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A High-Order Method for Weakly Compressible Flows

Part of: Partial differential equations, initial value and time-dependent initial-boundary value problems Equations of mathematical physics and other areas of application Numerical analysis: Ordinary differential equations Basic methods in fluid mechanics

Published online by Cambridge University Press:  28 July 2017

Klaus Kaiser  and
Jochen Schütz
Klaus Kaiser*
Affiliation:
IGPM, RWTH Aachen University, Templergraben 55, 52062 Aachen, Germany
Jochen Schütz*
Affiliation:
Faculty of Sciences, Hasselt University, Agoralaan Gebouw D, BE-3590 Diepenbeek, Belgium
*
*Corresponding author. Email addresses:kaiser@igpm.rwth-aachen.de (K. Kaiser), jochen.schuetz@uhasselt.be (J. Schütz)
*Corresponding author. Email addresses:kaiser@igpm.rwth-aachen.de (K. Kaiser), jochen.schuetz@uhasselt.be (J. Schütz)
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Abstract

In this work, we introduce an IMEX discontinuous Galerkin solver for the weakly compressible isentropic Euler equations. The splitting needed for the IMEX temporal integration is based on the recently introduced reference solution splitting [32, 52], which makes use of the incompressible solution. We show that the overall method is asymptotic preserving. Numerical results show the performance of the algorithm which is stable under a convective CFL condition and does not show any order degradation.

Keywords

Asymptotic preservingisentropic compressible EulerRS-IMEXIMEX Runge-Kuttadiscontinuous Galerkinlow Mach

MSC classification

Secondary: 35Q31: Euler equations 65L06: Multistep, Runge-Kutta and extrapolation methods 65M60: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 76M45: Asymptotic methods, singular perturbations
Type
Research Article
Information
Communications in Computational Physics , Volume 22 , Issue 4 , October 2017 , pp. 1150 - 1174
Copyright
Copyright © Global-Science Press 2017 

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Footnotes

Communicated by Chi-Wang Shu

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