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Volume 27, Issue 1
A Novel Full-Euler Low Mach Number IMEX Splitting

Jonas Zeifang, Jochen Schütz, Klaus Kaiser, Andrea Beck, Maria Lukáčová-Medvid'ová & Sebastian Noelle

Commun. Comput. Phys., 27 (2020), pp. 292-320.

Published online: 2019-10

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  • Abstract

In this paper, we introduce an extension of a splitting method for singularly perturbed equations, the so-called RS-IMEX splitting [Kaiser et al., Journal of Scientific Computing, 70(3), 1390–1407], to deal with the fully compressible Euler equations. The straightforward application of the splitting yields sub-equations that are, due to the occurrence of complex eigenvalues, not hyperbolic. A modification, slightly changing the convective flux, is introduced that overcomes this issue. It is shown that the splitting gives rise to a discretization that respects the low-Mach number limit of the Euler equations; numerical results using finite volume and discontinuous Galerkin schemes show the potential of the discretization.

  • Keywords

Euler equations, low-Mach, IMEX Runge-Kutta, RS-IMEX.

  • AMS Subject Headings

35L81, 65M08, 65M60, 76M45

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

zeifang@iag.uni-stuttgart.de (Jonas Zeifang)

jochen.schuetz@uhasselt.be (Jochen Schütz)

kaiser@igpm.rwth-aachen.de (Klaus Kaiser)

beck@iag.uni-stuttgart.de (Andrea Beck)

lukacova@uni-mainz.de (Maria Lukáčová-Medvid'ová)

noelle@igpm.rwth-aachen.de (Sebastian Noelle)

  • BibTex
  • RIS
  • TXT
@Article{CiCP-27-292, author = {Jonas and Zeifang and zeifang@iag.uni-stuttgart.de and 5258 and IAG, Universit¨at Stuttgart, Pfaffenwaldring 21, DE-70569 Stuttgart, Germany. and Jonas Zeifang and Jochen and Schütz and jochen.schuetz@uhasselt.be and 5259 and Faculty of Sciences, Hasselt University, Agoralaan Gebouw D, BE-3590 Diepenbeek, Belgium. and Jochen Schütz and Klaus and Kaiser and kaiser@igpm.rwth-aachen.de and 5260 and Faculty of Sciences, Hasselt University, Agoralaan Gebouw D, BE-3590 Diepenbeek, Belgium. and Klaus Kaiser and Andrea and Beck and beck@iag.uni-stuttgart.de and 5261 and IAG, Universit¨at Stuttgart, Pfaffenwaldring 21, DE-70569 Stuttgart, Germany. and Andrea Beck and Maria and Lukáčová-Medvid'ová and lukacova@uni-mainz.de and 5262 and Institut f ¨ur Mathematik, Johannes Gutenberg-Universit¨at Mainz, Staudingerweg 9, DE-55128 Mainz, Germany. and Maria Lukáčová-Medvid'ová and Sebastian and Noelle and noelle@igpm.rwth-aachen.de and 5263 and IGPM, RWTH Aachen University, Templergraben 55, DE-52062 Aachen, Germany. and Sebastian Noelle}, title = {A Novel Full-Euler Low Mach Number IMEX Splitting}, journal = {Communications in Computational Physics}, year = {2019}, volume = {27}, number = {1}, pages = {292--320}, abstract = {

In this paper, we introduce an extension of a splitting method for singularly perturbed equations, the so-called RS-IMEX splitting [Kaiser et al., Journal of Scientific Computing, 70(3), 1390–1407], to deal with the fully compressible Euler equations. The straightforward application of the splitting yields sub-equations that are, due to the occurrence of complex eigenvalues, not hyperbolic. A modification, slightly changing the convective flux, is introduced that overcomes this issue. It is shown that the splitting gives rise to a discretization that respects the low-Mach number limit of the Euler equations; numerical results using finite volume and discontinuous Galerkin schemes show the potential of the discretization.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2018-0270}, url = {http://global-sci.org/intro/article_detail/cicp/13323.html} }
TY - JOUR T1 - A Novel Full-Euler Low Mach Number IMEX Splitting AU - Zeifang , Jonas AU - Schütz , Jochen AU - Kaiser , Klaus AU - Beck , Andrea AU - Lukáčová-Medvid'ová , Maria AU - Noelle , Sebastian JO - Communications in Computational Physics VL - 1 SP - 292 EP - 320 PY - 2019 DA - 2019/10 SN - 27 DO - http://doi.org/10.4208/cicp.OA-2018-0270 UR - https://global-sci.org/intro/article_detail/cicp/13323.html KW - Euler equations, low-Mach, IMEX Runge-Kutta, RS-IMEX. AB -

In this paper, we introduce an extension of a splitting method for singularly perturbed equations, the so-called RS-IMEX splitting [Kaiser et al., Journal of Scientific Computing, 70(3), 1390–1407], to deal with the fully compressible Euler equations. The straightforward application of the splitting yields sub-equations that are, due to the occurrence of complex eigenvalues, not hyperbolic. A modification, slightly changing the convective flux, is introduced that overcomes this issue. It is shown that the splitting gives rise to a discretization that respects the low-Mach number limit of the Euler equations; numerical results using finite volume and discontinuous Galerkin schemes show the potential of the discretization.

Jonas Zeifang, Jochen Schütz, Klaus Kaiser, Andrea Beck, Maria Lukáčová-Medvid'ová & Sebastian Noelle. (2019). A Novel Full-Euler Low Mach Number IMEX Splitting. Communications in Computational Physics. 27 (1). 292-320. doi:10.4208/cicp.OA-2018-0270
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