Vol. 13, No. 2, 2018

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Efficient high-order discontinuous Galerkin computations of low Mach number flows

Jonas Zeifang, Klaus Kaiser, Andrea Beck, Jochen Schütz and Claus-Dieter Munz

Vol. 13 (2018), No. 2, 243–270
Abstract

We consider the efficient approximation of low Mach number flows by a high-order scheme, coupling a discontinuous Galerkin (DG) discretization in space with an implicit/explicit (IMEX) discretization in time. The splitting into linear implicit and nonlinear explicit parts relies heavily on the incompressible solution. The method has been originally developed for a singularly perturbed ODE and applied to the isentropic Euler equations. Here, we improve, extend, and investigate the so-called RS-IMEX splitting method. The resulting scheme can cope with a broader range of Mach numbers without running into roundoff errors, it is extended to realistic physical boundary conditions, and it is shown to be highly efficient in comparison to more standard solution techniques.

Keywords
discontinuous Galerkin, IMEX-Runge–Kutta, low Mach number, splitting, asymptotic preserving
Mathematical Subject Classification 2010
Primary: 35L65, 65N30
Milestones
Received: 24 May 2017
Revised: 28 March 2018
Accepted: 17 April 2018
Published: 25 September 2018
Authors
Jonas Zeifang
Institut für Aerodynamik und Gasdynamik
Universität Stuttgart
Stuttgart
Germany
Klaus Kaiser
Institut für Geometrie und Praktische Mathematik
Rheinisch-Westfälische Technische Hochschule Aachen
Aachen
Germany
Faculteit Wetenschappen
Universiteit Hasselt
Diepenbeek
Belgium
Andrea Beck
Institut für Aerodynamik und Gasdynamik
Universität Stuttgart
Stuttgart
Germany
Jochen Schütz
Faculteit Wetenschappen
Universiteit Hasselt
Diepenbeek
Belgium
Claus-Dieter Munz
Institut für Aerodynamik und Gasdynamik
Universität Stuttgart
Stuttgart
Germany