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A New Stable Splitting for the Isentropic Euler Equations

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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.

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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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Authors and Affiliations

  1. Institut für Geometrie und Praktische Mathematik, RWTH Aachen University, Templergraben 55, 52062, Aachen, Germany

    Klaus Kaiser & Sebastian Noelle

  2. Faculty of Sciences, Hasselt University, Campus Diepenbeek, Agoralaan Gebouw D, 3590, Diepenbeek, Belgium

    Klaus Kaiser & Jochen Schütz

  3. Institute for Advanced Simulation, Forschungszentrum Jülich GmbH, Wilhelm-Jonen-Straße, 52425, Jülich, Germany

    Ruth Schöbel

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  1. Klaus Kaiser
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  2. Jochen Schütz
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  4. Sebastian Noelle
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Correspondence to Klaus Kaiser.

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Kaiser, K., Schütz, J., Schöbel, R. et al. A New Stable Splitting for the Isentropic Euler Equations. J Sci Comput 70, 1390–1407 (2017). https://doi.org/10.1007/s10915-016-0286-6

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  • DOI: https://doi.org/10.1007/s10915-016-0286-6

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