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RKF45 algorithm

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This commit is contained in:
Ian Jauslin 2023-05-15 20:29:06 -04:00
parent 315e9a98de
commit 5db3680b31
5 changed files with 325 additions and 62 deletions
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13
README.md
View File

@ -68,7 +68,9 @@ should be a `;` sperated list of `key=value` pairs. The possible keys are
* `print_freq` (long int, default 1000): only print every `print_freq` steps. * `print_freq` (long int, default 1000): only print every `print_freq` steps.
* `starting_time` (long int, default 0): start the computation at this step. * `starting_step` (long int, default 0): start the computation at this step.
* `starting_time` (double, default starting_time*delta): start the computation at this time.
* `driving`: either `zero` for no driving, `test` (default) for a testing * `driving`: either `zero` for no driving, `test` (default) for a testing
driving force or `file:<filename>` or `file_txt:<filename>` to read the driving force or `file:<filename>` or `file_txt:<filename>` to read the
@ -91,7 +93,14 @@ should be a `;` sperated list of `key=value` pairs. The possible keys are
* `random_seed` (int, default ): seed for random initialization. * `random_seed` (int, default ): seed for random initialization.
* `algorithm`: either `RK4` for Runge-Kutta 4, or `RK2` for Runge-Kutta 2. * `algorithm`: either `RK4` for Runge-Kutta 4, `RK2` for Runge-Kutta 2, or
`RKF45` for the Runge-Kutta-Fehlberg adaptive step method.
* `adaptive_tolerance` (double, default 1e-11): when using an adaptive step
method, this is the maximal allowed relative error.
* `adaptive_factor` (double, default 0.9): when using the RKF45 method, the
step gets adjusted by `factor*delta*(tolerance/error)^(1/5)`.
# Interrupting/resuming the computation # Interrupting/resuming the computation

5
src/constants.cpp
View File

@ -29,6 +29,9 @@ limitations under the License.
#define INIT_FILE 3 #define INIT_FILE 3
#define INIT_FILE_TXT 4 #define INIT_FILE_TXT 4
#define ALGORITHM_RK4 4 #define ALGORITHM_RK4 1
#define ALGORITHM_RK2 2 #define ALGORITHM_RK2 2
#define ALGORITHM_ADAPTIVE_THRESHOLD 1000
// adaptive algorithms: index > ALGORITHM_ADAPTIVE_THRESHOLD
#define ALGORITHM_RKF45 1001

86
src/main.c
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@ -46,9 +46,12 @@ typedef struct nstrophy_parameters {
double nu; double nu;
double delta; double delta;
double L; double L;
double adaptive_tolerance;
double adaptive_factor;
uint64_t print_freq; uint64_t print_freq;
int seed; int seed;
uint64_t starting_time; uint64_t starting_step;
double starting_time;
unsigned int driving; unsigned int driving;
unsigned int init; unsigned int init;
unsigned int algorithm; unsigned int algorithm;
@ -64,12 +67,12 @@ int print_params(nstrophy_parameters parameters, char* initfile_str, char* drivi
// read command line arguments // read command line arguments
int read_args(int argc, const char* argv[], char** params, unsigned int* command, unsigned int* nthreads, char** savefile_str); int read_args(int argc, const char* argv[], char** params, unsigned int* command, unsigned int* nthreads, char** savefile_str);
int read_params(char* param_str, nstrophy_parameters* parameters, char** initfile_str, char** drivingfile_str); int read_params(char* param_str, nstrophy_parameters* parameters, char** initfile_str, char** drivingfile_str);
int set_parameter(char* lhs, char* rhs, nstrophy_parameters* parameters, bool* setN1, bool* setN2, char** initfile_str, char** drivingfile_str); int set_parameter(char* lhs, char* rhs, nstrophy_parameters* parameters, bool* setN1, bool* setN2, bool* set_starting_time, char** initfile_str, char** drivingfile_str);
// set driving force // set driving force
_Complex double* set_driving(nstrophy_parameters parameters); _Complex double* set_driving(nstrophy_parameters parameters);
// set initial condition // set initial condition
_Complex double* set_init(nstrophy_parameters parameters); _Complex double* set_init(nstrophy_parameters* parameters);
// signal handler // signal handler
void sig_handler (int signo); void sig_handler (int signo);
@ -134,7 +137,7 @@ int main (
// set driving force // set driving force
g=set_driving(parameters); g=set_driving(parameters);
// set initial condition // set initial condition
u0=set_init(parameters); u0=set_init(&parameters);
// close initfile (do this early, so that it is possible to use the same file for init and save) // close initfile (do this early, so that it is possible to use the same file for init and save)
