Two-Derivative Schemes for Low-Mach Flows

Abstract

In this paper, we analyze two-derivative IMEX (implicit/explicit) schemes applied to the isentropic Euler equations. In particular, we investigate a broad range of stiffness, varying from a weakly compressible regime (ε ≪ 1) to a fully compressible regime (ε≈1). The high-order discontinuous Galerkin spectral element method is used as spatial discretization. We prove that the considered two-derivative IMEX schemes for the splitting described in [Degond, Tang, 2011] are asymptotically preserving. We show experimentally that the schemes are stable and convergent under a convective CFL condition independent of the stiffness parameter ε.