// Linear forms coming from the DG formulation, evaluated on the inner edges of the triangulation. Linear with respect to the test function v.
// Forms use riemann solvers (where the supplied states are from the previous time level).
// The first function does the calculation, the next ones are added to the weakform and they call the first function, asking for
// the correct element of the vector.
double linear_form_interface(int element, int n, double *wt, Func<double> *ue[], Func<double> *v, Geom<double> *e, ExtData<double> *ext)
{
double result = 0;
double w_l[4], w_r[4];
for (int i = 0; i < n; i++)
{
w_l[0] = ext->fn[0]->get_val_central(i);
w_r[0] = ext->fn[0]->get_val_neighbor(i);
w_l[1] = ext->fn[1]->get_val_central(i);
w_r[1] = ext->fn[1]->get_val_neighbor(i);
w_l[2] = ext->fn[2]->get_val_central(i);
w_r[2] = ext->fn[2]->get_val_neighbor(i);
w_l[3] = ext->fn[3]->get_val_central(i);
w_r[3] = ext->fn[3]->get_val_neighbor(i);
result -= wt[i] * v->val[i] * num_flux.numerical_flux_i(element, w_l, w_r, e->nx[i], e->ny[i]);
}
return result * TAU;
}
// Surface linear forms representing the inlet/outlet part of the boundary.
// For details, see comments in the following function.
// The first function does the calculation, the next ones are added to the weakform and they call the first function, asking for
// the correct element of the vector.
double bdy_flux_inlet_outlet_comp(int element, int n, double *wt, Func<scalar> *ue[], Func<double> *v, Geom<double> *e, ExtData<double> *ext)
{
double result = 0;
// Left (inner) state.
double w_l[4];
// Right (boundary) state.
double w_r[4];
// Eulerian flux.
//double flux[4];
for (int i = 0; i < n; i++)
{
// Left (inner) state from the previous time level solution.
w_l[0] = ext->fn[0]->val[i];
w_l[1] = ext->fn[1]->val[i];
w_l[2] = ext->fn[2]->val[i];
w_l[3] = ext->fn[3]->val[i];
w_r[0] = RHO_EXT;
w_r[1] = RHO_EXT * V1_EXT;
w_r[2] = RHO_EXT * V2_EXT;
w_r[3] = ENERGY_EXT;
/*
// The inlet part (left part of the computational domain).
if(e->nx[i] < 0)
{
// Boundary state calculation.
double rho_b = bc_density(e->y[i]);
double velocity_x_b = bc_density_vel_x(e->y[i]) / bc_density(e->y[i]);
double velocity_y_b = bc_density_vel_y(e->y[i]) / bc_density(e->y[i]);
// Sound speed on the left (inner) side of the boundary.
double sound_speed_l = calc_sound_speed(w_l[0], w_l[1], w_l[2], w_l[3]);
// Intersection state calculation (marked with an underscore1 (_1)).
double sound_speed_1 = sound_speed_l + (num_flux.R/num_flux.c_v) * (w_l[1]/w_l[0] - velocity_x_b);
double rho_1 = std::pow(sound_speed_1*sound_speed_1*w_l[0]/(num_flux.kappa*calc_pressure(w_l[0], w_l[1], w_l[2], w_l[3])), num_flux.c_v/num_flux.R) * w_l[0];
double velocity_x_1 = velocity_x_b;
double velocity_y_1 = w_l[2] / w_l[0];
// Boundary pressure calculated from the intersection state.
double p_b = rho_1 * sound_speed_1 * sound_speed_1 / num_flux.kappa;
// Calculation of the energy component of the intersection state.
double energy_1 = calc_energy<double>(rho_1, velocity_x_1* rho_1, velocity_y_1 * rho_1, p_b);
// Calculation of the state for inflow/outlow velocities above the local speed of sound.
double sound_speed_l_star = num_flux.R/(num_flux.c_v * (2+num_flux.R/num_flux.c_v)) * w_l[1] / w_l[0] + 2 * sound_speed_l / (2+num_flux.R/num_flux.c_v);
double rho_l_star = std::pow(sound_speed_l_star/sound_speed_l, 2*num_flux.c_v / num_flux.R) * w_l[0];
double velocity_x_l_star = sound_speed_l_star;
double velocity_y_l_star = w_l[2] / w_l[0];
double p_l_star = rho_l_star * sound_speed_l_star * sound_speed_l_star / num_flux.kappa;
double energy_l_star = calc_energy<double>(rho_l_star, velocity_x_l_star * rho_l_star, velocity_y_l_star * rho_l_star, p_l_star);
// Inflow velocity below the local speed of sound (of the intersection state).
if(velocity_x_b < sound_speed_1)
{
//Ondrej's code.
double alpha = atan2(e->ny[i], e->nx[i]);
double mat_rot_inv[4][4];
double flux_local[4];
double flux_global[4];
double mat_rot[4][4];
num_flux.T_rot(mat_rot, alpha);
flux_global[0] = rho_1;
flux_global[1] = velocity_x_1 * rho_1;
flux_global[2] = velocity_y_1 * rho_1;
flux_global[3] = energy_1;
num_flux.dot_vector(flux_local, mat_rot, flux_global);
flux[0] = f_x(0, flux_local[0], flux_local[1], flux_local[2], flux_local[3]);
flux[1] = f_x(1, flux_local[0], flux_local[1], flux_local[2], flux_local[3]);
flux[2] = f_x(2, flux_local[0], flux_local[1], flux_local[2], flux_local[3]);
flux[3] = f_x(3, flux_local[0], flux_local[1], flux_local[2], flux_local[3]);
num_flux.T_rot(mat_rot_inv, -alpha);
num_flux.dot_vector(flux, mat_rot_inv, flux);
}
// Inflow velocity above the local speed of sound (of the intersection state).
