Large time step and asymptotic preserving numerical schemes for the gas dynamics equations with source terms

Christophe Chalons (1) , Samuel Kokh (1) , Mathieu Girardin (1)

1 LJLL - Laboratoire Jacques-Louis Lions

We propose a large time step and asymptotic preserving scheme 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 behaviour 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 as it is customary in Godunov-type schemes. Numerical evidences are proposed and show a gain of several orders of magnitude in both accuracy and efficiency.

Mots clés: Large time step method; asymptotic preserving scheme; gas dynamics equations; source terms; hyperbolic equations; parabolic limit

Domaines: Modélisation et simulation; Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Christophe Chalons, Samuel Kokh, Mathieu Girardin. Large time step and asymptotic preserving numerical schemes for the gas dynamics equations with source terms. 2012. ⟨hal-00718022⟩