if (parameters.initfile!=NULL){ if (parameters.initfile!=NULL){
@ -169,15 +172,15 @@ int main (
// run command // run command
if (command==COMMAND_UK){ if (command==COMMAND_UK){
uk(parameters.K1, parameters.K2, parameters.N1, parameters.N2, parameters.nsteps, parameters.nu, parameters.delta, parameters.L, u0, g, parameters.irreversible, parameters.algorithm, parameters.print_freq, parameters.starting_time, nthreads, savefile); uk(parameters.K1, parameters.K2, parameters.N1, parameters.N2, parameters.nsteps, parameters.nu, parameters.delta, parameters.L, parameters.adaptive_tolerance, parameters.adaptive_factor, u0, g, parameters.irreversible, parameters.algorithm, parameters.print_freq, parameters.starting_step, parameters.starting_time, nthreads, savefile);
} }
else if(command==COMMAND_ENSTROPHY){ else if(command==COMMAND_ENSTROPHY){
// register signal handler to handle aborts // register signal handler to handle aborts
signal(SIGINT, sig_handler); signal(SIGINT, sig_handler);
enstrophy(parameters.K1, parameters.K2, parameters.N1, parameters.N2, parameters.nsteps, parameters.nu, parameters.delta, parameters.L, u0, g, parameters.irreversible, parameters.algorithm, parameters.print_freq, parameters.starting_time, nthreads, savefile, (char*)argv[0], param_str, savefile_str); enstrophy(parameters.K1, parameters.K2, parameters.N1, parameters.N2, parameters.nsteps, parameters.nu, parameters.delta, parameters.L, parameters.adaptive_tolerance, parameters.adaptive_factor, u0, g, parameters.irreversible, parameters.algorithm, parameters.print_freq, parameters.starting_step, parameters.starting_time, nthreads, savefile, (char*)argv[0], param_str, savefile_str);
} }
else if(command==COMMAND_QUIET){ else if(command==COMMAND_QUIET){
quiet(parameters.K1, parameters.K2, parameters.N1, parameters.N2, parameters.nsteps, parameters.nu, parameters.delta, parameters.L, parameters.starting_time, u0, g, parameters.irreversible, parameters.algorithm, nthreads, savefile); quiet(parameters.K1, parameters.K2, parameters.N1, parameters.N2, parameters.nsteps, parameters.nu, parameters.delta, parameters.L, parameters.adaptive_tolerance, parameters.adaptive_factor, parameters.starting_step, u0, g, parameters.irreversible, parameters.algorithm, nthreads, savefile);
} }
else if(command==0){ else if(command==0){
fprintf(stderr, "error: no command specified\n"); fprintf(stderr, "error: no command specified\n");
@ -261,6 +264,9 @@ int print_params(
case ALGORITHM_RK2: case ALGORITHM_RK2:
fprintf(file,", algorithm=RK2"); fprintf(file,", algorithm=RK2");
break; break;
case ALGORITHM_RKF45:
fprintf(file,", algorithm=RKF45, tolerance=%.15e, factor=%.15e",parameters.adaptive_tolerance, parameters.adaptive_factor);
break;
default: default:
fprintf(file,", algorithm=RK4"); fprintf(file,", algorithm=RK4");
break; break;
@ -371,6 +377,7 @@ int read_params(
// whether N was set explicitly // whether N was set explicitly
bool setN1=false; bool setN1=false;
bool setN2=false; bool setN2=false;
bool set_starting_time=false;
// whether lhs (false is rhs) // whether lhs (false is rhs)
bool lhs=true; bool lhs=true;
@ -384,9 +391,12 @@ int read_params(
//nu=2^-11 //nu=2^-11
parameters->nu=0.00048828125; parameters->nu=0.00048828125;
parameters->L=2*M_PI; parameters->L=2*M_PI;
parameters->adaptive_tolerance=1e-11;
parameters->adaptive_factor=0.9;
parameters->nsteps=10000000; parameters->nsteps=10000000;
parameters->print_freq=1000; parameters->print_freq=1000;
parameters->starting_time=0; parameters->starting_time=0;
parameters->starting_step=0;
parameters->seed=17; parameters->seed=17;
parameters->driving=DRIVING_TEST; parameters->driving=DRIVING_TEST;
parameters->drivingfile=NULL; parameters->drivingfile=NULL;
@ -413,7 +423,7 @@ int read_params(
break; break;
case ';': case ';':
//set parameter //set parameter
ret=set_parameter(buffer_lhs, buffer_rhs, parameters, &setN1, &setN2, initfile_str, drivingfile_str); ret=set_parameter(buffer_lhs, buffer_rhs, parameters, &setN1, &setN2, &set_starting_time, initfile_str, drivingfile_str);
if(ret<0){ if(ret<0){
return ret; return ret;
} }
@ -440,7 +450,7 @@ int read_params(
// set last param // set last param
if (*param_str!='\0'){ if (*param_str!='\0'){
ret=set_parameter(buffer_lhs, buffer_rhs, parameters, &setN1, &setN2, initfile_str, drivingfile_str); ret=set_parameter(buffer_lhs, buffer_rhs, parameters, &setN1, &setN2, &set_starting_time, initfile_str, drivingfile_str);
if(ret<0){ if(ret<0){
return ret; return ret;
} }
@ -459,6 +469,10 @@ int read_params(
parameters->N2=smallest_pow2(3*(parameters->K2)); parameters->N2=smallest_pow2(3*(parameters->K2));
