A Novel Full-Euler Low Mach Number IMEX Splitting

Authors

  • Jonas Zeifang IAG, Universit¨at Stuttgart, Pfaffenwaldring 21, DE-70569 Stuttgart, Germany.
  • Jochen Schütz Faculty of Sciences, Hasselt University, Agoralaan Gebouw D, BE-3590 Diepenbeek, Belgium.
  • Klaus Kaiser Faculty of Sciences, Hasselt University, Agoralaan Gebouw D, BE-3590 Diepenbeek, Belgium.
  • Andrea Beck IAG, Universit¨at Stuttgart, Pfaffenwaldring 21, DE-70569 Stuttgart, Germany.
  • Maria Lukáčová-Medvid'ová Institut f ¨ur Mathematik, Johannes Gutenberg-Universit¨at Mainz, Staudingerweg 9, DE-55128 Mainz, Germany.
  • Sebastian Noelle IGPM, RWTH Aachen University, Templergraben 55, DE-52062 Aachen, Germany.

DOI:

https://doi.org/10.4208/cicp.OA-2018-0270

Keywords:

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.

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Published

2020-03-06

Issue

Vol. 27 No. 1 (2020)

Section

Articles