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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 |
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Vol. 13 (2018), No. 2, 243–270
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Abstract |
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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. |
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Keywords
discontinuous Galerkin, IMEX-Runge–Kutta, low Mach number,
splitting, asymptotic preserving
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Mathematical Subject Classification 2010
Primary: 35L65, 65N30
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Milestones
Received: 24 May 2017
Revised: 28 March 2018
Accepted: 17 April 2018
Published: 25 September 2018
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Authors |
| Jonas Zeifang | |
| Institut für Aerodynamik und
Gasdynamik Universität Stuttgart Stuttgart Germany |
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| 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 |
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| Jochen Schütz | |
| Faculteit Wetenschappen Universiteit Hasselt Diepenbeek Belgium |
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| Claus-Dieter Munz | |
| Institut für Aerodynamik und
Gasdynamik Universität Stuttgart Stuttgart Germany |
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