} }
// if starting_time not set explicitly and algorithm is not adaptive, set it to delta*starting_step
if (!set_starting_time && parameters->algorithm<ALGORITHM_ADAPTIVE_THRESHOLD){
parameters->starting_time=parameters->delta*parameters->starting_step;
}
return(0); return(0);
} }
@ -470,6 +484,7 @@ int set_parameter(
nstrophy_parameters* parameters, nstrophy_parameters* parameters,
bool* setN1, bool* setN1,
bool* setN2, bool* setN2,
bool* set_starting_time,
char** initfile_str, char** initfile_str,
char** drivingfile_str char** drivingfile_str
){ ){
@ -570,6 +585,20 @@ int set_parameter(
return(-1); return(-1);
} }
} }
else if (strcmp(lhs,"adaptive_tolerance")==0){
ret=sscanf(rhs,"%lf",&(parameters->adaptive_tolerance));
if(ret!=1){
fprintf(stderr, "error: parameter 'adaptive_tolerance' should be a double\n got '%s'\n",rhs);
return(-1);
}
}
else if (strcmp(lhs,"adaptive_factor")==0){
ret=sscanf(rhs,"%lf",&(parameters->adaptive_factor));
if(ret!=1){
fprintf(stderr, "error: parameter 'adaptive_factor' should be a double\n got '%s'\n",rhs);
return(-1);
}
}
else if (strcmp(lhs,"print_freq")==0){ else if (strcmp(lhs,"print_freq")==0){
ret=sscanf(rhs,"%lu",&(parameters->print_freq)); ret=sscanf(rhs,"%lu",&(parameters->print_freq));
if(ret!=1){ if(ret!=1){
@ -584,13 +613,21 @@ int set_parameter(
return(-1); return(-1);
} }
} }
else if (strcmp(lhs,"starting_time")==0){ else if (strcmp(lhs,"starting_step")==0){
ret=sscanf(rhs,"%lu",&(parameters->starting_time)); ret=sscanf(rhs,"%lu",&(parameters->starting_step));
if(ret!=1){ if(ret!=1){
fprintf(stderr, "error: parameter 'starting_time' should be an unsigned integer\n got '%s'\n",rhs); fprintf(stderr, "error: parameter 'starting_step' should be a long unsigned integer\n got '%s'\n",rhs);
return(-1); return(-1);
} }
} }
else if (strcmp(lhs,"starting_time")==0){
ret=sscanf(rhs,"%lf",&(parameters->starting_time));
if(ret!=1){
fprintf(stderr, "error: parameter 'starting_time' should be a double\n got '%s'\n",rhs);
return(-1);
}
*set_starting_time=true;
}
else if (strcmp(lhs,"driving")==0){ else if (strcmp(lhs,"driving")==0){
if (strcmp(rhs,"zero")==0){ if (strcmp(rhs,"zero")==0){
parameters->driving=DRIVING_ZERO; parameters->driving=DRIVING_ZERO;
@ -648,6 +685,9 @@ int set_parameter(
else if (strcmp(rhs,"RK2")==0){ else if (strcmp(rhs,"RK2")==0){
parameters->algorithm=ALGORITHM_RK2; parameters->algorithm=ALGORITHM_RK2;
} }
else if (strcmp(rhs,"RKF45")==0){
parameters->algorithm=ALGORITHM_RKF45;
}
else{ else{
fprintf(stderr, "error: unrecognized algorithm '%s'\n",rhs); fprintf(stderr, "error: unrecognized algorithm '%s'\n",rhs);
return(-1); return(-1);
@ -692,29 +732,35 @@ _Complex double* set_driving(
// set initial condition // set initial condition
_Complex double* set_init( _Complex double* set_init(
nstrophy_parameters parameters nstrophy_parameters* parameters
){ ){
_Complex double* u0=calloc(sizeof(_Complex double),parameters.K1*(2*parameters.K2+1)+parameters.K2); _Complex double* u0=calloc(sizeof(_Complex double),parameters->K1*(2*parameters->K2+1)+parameters->K2);
switch(parameters.init){ switch(parameters->init){
case INIT_RANDOM: case INIT_RANDOM:
init_random(u0, parameters.init_en, parameters.K1, parameters.K2, parameters.L, parameters.seed, parameters.irreversible); init_random(u0, parameters->init_en, parameters->K1, parameters->K2, parameters->L, parameters->seed, parameters->irreversible);
break; break;
case INIT_GAUSSIAN: case INIT_GAUSSIAN:
init_gaussian(u0, parameters.init_en, parameters.K1, parameters.K2, parameters.L, parameters.irreversible); init_gaussian(u0, parameters->init_en, parameters->K1, parameters->K2, parameters->L, parameters->irreversible);
break; break;
case INIT_FILE: case INIT_FILE:
init_file_bin(u0, parameters.K1, parameters.K2, parameters.initfile); init_file_bin(u0, parameters->K1, parameters->K2, parameters->initfile);
if(parameters->algorithm>ALGORITHM_ADAPTIVE_THRESHOLD){
// read delta
fread(&(parameters->delta), sizeof(double), 1, parameters->initfile);
// read start time
fread(&(parameters->starting_time), sizeof(double), 1, parameters->initfile);
}
break; break;
case INIT_FILE_TXT: case INIT_FILE_TXT:
init_file_txt(u0, parameters.K1, parameters.K2, parameters.initfile); init_file_txt(u0, parameters->K1, parameters->K2, parameters->initfile);
break; break;
default: default:
init_gaussian(u0, parameters.init_en, parameters.K1, parameters.K2, parameters.L, parameters.irreversible); init_gaussian(u0, parameters->init_en, parameters->K1, parameters->K2, parameters->L, parameters->irreversible);