else
{
//Ondrej's code.
double alpha = atan2(e->ny[i], e->nx[i]);
double mat_rot_inv[4][4];
double flux_local[4];
double flux_global[4];
double mat_rot[4][4];
num_flux.T_rot(mat_rot, alpha);
flux_global[0] = rho_l_star;
flux_global[1] = velocity_x_l_star * rho_l_star;
flux_global[2] = velocity_y_l_star * rho_l_star;
flux_global[3] = energy_l_star;
num_flux.dot_vector(flux_local, mat_rot, flux_global);
flux[0] = f_x(0, flux_local[0], flux_local[1], flux_local[2], flux_local[3]);
flux[1] = f_x(1, flux_local[0], flux_local[1], flux_local[2], flux_local[3]);
flux[2] = f_x(2, flux_local[0], flux_local[1], flux_local[2], flux_local[3]);
flux[3] = f_x(3, flux_local[0], flux_local[1], flux_local[2], flux_local[3]);
num_flux.T_rot(mat_rot_inv, -alpha);
num_flux.dot_vector(flux, mat_rot_inv, flux);
}
}
// The outlet part (the right part of the boundary).
else
{
// These calculations are the same as above.
double p_b = bc_pressure(e->y[i]);
double rho_b = w_l[0] * std::pow(p_b/calc_pressure(w_l[0], w_l[1], w_l[2], w_l[3]), (1/num_flux.kappa));
double velocity_x_b = (w_l[1] / w_l[0]) + 2*(num_flux.c_v/num_flux.R)*(calc_sound_speed<double>(w_l[0], w_l[1], w_l[2], w_l[3]) - std::sqrt(num_flux.kappa * p_b / rho_b));
double velocity_y_b = w_l[2] / w_l[0];
double energy_b = calc_energy<double>(rho_b, velocity_x_b*rho_b, velocity_y_b*rho_b, p_b);
double sound_speed_l_star = num_flux.R/(num_flux.c_v * (2+num_flux.R/num_flux.c_v)) * w_l[1] / w_l[0] + 2 * calc_sound_speed<double>(w_l[0], w_l[1], w_l[2], w_l[3]) / (2+num_flux.R/num_flux.c_v);
double rho_l_star = std::pow(sound_speed_l_star/calc_sound_speed<double>(w_l[0], w_l[1], w_l[2], w_l[3]), 2*num_flux.c_v / num_flux.R) * w_l[0];
double velocity_x_l_star = sound_speed_l_star;
double velocity_y_l_star = w_l[2] / w_l[0];
double p_l_star = rho_l_star * sound_speed_l_star * sound_speed_l_star / num_flux.kappa;
double energy_l_star = calc_energy<double>(rho_l_star, velocity_x_l_star * rho_l_star, velocity_y_l_star * rho_l_star, p_l_star);
double sound_speed_b = calc_sound_speed(rho_b, velocity_x_b*rho_b, velocity_y_b*rho_b, energy_b);
// Inflow velocity below the local speed of sound (of the intersection state).
if(velocity_x_b < sound_speed_b)
{
//Ondrej's code.
double alpha = atan2(e->ny[i], e->nx[i]);
double mat_rot_inv[4][4];
double flux_local[4];
double flux_global[4];
double mat_rot[4][4];
num_flux.T_rot(mat_rot, alpha);
flux_global[0] = rho_b;
flux_global[1] = velocity_x_b * rho_b;
flux_global[2] = velocity_y_b * rho_b;
flux_global[3] = energy_b;
num_flux.dot_vector(flux_local, mat_rot, flux_global);
flux[0] = f_x(0, flux_local[0], flux_local[1], flux_local[2], flux_local[3]);
flux[1] = f_x(1, flux_local[0], flux_local[1], flux_local[2], flux_local[3]);
flux[2] = f_x(2, flux_local[0], flux_local[1], flux_local[2], flux_local[3]);
flux[3] = f_x(3, flux_local[0], flux_local[1], flux_local[2], flux_local[3]);
num_flux.T_rot(mat_rot_inv, -alpha);
num_flux.dot_vector(flux, mat_rot_inv, flux);
}
// Outflow velocity above the local speed of sound (of the intersection state).
else
{
//Ondrej's code.
double alpha = atan2(e->ny[i], e->nx[i]);
double mat_rot_inv[4][4];
double flux_local[4];
double flux_global[4];
double mat_rot[4][4];
num_flux.T_rot(mat_rot, alpha);
flux_global[0] = rho_l_star;
flux_global[1] = velocity_x_l_star * rho_l_star;
flux_global[2] = velocity_y_l_star * rho_l_star;
flux_global[3] = energy_l_star;
num_flux.dot_vector(flux_local, mat_rot, flux_global);
flux[0] = f_x(0, flux_local[0], flux_local[1], flux_local[2], flux_local[3]);
flux[1] = f_x(1, flux_local[0], flux_local[1], flux_local[2], flux_local[3]);
flux[2] = f_x(2, flux_local[0], flux_local[1], flux_local[2], flux_local[3]);
flux[3] = f_x(3, flux_local[0], flux_local[1], flux_local[2], flux_local[3]);
num_flux.T_rot(mat_rot_inv, -alpha);
num_flux.dot_vector(flux, mat_rot_inv, flux);
}
}
*/
result -= wt[i] * v->val[i] * num_flux.numerical_flux_i(element, w_l, w_r, e->nx[i], e->ny[i]);
}
return result * TAU;
}