virtual void compute_numerical_flux(PhysData& left, PhysData& right, const RealVectorNDIM& unit_normal,
RealVectorNEQS& flux, Real& wave_speed)
{
set_meanflow_properties(left);
// Compute left and right fluxes
PHYS::compute_properties(left.coord, left.solution, dummy_grads, p);
PHYS::flux(p , unit_normal, flux_left);
PHYS::compute_properties(left.coord, right.solution, dummy_grads, p);
PHYS::flux(p , unit_normal, flux_right);
// Compute the averaged properties
sol_avg.noalias() = 0.5*(left.solution+right.solution);
PHYS::compute_properties(left.coord, sol_avg, dummy_grads, p);
// Compute absolute jacobian using averaged properties
PHYS::flux_jacobian_eigen_structure(p,unit_normal,right_eigenvectors,left_eigenvectors,eigenvalues);
abs_jacobian.noalias() = right_eigenvectors * eigenvalues.cwiseAbs().asDiagonal() * left_eigenvectors;
// flux = central flux - upwind flux
flux.noalias() = 0.5*(flux_left + flux_right);
flux.noalias() -= 0.5*abs_jacobian*(right.solution-left.solution);
wave_speed = eigenvalues.cwiseAbs().maxCoeff();
}
virtual void compute_analytical_flux(PhysData& data, const RealVectorNDIM& unit_normal,
RealVectorNEQS& flux, Real& wave_speed)
{
set_meanflow_properties(data);
PHYS::compute_properties(data.coord, data.solution , dummy_grads, p);
PHYS::flux(p, unit_normal, flux);
PHYS::flux_jacobian_eigen_values(p, unit_normal, eigenvalues);
wave_speed = eigenvalues.cwiseAbs().maxCoeff();
}
virtual void compute_solution(const PhysData &inner_cell_data, const RealVectorNDIM &boundary_face_normal, RealVectorNEQS &boundary_face_solution)
{
set_meanflow_properties(inner_cell_data);
RealVectorNEQS char_cell_sol;
RealVectorNEQS char_bdry_sol;
outward_normal = flx_pt_plane_jacobian_normal->get().plane_unit_normal[cell_flx_pt] * flx_pt_plane_jacobian_normal->get().sf->flx_pt_sign(cell_flx_pt);
// COMMENTED HERE IS A STANDARD FORM NOT BASED ON CHARACTERISTIC THEORY
// velocity on the inside of the face
// rho0u[XX] = inner_cell_data.solution[1];
// rho0u[YY] = inner_cell_data.solution[2];
// // velocity in outward_normal direction
// rho0u_normal = rho0u.transpose()*outward_normal;
// // Modify velocity to become the outside velocity of the face,
// // and being the mirror of the inside velocity
// rho0u.noalias() -= 2.*rho0u_normal*outward_normal;
// boundary_face_solution = inner_cell_data.solution;
// boundary_face_solution[1] = rho0u[XX];
// boundary_face_solution[2] = rho0u[YY];
cons_to_char(inner_cell_data.solution,outward_normal,char_cell_sol);
const Real& S = char_cell_sol[0];
const Real& Omega = char_cell_sol[1];
const Real& Aplus = char_cell_sol[2];
const Real& Amin = char_cell_sol[3];
char_bdry_sol[0] = S;
char_bdry_sol[1] = Omega;
char_bdry_sol[2] = Aplus;
char_bdry_sol[3] = Aplus; // Amin = Aplus is the magic here
char_to_cons(char_bdry_sol,outward_normal,boundary_face_solution);
}