break; break;
} }

261
src/navier-stokes.c
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@ -32,26 +32,34 @@ int uk(
double nu, double nu,
double delta, double delta,
double L, double L,
double adaptive_tolerance,
double adaptive_factor,
_Complex double* u0, _Complex double* u0,
_Complex double* g, _Complex double* g,
bool irreversible, bool irreversible,
unsigned int algorithm, unsigned int algorithm,
uint64_t print_freq, uint64_t print_freq,
uint64_t starting_time, uint64_t starting_step,
double starting_time,
unsigned int nthreads, unsigned int nthreads,
FILE* savefile FILE* savefile
){ ){
double time=starting_time;
_Complex double* u; _Complex double* u;
_Complex double* tmp1; _Complex double* tmp1;
_Complex double* tmp2; _Complex double* tmp2;
_Complex double* tmp3; _Complex double* tmp3;
_Complex double* tmp4;
_Complex double* tmp5;
_Complex double* tmp6;
_Complex double* tmp7;
uint64_t t; uint64_t t;
fft_vect fft1; fft_vect fft1;
fft_vect fft2; fft_vect fft2;
fft_vect ifft; fft_vect ifft;
int kx,ky; int kx,ky;
ns_init_tmps(&u, &tmp1, &tmp2, &tmp3, &fft1, &fft2, &ifft, K1, K2, N1, N2, nthreads); ns_init_tmps(&u, &tmp1, &tmp2, &tmp3, &tmp4, &tmp5, &tmp6, &tmp7, &fft1, &fft2, &ifft, K1, K2, N1, N2, nthreads, algorithm);
// copy initial condition // copy initial condition
copy_u(u, u0, K1, K2); copy_u(u, u0, K1, K2);
@ -68,16 +76,22 @@ int uk(
} }
// iterate // iterate
for(t=starting_time;nsteps==0 || t<starting_time+nsteps;t++){ for(t=starting_step;nsteps==0 || t<starting_step+nsteps;t++){
if(algorithm==ALGORITHM_RK2){ if(algorithm==ALGORITHM_RK2){
ns_step_rk2(u, K1, K2, N1, N2, nu, delta, L, g, fft1, fft2, ifft, tmp1, tmp2, irreversible); ns_step_rk2(u, K1, K2, N1, N2, nu, delta, L, g, fft1, fft2, ifft, tmp1, tmp2, irreversible);
} else { } else if (algorithm==ALGORITHM_RK4) {
ns_step_rk4(u, K1, K2, N1, N2, nu, delta, L, g, fft1, fft2, ifft, tmp1, tmp2, tmp3, irreversible); ns_step_rk4(u, K1, K2, N1, N2, nu, delta, L, g, fft1, fft2, ifft, tmp1, tmp2, tmp3, irreversible);
} else if (algorithm==ALGORITHM_RKF45) {
delta=ns_step_rkf45(u, adaptive_tolerance, adaptive_factor, K1, K2, N1, N2, nu, delta, L, g, fft1, fft2, ifft, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7, irreversible);
} else {
fprintf(stderr,"bug: unknown algorithm: %u, contact ian.jauslin@rutgers,edu\n",algorithm);
} }
time+=delta;
if(t%print_freq==0){ if(t%print_freq==0){
fprintf(stderr,"%lu % .8e ",t,t*delta); fprintf(stderr,"%lu % .8e ",t,time);
printf("%8lu % .15e ",t,t*delta); printf("%8lu % .15e ",t,time);
for(kx=-K1;kx<=K1;kx++){ for(kx=-K1;kx<=K1;kx++){
for (ky=-K2;ky<=K2;ky++){ for (ky=-K2;ky<=K2;ky++){
@ -96,7 +110,7 @@ int uk(
// save final entry to savefile // save final entry to savefile
write_vec_bin(u, K1, K2, savefile); write_vec_bin(u, K1, K2, savefile);
ns_free_tmps(u, tmp1, tmp2, tmp3, fft1, fft2, ifft); ns_free_tmps(u, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7, fft1, fft2, ifft, algorithm);
return(0); return(0);
} }
@ -110,12 +124,15 @@ int enstrophy(
double nu, double nu,
double delta, double delta,
double L, double L,
double adaptive_tolerance,
double adaptive_factor,
_Complex double* u0, _Complex double* u0,
_Complex double* g, _Complex double* g,
bool irreversible, bool irreversible,
unsigned int algorithm, unsigned int algorithm,
uint64_t print_freq, uint64_t print_freq,
uint64_t starting_time, uint64_t starting_step,
double starting_time,
unsigned int nthreads, unsigned int nthreads,
FILE* savefile, FILE* savefile,
// for interrupt recovery // for interrupt recovery
@ -127,6 +144,11 @@ int enstrophy(
_Complex double* tmp1; _Complex double* tmp1;
_Complex double* tmp2; _Complex double* tmp2;
_Complex double* tmp3; _Complex double* tmp3;
_Complex double* tmp4;
_Complex double* tmp5;
_Complex double* tmp6;
_Complex double* tmp7;
double time=starting_time;
double alpha, enstrophy; double alpha, enstrophy;
double avg_a,avg_en,avg_en_x_a; double avg_a,avg_en,avg_en_x_a;
// index // index
@ -135,7 +157,7 @@ int enstrophy(
fft_vect fft2; fft_vect fft2;
fft_vect ifft; fft_vect ifft;
ns_init_tmps(&u, &tmp1, &tmp2, &tmp3, &fft1, &fft2, &ifft, K1, K2, N1, N2, nthreads); ns_init_tmps(&u, &tmp1, &tmp2, &tmp3, &tmp4, &tmp5, &tmp6, &tmp7, &fft1, &fft2, &ifft, K1, K2, N1, N2, nthreads, algorithm);
// copy initial condition // copy initial condition
copy_u(u, u0, K1, K2); copy_u(u, u0, K1, K2);
@ -146,26 +168,38 @@ int enstrophy(
avg_en_x_a=0; avg_en_x_a=0;
// special first case when starting_time is not a multiple of print_freq // special first case when starting_time is not a multiple of print_freq
