Adaptive timestep: do nto change delta before all the printing
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@ -77,20 +77,25 @@ int uk(
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// add 0.1 to ensure proper rounding
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uint64_t n=(uint64_t)((starting_time-fmod(starting_time, print_freq))/print_freq+0.1);
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// store step (useful for adaptive step methods
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double step=delta;
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double next_step=step;
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// iterate
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time=starting_time;
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while(final_time<0 || time<final_time){
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if(algorithm==ALGORITHM_RK2){
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ns_step_rk2(u, K1, K2, N1, N2, nu, delta, L, g, fft1, fft2, ifft, tmp1, tmp2, irreversible);
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ns_step_rk2(u, K1, K2, N1, N2, nu, step, L, g, fft1, fft2, ifft, tmp1, tmp2, irreversible);
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} else if (algorithm==ALGORITHM_RK4) {
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ns_step_rk4(u, K1, K2, N1, N2, nu, delta, L, g, fft1, fft2, ifft, tmp1, tmp2, tmp3, irreversible);
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ns_step_rk4(u, K1, K2, N1, N2, nu, step, L, g, fft1, fft2, ifft, tmp1, tmp2, tmp3, irreversible);
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} else if (algorithm==ALGORITHM_RKF45) {
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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);
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ns_step_rkf45(u, adaptive_tolerance, adaptive_factor, K1, K2, N1, N2, nu, &step, &next_step, L, g, fft1, fft2, ifft, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7, irreversible);
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} else {
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fprintf(stderr,"bug: unknown algorithm: %u, contact ian.jauslin@rutgers,edu\n",algorithm);
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}
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time+=delta;
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time+=step;
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step=next_step;
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if(time>(n+1)*print_freq){
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n++;
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@ -165,6 +170,9 @@ int enstrophy(
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// copy initial condition
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copy_u(u, u0, K1, K2);
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// store step (useful for adaptive step methods
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double step=delta;
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double next_step=step;
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// init running average
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avg_a=0;
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@ -180,24 +188,24 @@ int enstrophy(
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time=starting_time;
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while(final_time<0 || time<final_time){
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if(algorithm==ALGORITHM_RK2){
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ns_step_rk2(u, K1, K2, N1, N2, nu, delta, L, g, fft1, fft2, ifft, tmp1, tmp2, irreversible);
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ns_step_rk2(u, K1, K2, N1, N2, nu, step, L, g, fft1, fft2, ifft, tmp1, tmp2, irreversible);
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} else if (algorithm==ALGORITHM_RK4) {
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ns_step_rk4(u, K1, K2, N1, N2, nu, delta, L, g, fft1, fft2, ifft, tmp1, tmp2, tmp3, irreversible);
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ns_step_rk4(u, K1, K2, N1, N2, nu, step, L, g, fft1, fft2, ifft, tmp1, tmp2, tmp3, irreversible);
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} else if (algorithm==ALGORITHM_RKF45) {
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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);
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ns_step_rkf45(u, adaptive_tolerance, adaptive_factor, K1, K2, N1, N2, nu, &step, &next_step, L, g, fft1, fft2, ifft, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7, irreversible);
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} else {
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fprintf(stderr,"bug: unknown algorithm: %u, contact ian.jauslin@rutgers,edu\n",algorithm);
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}
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time+=delta;
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time+=step;
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alpha=compute_alpha(u, K1, K2, g, L);
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enstrophy=compute_enstrophy(u, K1, K2, L);
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// add to running averages (estimate the total duration of interval as print_freq, will be adjusted later)
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avg_a+=alpha*(delta/print_freq);
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avg_en+=enstrophy*(delta/print_freq);
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avg_en_x_a+=enstrophy*alpha*(delta/print_freq);
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avg_a+=alpha*(step/print_freq);
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avg_en+=enstrophy*(step/print_freq);
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avg_en_x_a+=enstrophy*alpha*(step/print_freq);
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if(time>(n+1)*print_freq){
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n++;
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@ -209,8 +217,8 @@ int enstrophy(
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// print to stderr so user can follow along
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if(algorithm==ALGORITHM_RKF45){
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fprintf(stderr,"% .8e % .8e % .8e % .8e % .8e % .8e % .8e % .8e\n",time, avg_a, avg_en, avg_en_x_a, alpha, enstrophy, alpha*enstrophy, delta);
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printf("% .15e % .15e % .15e % .15e % .15e % .15e % .15e % .15e\n",time, avg_a, avg_en_x_a, avg_en, alpha, alpha*enstrophy, enstrophy, delta);
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fprintf(stderr,"% .8e % .8e % .8e % .8e % .8e % .8e % .8e % .8e\n",time, avg_a, avg_en, avg_en_x_a, alpha, enstrophy, alpha*enstrophy, step);
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printf("% .15e % .15e % .15e % .15e % .15e % .15e % .15e % .15e\n",time, avg_a, avg_en_x_a, avg_en, alpha, alpha*enstrophy, enstrophy, step);
