1[KLOOKUP(kx,ky,params.S)];
|
||||
for(kx=-K1;kx<=K1;kx++){
|
||||
for(ky=-K2;ky<=K2;ky++){
|
||||
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)];
|
||||
}
|
||||
}
|
||||
|
||||
// u+h*k1/2
|
||||
for(kx=-params.K;kx<=params.K;kx++){
|
||||
for(ky=-params.K;ky<=params.K;ky++){
|
||||
tmp2[KLOOKUP(kx,ky,params.S)]=u[KLOOKUP(kx,ky,params.S)]+params.h/2*tmp1[KLOOKUP(kx,ky,params.S)];
|
||||
for(kx=-K1;kx<=K1;kx++){
|
||||
for(ky=-K2;ky<=K2;ky++){
|
||||
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)];
|
||||
}
|
||||
}
|
||||
// k2
|
||||
ins_rhs(tmp1, tmp2, params, vects);
|
||||
ins_rhs(tmp1, tmp2, K1, K2, N1, N2, nu, g, fft1, fft2, ifft);
|
||||
// add to output
|
||||
for(kx=-params.K;kx<=params.K;kx++){
|
||||
for(ky=-params.K;ky<=params.K;ky++){
|
||||
tmp3[KLOOKUP(kx,ky,params.S)]+=params.h/3*tmp1[KLOOKUP(kx,ky,params.S)];
|
||||
for(kx=-K1;kx<=K1;kx++){
|
||||
for(ky=-K2;ky<=K2;ky++){
|
||||
tmp3[klookup(kx,ky,2*K1+1,2*K2+1)]+=delta/3*tmp1[klookup(kx,ky,2*K1+1,2*K2+1)];
|
||||
}
|
||||
}
|
||||
|
||||
// u+h*k2/2
|
||||
for(kx=-params.K;kx<=params.K;kx++){
|
||||
for(ky=-params.K;ky<=params.K;ky++){
|
||||
tmp2[KLOOKUP(kx,ky,params.S)]=u[KLOOKUP(kx,ky,params.S)]+params.h/2*tmp1[KLOOKUP(kx,ky,params.S)];
|
||||
for(kx=-K1;kx<=K1;kx++){
|
||||
for(ky=-K2;ky<=K2;ky++){
|
||||
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)];
|
||||
}
|
||||
}
|
||||
// k3
|
||||
ins_rhs(tmp1, tmp2, params, vects);
|
||||
ins_rhs(tmp1, tmp2, K1, K2, N1, N2, nu, g, fft1, fft2, ifft);
|
||||
// add to output
|
||||
for(kx=-params.K;kx<=params.K;kx++){
|
||||
for(ky=-params.K;ky<=params.K;ky++){
|
||||
tmp3[KLOOKUP(kx,ky,params.S)]+=params.h/3*tmp1[KLOOKUP(kx,ky,params.S)];
|
||||
for(kx=-K1;kx<=K1;kx++){
|
||||
for(ky=-K2;ky<=K2;ky++){
|
||||
tmp3[klookup(kx,ky,2*K1+1,2*K2+1)]+=delta/3*tmp1[klookup(kx,ky,2*K1+1,2*K2+1)];
|
||||
}
|
||||
}
|
||||
|
||||
// u+h*k3
|
||||
for(kx=-params.K;kx<=params.K;kx++){
|
||||
for(ky=-params.K;ky<=params.K;ky++){
|
||||
tmp2[KLOOKUP(kx,ky,params.S)]=u[KLOOKUP(kx,ky,params.S)]+params.h*tmp1[KLOOKUP(kx,ky,params.S)];
|
||||
for(kx=-K1;kx<=K1;kx++){
|
||||
for(ky=-K2;ky<=K2;ky++){
|
||||
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)];
|
||||
}
|
||||
}
|
||||
// k4
|
||||
ins_rhs(tmp1, tmp2, params, vects);
|
||||
ins_rhs(tmp1, tmp2, K1, K2, N1, N2, nu, g, fft1, fft2, ifft);
|
||||
// add to output
|
||||
for(kx=-params.K;kx<=params.K;kx++){
|
||||
for(ky=-params.K;ky<=params.K;ky++){
|
||||
u[KLOOKUP(kx,ky,params.S)]=tmp3[KLOOKUP(kx,ky,params.S)]+params.h/6*tmp1[KLOOKUP(kx,ky,params.S)];
|
||||
for(kx=-K1;kx<=K1;kx++){
|
||||
for(ky=-K2;ky<=K2;ky++){
|
||||
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)];
|
||||
}
|
||||
}
|
||||
|
||||
@@ -65,74 +313,82 @@ int ins_step(_Complex double* u, ns_params params, fft_vects vects, _Complex dou
|
||||
}
|
||||
|
||||
// right side of Irreversible Navier-Stokes equation
|
||||
int ins_rhs(_Complex double* out, _Complex double* u, ns_params params, fft_vects vects){
|
||||
int ins_rhs(
|
||||
_Complex double* out,
|
||||
_Complex double* u,
|
||||
int K1,
|
||||
int K2,
|
||||
int N1,
|
||||
int N2,
|
||||
double nu,
|
||||
_Complex double (*g)(int,int),
|
||||
fft_vect fft1,
|
||||
fft_vect fft2,
|
||||
fft_vect ifft
|
||||
){
|
||||
int kx,ky;
|
||||
int i;
|
||||
|
||||
// F(px/|p|*u)*F(qy*|q|*u)
|
||||
// init to 0
|
||||
for(kx=0; kx<params.N*params.N; kx++){
|
||||
vects.fft1[kx]=0;