uint64_t first_box = print_freq - (starting_time % print_freq); uint64_t first_box = print_freq - (starting_step % print_freq);
// iterate // iterate
for(t=starting_time;nsteps==0 || t<starting_time+nsteps;t++){ for(t=starting_step;nsteps==0 || t<starting_step+nsteps;t++){
if(algorithm==ALGORITHM_RK2){ if(algorithm==ALGORITHM_RK2){
ns_step_rk2(u, K1, K2, N1, N2, nu, delta, L, g, fft1, fft2, ifft, tmp1, tmp2, irreversible); ns_step_rk2(u, K1, K2, N1, N2, nu, delta, L, g, fft1, fft2, ifft, tmp1, tmp2, irreversible);
} else { } else if (algorithm==ALGORITHM_RK4) {
ns_step_rk4(u, K1, K2, N1, N2, nu, delta, L, g, fft1, fft2, ifft, tmp1, tmp2, tmp3, irreversible); ns_step_rk4(u, K1, K2, N1, N2, nu, delta, L, g, fft1, fft2, ifft, tmp1, tmp2, tmp3, irreversible);
} else if (algorithm==ALGORITHM_RKF45) {
delta=ns_step_rkf45(u, adaptive_tolerance, adaptive_factor, K1, K2, N1, N2, nu, delta, L, g, fft1, fft2, ifft, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7, irreversible);
} else {
fprintf(stderr,"bug: unknown algorithm: %u, contact ian.jauslin@rutgers,edu\n",algorithm);
} }
time+=delta;
alpha=compute_alpha(u, K1, K2, g, L); alpha=compute_alpha(u, K1, K2, g, L);
enstrophy=compute_enstrophy(u, K1, K2, L); enstrophy=compute_enstrophy(u, K1, K2, L);
avg_a=average_step(alpha, avg_a, t, starting_time, print_freq, first_box); avg_a=average_step(alpha, avg_a, t, starting_step, print_freq, first_box);
avg_en=average_step(enstrophy, avg_en, t, starting_time, print_freq, first_box); avg_en=average_step(enstrophy, avg_en, t, starting_step, print_freq, first_box);
avg_en_x_a=average_step(enstrophy*alpha, avg_en_x_a, t, starting_time, print_freq, first_box); avg_en_x_a=average_step(enstrophy*alpha, avg_en_x_a, t, starting_step, print_freq, first_box);
if(t>starting_time && t%print_freq==0){ if(t>starting_step && t%print_freq==0){
fprintf(stderr,"%lu % .8e % .8e % .8e % .8e % .8e % .8e % .8e\n",t,t*delta, avg_a, avg_en_x_a, avg_en, alpha, alpha*enstrophy, enstrophy); // print to stderr so user can follow along
printf("%8lu % .15e % .15e % .15e % .15e % .15e % .15e % .15e\n",t,t*delta, avg_a, avg_en_x_a, avg_en, alpha, alpha*enstrophy, enstrophy); if(algorithm==ALGORITHM_RKF45){
fprintf(stderr,"%lu % .8e % .8e % .8e % .8e % .8e % .8e % .8e % .8e\n",t,time, avg_a, avg_en_x_a, avg_en, alpha, alpha*enstrophy, enstrophy, delta);
} else {
fprintf(stderr,"%lu % .8e % .8e % .8e % .8e % .8e % .8e % .8e\n",t,time, avg_a, avg_en_x_a, avg_en, alpha, alpha*enstrophy, enstrophy);
}
// print to stdout
printf("%8lu % .15e % .15e % .15e % .15e % .15e % .15e % .15e\n",t,time, avg_a, avg_en_x_a, avg_en, alpha, alpha*enstrophy, enstrophy);
} }
// catch abort signal // catch abort signal
@ -189,11 +223,24 @@ int enstrophy(
if(params_string!=NULL) { if(params_string!=NULL) {
char* params=calloc(sizeof(char), strlen(params_string)+1); char* params=calloc(sizeof(char), strlen(params_string)+1);
strcpy(params, params_string); strcpy(params, params_string);
remove_entry(params, "starting_step");
remove_entry(params, "starting_time"); remove_entry(params, "starting_time");
remove_entry(params, "init"); remove_entry(params, "init");
remove_entry(params, "nsteps"); remove_entry(params, "nsteps");
fprintf(savefile," -p \"%s;starting_time=%lu;nsteps=%lu;init=file:%s\"", params, t+1, (nsteps+starting_time < t+1 ? 0 : nsteps+starting_time-t-1), savefile_string); if(algorithm>ALGORITHM_ADAPTIVE_THRESHOLD){
remove_entry(params, "delta");
}
fprintf(savefile," -p \"%s;starting_step=%lu;nsteps=%lu;init=file:%s", params, t+1, (nsteps+starting_step < t+1 ? 0 : nsteps+starting_step-t-1), savefile_string);
free(params); free(params);
// write delta if adaptive, and not writing binary
if(algorithm>ALGORITHM_ADAPTIVE_THRESHOLD && (savefile==stderr || savefile==stdout)){
fprintf(savefile,";delta=%.15e;starting_time=%.15e", delta, starting_time);
}
// write starting_time if not adaptive
if(algorithm<ALGORITHM_ADAPTIVE_THRESHOLD){
fprintf(savefile,";starting_time=%.15e", starting_time);
}
fprintf(savefile,"\"");
} }
fprintf(savefile," enstrophy\n"); fprintf(savefile," enstrophy\n");
@ -202,10 +249,17 @@ int enstrophy(
write_vec(u, K1, K2, savefile); write_vec(u, K1, K2, savefile);
} else { } else {
write_vec_bin(u, K1, K2, savefile); write_vec_bin(u, K1, K2, savefile);
// extra binary data for adaptive algorithm
if(algorithm>ALGORITHM_ADAPTIVE_THRESHOLD){
// first binary entry: delta
fwrite(&delta, sizeof(double), 1, savefile);
// ssecond binary entry: starting time
fwrite(&starting_time, sizeof(double), 1, savefile);
}
} }
} }