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} else {
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fprintf(stderr,"% .8e % .8e % .8e % .8e % .8e % .8e % .8e\n",time, avg_a, avg_en, avg_en_x_a, alpha, enstrophy, alpha*enstrophy);
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printf("% .15e % .15e % .15e % .15e % .15e % .15e % .15e\n",time, avg_a, avg_en_x_a, avg_en, alpha, alpha*enstrophy, enstrophy);
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@ -224,6 +232,10 @@ int enstrophy(
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avg_en_x_a=0;
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prevtime=time;
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// get ready for next step
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step=next_step;
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// catch abort signal
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if (g_abort){
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// print u to stderr if no savefile
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@ -254,7 +266,7 @@ int enstrophy(
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free(params);
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// write delta if adaptive, and not writing binary
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if(algorithm>ALGORITHM_ADAPTIVE_THRESHOLD && (savefile==stderr || savefile==stdout)){
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fprintf(savefile,";delta=%.15e", delta);
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fprintf(savefile,";delta=%.15e", step);
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}
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// write starting_time if not writing binary
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if(savefile==stderr || savefile==stdout){
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@ -273,7 +285,7 @@ int enstrophy(
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fwrite(&time, sizeof(double), 1, savefile);
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// extra binary data for adaptive algorithm
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if(algorithm>ALGORITHM_ADAPTIVE_THRESHOLD){
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fwrite(&delta, sizeof(double), 1, savefile);
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fwrite(&step, sizeof(double), 1, savefile);
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}
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}
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}
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@ -319,20 +331,26 @@ int quiet(
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// copy initial condition
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copy_u(u, u0, K1, K2);
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// store delta (useful for adaptive step algorithms)
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double step=delta;
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double next_step=step;
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// iterate
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time=starting_time;
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while(final_time<0 || time<final_time){
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if(algorithm==ALGORITHM_RK2){
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ns_step_rk2(u, K1, K2, N1, N2, nu, delta, L, g, fft1, fft2, ifft, tmp1, tmp2, irreversible);
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ns_step_rk2(u, K1, K2, N1, N2, nu, step, L, g, fft1, fft2, ifft, tmp1, tmp2, irreversible);
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} else if (algorithm==ALGORITHM_RK4) {
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ns_step_rk4(u, K1, K2, N1, N2, nu, delta, L, g, fft1, fft2, ifft, tmp1, tmp2, tmp3, irreversible);
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ns_step_rk4(u, K1, K2, N1, N2, nu, step, L, g, fft1, fft2, ifft, tmp1, tmp2, tmp3, irreversible);
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} else if (algorithm==ALGORITHM_RKF45) {
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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);
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ns_step_rkf45(u, adaptive_tolerance, adaptive_factor, K1, K2, N1, N2, nu, &step, &next_step, L, g, fft1, fft2, ifft, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7, irreversible);
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} else {
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fprintf(stderr,"bug: unknown algorithm: %u, contact ian.jauslin@rutgers,edu\n",algorithm);
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}
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time+=delta;
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time+=step;
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step=next_step;
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}
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// save final entry to savefile
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@ -590,7 +608,7 @@ int ns_step_rk2(
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// next time step
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// adaptive RK algorithm (Runge-Kutta-Fehlberg)
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double ns_step_rkf45(
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int ns_step_rkf45(
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_Complex double* u,
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double tolerance,
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double factor,
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@ -599,7 +617,8 @@ double ns_step_rkf45(
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int N1,
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int N2,
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double nu,
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double delta,
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double* delta,
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double* next_delta,
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double L,
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_Complex double* g,
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fft_vect fft1,
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@ -623,7 +642,7 @@ double ns_step_rkf45(
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// k2 : u(t+1/4*delta)
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for(kx=0;kx<=K1;kx++){
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for(ky=(kx>0 ? -K2 : 1);ky<=K2;ky++){
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tmp[klookup_sym(kx,ky,K2)]=u[klookup_sym(kx,ky,K2)]+delta/4*k1[klookup_sym(kx,ky,K2)];
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tmp[klookup_sym(kx,ky,K2)]=u[klookup_sym(kx,ky,K2)]+(*delta)/4*k1[klookup_sym(kx,ky,K2)];
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}
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}
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ns_rhs(k2, tmp, K1, K2, N1, N2, nu, L, g, fft1, fft2, ifft, irreversible);
