An asymptotic preserving scheme satisfying entropy stability for the barotropic Euler system

Abstract

In this paper we study structure-preserving numerical methods for low Mach number barotropic Euler equations. Besides their asymptotic preserving properties that are crucial in order to obtain uniformly consistent and stable approximations of the Euler equations in their singular limit as the Mach number approaches zero, our aim is also to preserve discrete entropy stability. Suitable acoustic/advection splitting approach combined with time implicit-explicit approximations are used to achieve the asymptotic preserving property. The entropy stability of different space discretisation strategies is studied for different values of Mach number and is validated by the numerical experiments.