ns_free_tmps(u, tmp1, tmp2, tmp3, fft1, fft2, ifft); ns_free_tmps(u, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7, fft1, fft2, ifft, algorithm);
return(0); return(0);
} }
@ -219,7 +273,9 @@ int quiet(
double nu, double nu,
double delta, double delta,
double L, double L,
uint64_t starting_time, double adaptive_tolerance,
double adaptive_factor,
uint64_t starting_step,
_Complex double* u0, _Complex double* u0,
_Complex double* g, _Complex double* g,
bool irreversible, bool irreversible,
@ -231,28 +287,36 @@ int quiet(
_Complex double* tmp1; _Complex double* tmp1;
_Complex double* tmp2; _Complex double* tmp2;
_Complex double* tmp3; _Complex double* tmp3;
_Complex double* tmp4;
_Complex double* tmp5;
_Complex double* tmp6;
_Complex double* tmp7;
uint64_t t; uint64_t t;
fft_vect fft1; fft_vect fft1;
fft_vect fft2; fft_vect fft2;
fft_vect ifft; fft_vect ifft;
ns_init_tmps(&u, &tmp1, &tmp2, &tmp3, &fft1, &fft2, &ifft, K1, K2, N1, N2, nthreads); ns_init_tmps(&u, &tmp1, &tmp2, &tmp3, &tmp4, &tmp5, &tmp6, &tmp7, &fft1, &fft2, &ifft, K1, K2, N1, N2, nthreads, algorithm);
// copy initial condition // copy initial condition
copy_u(u, u0, K1, K2); copy_u(u, u0, K1, K2);
// iterate // iterate
for(t=starting_time;nsteps==0 || t<starting_time+nsteps;t++){ for(t=starting_step;nsteps==0 || t<starting_step+nsteps;t++){
if(algorithm==ALGORITHM_RK2){ if(algorithm==ALGORITHM_RK2){
ns_step_rk2(u, K1, K2, N1, N2, nu, delta, L, g, fft1, fft2, ifft, tmp1, tmp2, irreversible); ns_step_rk2(u, K1, K2, N1, N2, nu, delta, L, g, fft1, fft2, ifft, tmp1, tmp2, irreversible);
} else { } else if (algorithm==ALGORITHM_RK4) {
ns_step_rk4(u, K1, K2, N1, N2, nu, delta, L, g, fft1, fft2, ifft, tmp1, tmp2, tmp3, irreversible); ns_step_rk4(u, K1, K2, N1, N2, nu, delta, L, g, fft1, fft2, ifft, tmp1, tmp2, tmp3, irreversible);
} else if (algorithm==ALGORITHM_RKF45) {
delta=ns_step_rkf45(u, adaptive_tolerance, adaptive_factor, K1, K2, N1, N2, nu, delta, L, g, fft1, fft2, ifft, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7, irreversible);
} else {
fprintf(stderr,"bug: unknown algorithm: %u, contact ian.jauslin@rutgers,edu\n",algorithm);
} }
} }
// save final entry to savefile // save final entry to savefile
write_vec(u, K1, K2, savefile); write_vec(u, K1, K2, savefile);
ns_free_tmps(u, tmp1, tmp2, tmp3, fft1, fft2, ifft); ns_free_tmps(u, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7, fft1, fft2, ifft, algorithm);
return(0); return(0);
} }
@ -263,6 +327,10 @@ int ns_init_tmps(
_Complex double ** tmp1, _Complex double ** tmp1,
_Complex double ** tmp2, _Complex double ** tmp2,
_Complex double ** tmp3, _Complex double ** tmp3,
_Complex double ** tmp4,
_Complex double ** tmp5,
_Complex double ** tmp6,
_Complex double ** tmp7,
fft_vect* fft1, fft_vect* fft1,
fft_vect* fft2, fft_vect* fft2,
fft_vect* ifft, fft_vect* ifft,
@ -270,15 +338,31 @@ int ns_init_tmps(
int K2, int K2,
int N1, int N1,
int N2, int N2,
unsigned int nthreads unsigned int nthreads,
unsigned int algorithm
){ ){
// velocity field // velocity field
*u=calloc(sizeof(_Complex double),K1*(2*K2+1)+K2); *u=calloc(sizeof(_Complex double),K1*(2*K2+1)+K2);
// allocate tmp vectors for computation // allocate tmp vectors for computation
if(algorithm==ALGORITHM_RK2){
*tmp1=calloc(sizeof(_Complex double),K1*(2*K2+1)+K2);
*tmp2=calloc(sizeof(_Complex double),K1*(2*K2+1)+K2);
} else if (algorithm==ALGORITHM_RK4){
*tmp1=calloc(sizeof(_Complex double),K1*(2*K2+1)+K2); *tmp1=calloc(sizeof(_Complex double),K1*(2*K2+1)+K2);
*tmp2=calloc(sizeof(_Complex double),K1*(2*K2+1)+K2); *tmp2=calloc(sizeof(_Complex double),K1*(2*K2+1)+K2);
*tmp3=calloc(sizeof(_Complex double),K1*(2*K2+1)+K2); *tmp3=calloc(sizeof(_Complex double),K1*(2*K2+1)+K2);
} else if (algorithm==ALGORITHM_RKF45){
*tmp1=calloc(sizeof(_Complex double),K1*(2*K2+1)+K2);
*tmp2=calloc(sizeof(_Complex double),K1*(2*K2+1)+K2);
*tmp3=calloc(sizeof(_Complex double),K1*(2*K2+1)+K2);
*tmp4=calloc(sizeof(_Complex double),K1*(2*K2+1)+K2);
*tmp5=calloc(sizeof(_Complex double),K1*(2*K2+1)+K2);
*tmp6=calloc(sizeof(_Complex double),K1*(2*K2+1)+K2);
*tmp7=calloc(sizeof(_Complex double),K1*(2*K2+1)+K2);
} else {
fprintf(stderr,"bug: unknown algorithm: %u, contact ian.jauslin@rutgers,edu\n",algorithm);
};
// init threads // init threads
fftw_init_threads(); fftw_init_threads();
@ -301,9 +385,14 @@ int ns_free_tmps(
_Complex double* tmp1, _Complex double* tmp1,
_Complex double* tmp2, _Complex double* tmp2,
_Complex double* tmp3, _Complex double* tmp3,
_Complex double* tmp4,
_Complex double* tmp5,
_Complex double* tmp6,
_Complex double* tmp7,
fft_vect fft1, fft_vect fft1,
fft_vect fft2, fft_vect fft2,
fft_vect ifft fft_vect ifft,