|
||||
vects.fft2[kx]=0;
|
||||
vects.invfft[kx]=0;
|
||||
for(i=0; i<N1*N2; i++){
|
||||
fft1.fft[i]=0;
|
||||
fft2.fft[i]=0;
|
||||
ifft.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)]=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)];
|
||||
fft1.fft[klookup(kx,ky,N1,N2)]=kx/sqrt(kx*kx+ky*ky)*u[klookup(kx,ky,2*K1+1,2*K2+1)];
|
||||
fft2.fft[klookup(kx,ky,N1,N2)]=ky*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.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);
|
||||
}
|
||||
|
||||
@@ -4,45 +4,38 @@
|
||||
#include <complex.h>
|
||||
#include <fftw3.h>
|
||||
|
||||
// to extract elements from array of size S representing a function of momentum, use
|
||||
// array[KEXTRACT(kx,ky,size)]
|
||||
#define KLOOKUP(X,Y,S) (X>=0?X:S+X)*S+(Y>=0?Y:S+Y)
|
||||
|
||||
|
||||
// parameters for the NS equation
|
||||
typedef struct ns_params {
|
||||
// number of modes
|
||||
int K;
|
||||
// 2*K+1
|
||||
int S;
|
||||
// 4*K+1
|
||||
int N;
|
||||
// forcing term
|
||||
_Complex double* g;
|
||||
// time step
|
||||
double h;
|
||||
// friction
|
||||
double nu;
|
||||
} ns_params;
|
||||
|
||||
// arrays on which the ffts are performed
|
||||
typedef struct fft_vects {
|
||||
fftw_complex* fft1;
|
||||
fftw_complex* fft2;
|
||||
fftw_complex* invfft;
|
||||
fftw_plan fft1_plan;
|
||||
fftw_plan fft2_plan;
|
||||
fftw_plan invfft_plan;
|
||||
} fft_vects;
|
||||
fftw_complex* fft;
|
||||
fftw_plan fft_plan;
|
||||
} fft_vect;
|
||||
|
||||
// compute u_k
|
||||
int uk( int K1, int K2, int N1, int N2, unsigned int nsteps, double nu, double delta, _Complex double (*g)(int,int), unsigned int print_freq);
|
||||
|
||||
// compute enstrophy
|
||||
int enstrophy( int K1, int K2, int N1, int N2, unsigned int nsteps, double nu, double delta, _Complex double (*g)(int,int), unsigned int print_freq);
|
||||
|
||||
// initialize vectors for computation
|
||||
int ns_init_tmps( _Complex double **u, _Complex double ** tmp1, _Complex double **tmp2, _Complex double **tmp3, fft_vect* fft1, fft_vect *fft2, fft_vect *ifft, int K1, int K2, int N1, int N2);
|
||||
// release vectors
|
||||
int ns_free_tmps( _Complex double* u, _Complex double* tmp1, _Complex double *tmp2,_Complex double *tmp3, fft_vect fft1, fft_vect fft2, fft_vect ifft);
|
||||
|
||||
// initial value
|
||||
int ns_init_u( _Complex double* u, int K1, int K2);
|
||||
|
||||
// next time step for Irreversible Navier-Stokes equation
|
||||
int ins_step(_Complex double* u, ns_params params, fft_vects vects, _Complex double* tmp1, _Complex double* tmp2, _Complex double* tmp3);
|
||||
int ins_step( _Complex double* u, int K1, int K2, int N1, int N2, double nu, double delta, _Complex double (*g)(int,int), fft_vect fft1, fft_vect fft2,fft_vect ifft, _Complex double* tmp1, _Complex double *tmp2, _Complex double *tmp3);
|
||||
|
||||
// right side of Irreversible Navier-Stokes equation
|
||||
int ins_rhs(_Complex double* out, _Complex double* u, ns_params params, fft_vects vects);
|
||||
int ins_rhs( _Complex double* out, _Complex double* u, int K1, int K2, int N1, int N2, double nu, _Complex double (*g)(int,int), fft_vect fft1, fft_vect fft2, fft_vect ifft);
|
||||
|
||||
// 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));
|
||||
|
||||
// get index for kx,ky in array of size S
|
||||
int klookup( int kx, int ky, int S1, int S2);
|
||||
|
||||
#endif
|
||||
|
||||
|
||||
Reference in New Issue
Block a user