void LaxFriedrichsStep() {
int i, j;
double rho, u, e, p;
// compute flux F from U
for (j = 0; j < N; j++) {
rho = U[j][0];
u = U[j][1]/U[j][0];
e = U[j][2];
p = (gama - 1) * (e - rho * u * u/ 2);
F[j][0] = rho * u;
F[j][1] = rho * u * u + p;
F[j][2] = (e + p) * u;
}
// Lax-Friedrichs step
for (j = 1; j < N - 1; j++)
for (i = 0; i < 3; i++){
newU[j][i] = (U[j + 1][i] + U[j - 1][i]) / 2 -
tau / h * (F[j + 1][i] - F[j - 1][i]);
}
boundaryConditions(newU);
// update U from newU
for (j = 1; j < N - 1; j++)
for (i = 0; i < 3; i++){
U[j][i] = newU[j][i];
}
}
void solve(solver stepAlgorithm, double tMax, char *filename, int plots)
{
initialize();
double t = 0.0;
int step = 0;
int plot = 0;
FILE *out;
char filename_tmp[1024];
int j;
double rho_avg = 0.0, u_avg = 0.0, e_avg = 0.0, P_avg = 0.0;
double rho, u, e, P;
tau = CFL * h / cMax();
while(plot<=plots) {
sprintf(filename_tmp, "%s_step_%d.dat", filename, plot);
if(!(out = fopen(filename_tmp, "w"))){
fprintf(stderr, "problem opening file %s\n", filename);
exit(1);
}
// write solution in plot files and print
double rho_avg = 0.0, u_avg = 0.0, e_avg = 0.0, P_avg = 0.0;
for (j = 0; j < N; j++) {
rho = U[j][0];
u = U[j][1] / U[j][0];
e = U[j][2];
P = (U[j][2] - U[j][1] * U[j][1] / U[j][0] / 2)
* (gama - 1.0);
rho_avg += rho;
u_avg += u;
e_avg += e;
P_avg += P;
fprintf(out, "%d\t%f\t%f\t%f\t%f\n", j, rho, u, e, P);
}
fclose(out);
if (rho_avg != 0.0){ rho_avg /= N;}
if (u_avg != 0.0){ u_avg /= N;}
if (e_avg != 0.0){ e_avg /= N;}
if (P_avg != 0.0){ P_avg /= N;}
fprintf(stdout,"Step %d Time %f\tRho_avg %f\t u_avg %f\t e_avg %f\t P_avg %f\n",
step, t,rho_avg,u_avg,e_avg,P_avg);
plot++;
while (t < tMax * plot / (double)(plots)) {
boundaryConditions(U);
tau = CFL * h / cMax();
stepAlgorithm();
t += tau;
step++;
}
}
}
int main(int argc, char** argv)
{
int nIterations = 10000;
if (argc > 1) {
nIterations = atoi(argv[1]);
}
Lattice lattice(4, 8, 5.5, 1.0, 1.0, 1.0, 0, 10, 0, 1, 4, -1);
vector<complex<double> > boundaryConditions(4, complex<double>(1.0, 0.0));
DWF linop(0.4, 1.8, 4, pyQCD::wilson, boundaryConditions, &lattice);
VectorXcd psi = VectorXcd::Zero(4 * 12 * 4 * 4 * 4 * 8);
psi(0) = 1.0;
std::cout << "Performing " << nIterations << " matrix-vector products."
<< std::endl;
boost::timer::cpu_timer timer;
for (int i = 0; i < nIterations; ++i) {
VectorXcd eta = linop.apply(psi);
}
boost::timer::cpu_times const elapsedTimes(timer.elapsed());
boost::timer::nanosecond_type const elapsed(elapsedTimes.system
+ elapsedTimes.user);
boost::timer::nanosecond_type const walltime(elapsedTimes.wall);
std::cout << "Total CPU time = " << elapsed / 1.0e9 << " s" << endl;
std::cout << "CPU time per iteration = " << elapsed / 1.0e9 / nIterations
<< " s" << endl;
std::cout << "Walltime = " << walltime / 1.0e9 << " s" << endl;
std::cout << "Walltime per iteration = " << walltime / 1.0e9 / nIterations
<< " s" << endl;
std::cout << "Performance: " << linop.getNumFlops()
<< " floating point operations; "
<< (double) linop.getNumFlops() / elapsed * 1000.0
<< " MFlops / thread" << endl;
return 0;
}
void solve(double tMax)
{
initialize();
double t = 0.0;
double rho, u, e, P;
tau = CFL*h/cMax();
while (t < tMax) {
boundaryConditions(U);
tau = CFL*h/cMax();
upwindGodunovStep();
t += tau;
}
//File to plot last step
FILE *final_step_file;
final_step_file = fopen("final_step.dat", "w");
double current_x;
int j;
for (j = 0; j < N; j++) {
rho = U[j][0];
u = U[j][1]/rho;
e = U[j][2];
P = (gama-1.0)*(e-rho*u*u/2.0);
current_x = j*h;
fprintf(final_step_file, "%f\t%.20f\t%.20f\t%.20f\t%.20f\n", current_x, rho, u, e, P);
}
}
