No. 2019.07
A Novel Full-Euler Low Mach Number IMEX Splitting
J. Zeifang , J. Schütz, K. Kaiser, A. Beck, M. Lukáčová-Medvidová and S. Noelle
Subject: Euler equations, low-Mach, IMEX Runge-Kutta, RS-IMEX
Abstract
In this paper, we introduce an extension of a splitting method for singularly perturbed equations, the so-called RS-IMEX splitting [Kaiser et al., Journal of Scientific Computing, 70(3), 1390–1407], to deal with the fully compressible Euler equations. The straightforward application of the splitting yields sub-equations that are, due to the occurrence of complex eigenvalues, not hyperbolic. A modification, slightly changing the convective flux, is introduced that overcomes this issue. It is shown that the splitting gives rise to a discretization that respects the low-Mach number limit of the Euler equations; numerical results using finite volume and discontinuous Galerkin schemes show the potential of the discretization.