unsigned int algorithm
){ ){
// free memory // free memory
fftw_destroy_plan(fft1.fft_plan); fftw_destroy_plan(fft1.fft_plan);
@ -315,9 +404,24 @@ int ns_free_tmps(
fftw_cleanup_threads(); fftw_cleanup_threads();
free(tmp3); if(algorithm==ALGORITHM_RK2){
free(tmp2);
free(tmp1); free(tmp1);
free(tmp2);
} else if (algorithm==ALGORITHM_RK4){
free(tmp1);
free(tmp2);
free(tmp3);
} else if (algorithm==ALGORITHM_RKF45){
free(tmp1);
free(tmp2);
free(tmp3);
free(tmp4);
free(tmp5);
free(tmp6);
free(tmp7);
} else {
fprintf(stderr,"bug: unknown algorithm: %u, contact ian.jauslin@rutgers,edu\n",algorithm);
};
free(u); free(u);
@ -462,6 +566,105 @@ int ns_step_rk2(
return(0); return(0);
} }
// next time step
// adaptive RK algorithm (Runge-Kutta-Fehlberg)
double ns_step_rkf45(
_Complex double* u,
double tolerance,
double factor,
int K1,
int K2,
int N1,
int N2,
double nu,
double delta,
double L,
_Complex double* g,
fft_vect fft1,
fft_vect fft2,
fft_vect ifft,
_Complex double* k1,
_Complex double* k2,
_Complex double* k3,
_Complex double* k4,
_Complex double* k5,
_Complex double* k6,
_Complex double* tmp,
bool irreversible
){
int kx,ky;
double err;
// k1: u(t)
ns_rhs(k1, u, K1, K2, N1, N2, nu, L, g, fft1, fft2, ifft, irreversible);
// k2 : u(t+1/4*delta)
for(kx=0;kx<=K1;kx++){
for(ky=(kx>0 ? -K2 : 1);ky<=K2;ky++){
tmp[klookup_sym(kx,ky,K2)]=u[klookup_sym(kx,ky,K2)]+delta/4*k1[klookup_sym(kx,ky,K2)];
}
}
ns_rhs(k2, tmp, K1, K2, N1, N2, nu, L, g, fft1, fft2, ifft, irreversible);
// k3 : u(t+3/8*delta)
for(kx=0;kx<=K1;kx++){
for(ky=(kx>0 ? -K2 : 1);ky<=K2;ky++){
tmp[klookup_sym(kx,ky,K2)]=u[klookup_sym(kx,ky,K2)]+delta*(3./32*k1[klookup_sym(kx,ky,K2)]+9./32*k2[klookup_sym(kx,ky,K2)]);
}
}
ns_rhs(k3, tmp, K1, K2, N1, N2, nu, L, g, fft1, fft2, ifft, irreversible);
// k4 : u(t+12./13*delta)
for(kx=0;kx<=K1;kx++){
for(ky=(kx>0 ? -K2 : 1);ky<=K2;ky++){
tmp[klookup_sym(kx,ky,K2)]=u[klookup_sym(kx,ky,K2)]+delta*(1932./2197*k1[klookup_sym(kx,ky,K2)]-7200./2197*k2[klookup_sym(kx,ky,K2)]+7296./2197*k3[klookup_sym(kx,ky,K2)]);
}
}
ns_rhs(k4, tmp, K1, K2, N1, N2, nu, L, g, fft1, fft2, ifft, irreversible);
// k5 : u(t+1*delta)
for(kx=0;kx<=K1;kx++){
for(ky=(kx>0 ? -K2 : 1);ky<=K2;ky++){
tmp[klookup_sym(kx,ky,K2)]=u[klookup_sym(kx,ky,K2)]+delta*(439./216*k1[klookup_sym(kx,ky,K2)]-8*k2[klookup_sym(kx,ky,K2)]+3680./513*k3[klookup_sym(kx,ky,K2)]-845./4104*k4[klookup_sym(kx,ky,K2)]);
}
}
ns_rhs(k5, tmp, K1, K2, N1, N2, nu, L, g, fft1, fft2, ifft, irreversible);
// k6 : u(t+1./2*delta)
for(kx=0;kx<=K1;kx++){
for(ky=(kx>0 ? -K2 : 1);ky<=K2;ky++){
tmp[klookup_sym(kx,ky,K2)]=u[klookup_sym(kx,ky,K2)]+delta*(-8./27*k1[klookup_sym(kx,ky,K2)]+2*k2[klookup_sym(kx,ky,K2)]-3544./2565*k3[klookup_sym(kx,ky,K2)]+1859./4104*k4[klookup_sym(kx,ky,K2)]-11./40*k5[klookup_sym(kx,ky,K2)]);
}
}
ns_rhs(k6, tmp, K1, K2, N1, N2, nu, L, g, fft1, fft2, ifft, irreversible);
// compute error
err=0;
for(kx=0;kx<=K1;kx++){
for(ky=(kx>0 ? -K2 : 1);ky<=K2;ky++){
// difference between 5th order and 4th order
err+=cabs(delta*(1./360*k1[klookup_sym(kx,ky,K2)]-128./4275*k3[klookup_sym(kx,ky,K2)]-2197./75240*k4[klookup_sym(kx,ky,K2)]+1./50*k5[klookup_sym(kx,ky,K2)]+2./55*k6[klookup_sym(kx,ky,K2)]));
}
}
// new delta
delta=factor*delta*pow(tolerance/err,0.2);
// compare relative error with tolerance
if(err<tolerance){
// add to output
for(kx=0;kx<=K1;kx++){
for(ky=(kx>0 ? -K2 : 1);ky<=K2;ky++){
u[klookup_sym(kx,ky,K2)]+=delta*(16./135*k1[klookup_sym(kx,ky,K2)]+6656./12825*k3[klookup_sym(kx,ky,K2)]+28561./56430*k4[klookup_sym(kx,ky,K2)]-9./50*k5[klookup_sym(kx,ky,K2)]+2./55*k6[klookup_sym(kx,ky,K2)]);
}
}
return delta;
}
// error too big: repeat with smaller step
else{
return(ns_step_rkf45(u,tolerance,factor,K1,K2,N1,N2,nu,delta,L,g,fft1,fft2,ifft,k1,k2,k3,k4,k5,k6,tmp,irreversible));
}
}
// right side of Irreversible/Reversible Navier-Stokes equation // right side of Irreversible/Reversible Navier-Stokes equation
int ns_rhs( int ns_rhs(
_Complex double* out, _Complex double* out,

12
src/navier-stokes.h
View File

@ -34,19 +34,19 @@ typedef struct fft_vects {
} fft_vect; } fft_vect;
// compute u_k // compute u_k
int uk( int K1, int K2, int N1, int N2, uint64_t nsteps, double nu, double delta, double L, _Complex double* u0, _Complex double* g, bool irreversible, unsigned int algorithm, uint64_t print_freq, uint64_t starting_time, unsigned int nthreadsl, FILE* savefile); int uk( int K1, int K2, int N1, int N2, uint64_t nsteps, double nu, double delta, double L, double adaptive_tolerance, double adaptive_factor, _Complex double* u0, _Complex double* g, bool irreversible, unsigned int algorithm, uint64_t print_freq, uint64_t starting_step, double starting_time, unsigned int nthreadsl, FILE* savefile);
