Volume 27, Issue 1
A Novel Full-Euler Low Mach Number IMEX Splitting

Jonas Zeifang, Jochen Schütz, Klaus Kaiser, Andrea Beck, Maria Lukáčová-Medvid'ová & Sebastian Noelle

10.4208/cicp.OA-2018-0270

Commun. Comput. Phys., 27 (2020), pp. 292-320.

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  • 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.

  • AMS Subject Headings

35L81, 65M08, 65M60, 76M45

Published online: 2019-10