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@ -631,7 +650,7 @@ double ns_step_rkf45(
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// k3 : u(t+3/8*delta)
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for(kx=0;kx<=K1;kx++){
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for(ky=(kx>0 ? -K2 : 1);ky<=K2;ky++){
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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)]);
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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)]);
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}
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}
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ns_rhs(k3, tmp, K1, K2, N1, N2, nu, L, g, fft1, fft2, ifft, irreversible);
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@ -639,7 +658,7 @@ double ns_step_rkf45(
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// k4 : u(t+12./13*delta)
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for(kx=0;kx<=K1;kx++){
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for(ky=(kx>0 ? -K2 : 1);ky<=K2;ky++){
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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)]);
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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)]);
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}
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}
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ns_rhs(k4, tmp, K1, K2, N1, N2, nu, L, g, fft1, fft2, ifft, irreversible);
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@ -647,7 +666,7 @@ double ns_step_rkf45(
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// k5 : u(t+1*delta)
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for(kx=0;kx<=K1;kx++){
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for(ky=(kx>0 ? -K2 : 1);ky<=K2;ky++){
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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)]);
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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)]);
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}
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}
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ns_rhs(k5, tmp, K1, K2, N1, N2, nu, L, g, fft1, fft2, ifft, irreversible);
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@ -655,7 +674,7 @@ double ns_step_rkf45(
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// k6 : u(t+1./2*delta)
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for(kx=0;kx<=K1;kx++){
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for(ky=(kx>0 ? -K2 : 1);ky<=K2;ky++){
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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)]);
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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)]);
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}
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}
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ns_rhs(k6, tmp, K1, K2, N1, N2, nu, L, g, fft1, fft2, ifft, irreversible);
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@ -666,15 +685,13 @@ double ns_step_rkf45(
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for(kx=0;kx<=K1;kx++){
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for(ky=(kx>0 ? -K2 : 1);ky<=K2;ky++){
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// difference between 5th order and 4th order
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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)]));
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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)]));
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// next step
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tmp[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)]);
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tmp[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)]);
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relative+=cabs(tmp[klookup_sym(kx,ky,K2)]);
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}
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}
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// new delta
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delta=factor*delta*pow(relative*tolerance/err,0.2);
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// compare relative error with tolerance
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if(err<relative*tolerance){
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// add to output
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@ -683,12 +700,16 @@ double ns_step_rkf45(
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u[klookup_sym(kx,ky,K2)]+=tmp[klookup_sym(kx,ky,K2)];
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}
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}
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return delta;
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// next delta to use in future steps
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*next_delta=factor*(*delta)*pow(relative*tolerance/err,0.2);
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}
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// error too big: repeat with smaller step
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else{
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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));
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*delta=factor*(*delta)*pow(relative*tolerance/err,0.2);
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ns_step_rkf45(u,tolerance,factor,K1,K2,N1,N2,nu,delta,next_delta,L,g,fft1,fft2,ifft,k1,k2,k3,k4,k5,k6,tmp,irreversible);
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}
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return 0;
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}
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// right side of Irreversible/Reversible Navier-Stokes equation
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@ -56,7 +56,7 @@ int ns_step_rk4( _Complex double* u, int K1, int K2, int N1, int N2, double nu,
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// RK2
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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);
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// adaptive RK algorithm (Runge-Kutta-Fehlberg)
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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);
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int ns_step_rkf45( _Complex double* u, double tolerance, double factor, int K1, int K2, int N1, int N2, double nu, double* delta, double* next_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);
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// right side of Irreversible/reversible Navier-Stokes equation
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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);
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