Large Time Step and Asymptotic Preserving Numerical Schemes for the Gas Dynamics Equations with Source Terms

We propose large time step and asymptotic preserving schemes for the gas dynamics equations with external forces and friction terms. By asymptotic preserving, we mean that the numerical scheme is able to reproduce at the discrete level the parabolic-type asymptotic behavior satisfied by the continuous equations. By large time step, we mean that the scheme is stable under a CFL stability condition driven by the (slow) material waves, and not by the (fast) acoustic waves customary in Godunov-type schemes. Numerical evidence is proposed and shows a gain of several orders of magnitude in both accuracy and efficiency.