// compute enstrophy and alpha // compute enstrophy and alpha
int enstrophy( int K1, int K2, int N1, int N2, uint64_t nsteps, double nu, double delta, double L, _Complex double* u0, _Complex double* g, bool irreversible, unsigned int algorithm, uint64_t print_freq, uint64_t starting_time, unsigned int nthreads, FILE* savefile, char* cmd_string, char* params_string, char* savefile_string); int enstrophy( int K1, int K2, int N1, int N2, uint64_t nsteps, double nu, double delta, double L, double adaptive_tolerance, double adaptive_factor, _Complex double* u0, _Complex double* g, bool irreversible, unsigned int algorithm, uint64_t print_freq, uint64_t starting_step, double starting_time, unsigned int nthreads, FILE* savefile, char* cmd_string, char* params_string, char* savefile_string);
// compute solution as a function of time, but do not print anything (useful for debugging) // compute solution as a function of time, but do not print anything (useful for debugging)
int quiet( int K1, int K2, int N1, int N2, uint64_t nsteps, double nu, double delta, double L, uint64_t starting_time, _Complex double* u0, _Complex double* g, bool irreversible, unsigned int algorithm, unsigned int nthreads, FILE* savefile); int quiet( int K1, int K2, int N1, int N2, uint64_t nsteps, double nu, double delta, double L, double adaptive_tolerance, double adaptive_factor, uint64_t starting_step, _Complex double* u0, _Complex double* g, bool irreversible, unsigned int algorithm, unsigned int nthreads, FILE* savefile);
// initialize vectors for computation // 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, unsigned int nthreads); int ns_init_tmps( _Complex double **u, _Complex double ** tmp1, _Complex double **tmp2, _Complex double **tmp3, _Complex double **tmp4, _Complex double **tmp5, _Complex double **tmp6, _Complex double **tmp7, fft_vect* fft1, fft_vect *fft2, fft_vect *ifft, int K1, int K2, int N1, int N2, unsigned int nthreads, unsigned int algorithm);
// release vectors // 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); int ns_free_tmps( _Complex double* u, _Complex double* tmp1, _Complex double *tmp2,_Complex double *tmp3, _Complex double *tmp4, _Complex double *tmp5, _Complex double *tmp6, _Complex double *tmp7, fft_vect fft1, fft_vect fft2, fft_vect ifft, unsigned int algorithm);
// copy u0 to u // copy u0 to u
int copy_u( _Complex double* u, _Complex double* u0, int K1, int K2); int copy_u( _Complex double* u, _Complex double* u0, int K1, int K2);
@ -56,6 +56,8 @@ int copy_u( _Complex double* u, _Complex double* u0, int K1, int K2);
int ns_step_rk4( _Complex double* u, int K1, int K2, int N1, int N2, double nu, double delta, double L, _Complex double* g, fft_vect fft1, fft_vect fft2,fft_vect ifft, _Complex double* tmp1, _Complex double *tmp2, _Complex double *tmp3, bool irreversible); int ns_step_rk4( _Complex double* u, int K1, int K2, int N1, int N2, double nu, double delta, double L, _Complex double* g, fft_vect fft1, fft_vect fft2,fft_vect ifft, _Complex double* tmp1, _Complex double *tmp2, _Complex double *tmp3, bool irreversible);
// RK2 // RK2
int ns_step_rk2( _Complex double* u, int K1, int K2, int N1, int N2, double nu, double delta, double L, _Complex double* g, fft_vect fft1, fft_vect fft2,fft_vect ifft, _Complex double* tmp1, _Complex double *tmp2, bool irreversible); int ns_step_rk2( _Complex double* u, int K1, int K2, int N1, int N2, double nu, double delta, double L, _Complex double* g, fft_vect fft1, fft_vect fft2,fft_vect ifft, _Complex double* tmp1, _Complex double *tmp2, bool irreversible);
// adaptive RK algorithm (Runge-Kutta-Fehlberg)
double ns_step_rkf45( _Complex double* u, double tolerance, double factor, int K1, int K2, int N1, int N2, double nu, double delta, double L, _Complex double* g, fft_vect fft1, fft_vect fft2, fft_vect ifft, _Complex double* k1, _Complex double* k2, _Complex double* k3, _Complex double* k4, _Complex double* k5, _Complex double* k6, _Complex double* tmp, bool irreversible);
// right side of Irreversible/reversible Navier-Stokes equation // right side of Irreversible/reversible Navier-Stokes equation
int ns_rhs( _Complex double* out, _Complex double* u, int K1, int K2, int N1, int N2, double nu, double L, _Complex double* g, fft_vect fft1, fft_vect fft2, fft_vect ifft, bool irreversible); int ns_rhs( _Complex double* out, _Complex double* u, int K1, int K2, int N1, int N2, double nu, double L, _Complex double* g, fft_vect fft1, fft_vect fft2, fft_vect ifft, bool irreversible);