Journal of Scientific Computing

, Volume 70, Issue 3, pp 1390–1407 | Cite as

A New Stable Splitting for the Isentropic Euler Equations

  • Klaus Kaiser
  • Jochen Schütz
  • Ruth Schöbel
  • Sebastian Noelle
Article
  • 608 Downloads

Abstract

In this work, we propose a new way of splitting the flux function of the isentropic compressible Euler equations at low Mach number into stiff and non-stiff parts. Following the IMEX methodology, the latter ones are treated explicitly, while the first ones are treated implicitly. The splitting is based on the incompressible limit solution, which we call reference solution. An analysis concerning the asymptotic consistency and numerical results demonstrate the advantages of this splitting.

Keywords

Flux splitting Isentropic Euler equations Low Mach IMEX Reference solution 

Mathematical Subject Classification

35L65 76N 76M45 65M08 

Notes

Acknowledgments

The first author has been partially supported by the German Research Foundation (DFG) Project NO 361/3-3, and the University of Hasselt in the framework of the BOF 2016. The authors would like to thank Arun K.R., Georgij Bispen, Rupert Klein, Mária Lukáčová-Medvid’ová, Claus-Dieter Munz and Hamed Zakerzadeh for the discussions and collaborations leading to the RS-IMEX approach.

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Klaus Kaiser
    • 1
    • 2
  • Jochen Schütz
    • 2
  • Ruth Schöbel
    • 3
  • Sebastian Noelle
    • 1
  1. 1.Institut für Geometrie und Praktische MathematikRWTH Aachen UniversityAachenGermany
  2. 2.Faculty of SciencesHasselt UniversityDiepenbeekBelgium
  3. 3.Institute for Advanced Simulation, Forschungszentrum Jülich GmbHJülichGermany

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