An exact Riemann solver for the Euler equations, with interactive widgets. #riemann-problem #euler-equations

Euler_exact_Riemann_solver.ipynb

There is a bug in this exact Riemann solver. When computing rho_l_star and rho_r_star you need to use

Find middle state densities

if (p<=p_l):
    rho_l_star = (p/p_l)**(1.0/gamma) * rho_l
else:
    rho_l_star = ((1.0+beta*p/p_l)/((p/p_l)+beta))*rho_l;

if (p<=p_r):
    rho_r_star = (p/p_r)**(1.0/gamma) * rho_r
else:
    rho_r_star = ((1.0+beta*p/p_r)/((p/p_r)+beta))*rho_r;