Journal of Scientific Computing

, Volume 72, Issue 2, pp 623–646 | Cite as

A Numerical Scheme for the Compressible Low-Mach Number Regime of Ideal Fluid Dynamics

  • Wasilij Barsukow
  • Philipp V. F. Edelmann
  • Christian Klingenberg
  • Fabian Miczek
  • Friedrich K. Röpke
Article
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Abstract

Based on the Roe solver a new technique that allows to correctly represent low Mach number flows with a discretization of the compressible Euler equations was proposed in Miczek et al. (Astron Astrophys 576:A50, 2015). We analyze properties of this scheme and demonstrate that its limit yields a discretization of the continuous limit system. Furthermore we perform a linear stability analysis for the case of explicit time integration and study the performance of the scheme under implicit time integration via the evolution of its condition number. A numerical implementation demonstrates the capabilities of the scheme on the example of the Gresho vortex which can be accurately followed down to Mach numbers of \({\sim }10^{-10}\).

Keywords

Compressible Euler equations Low Mach number Asymptotic preserving Flux preconditioning 

Mathematics Subject Classification

65M08 76N15 35B40 35Q31 
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Notes

Acknowledgements

We thank Philipp Birken for stimulating discussions. WB gratefully acknowledges support from the German National Academic Foundation. The work of FKR and PVFE was supported by the Klaus Tschira Foundation. CK acknowledges support of the DFG priority program SPPEXA. The authors gratefully acknowledge the Gauss Centre for Supercomputing (GCS) for providing computing time through the John von Neumann Institute for Computing (NIC) on the GCS share of the supercomputer JUQUEEN [29] at Jülich Supercomputing Centre (JSC). GCS is the alliance of the three national supercomputing centres HLRS (Universität Stuttgart), JSC (Forschungszentrum Jülich), and LRZ (Bayerische Akademie der Wissenschaften), funded by the German Federal Ministry of Education and Research (BMBF) and the German State Ministries for Research of Baden-Württemberg (MWK), Bayern (StMWFK) and Nordrhein-Westfalen (MIWF).

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • Wasilij Barsukow
    • 1
  • Philipp V. F. Edelmann
    • 2
  • Christian Klingenberg
    • 1
  • Fabian Miczek
    • 1
  • Friedrich K. Röpke
    • 2
  1. 1.Institute for MathematicsWürzburg UniversityWürzburgGermany
  2. 2.Heidelberg Institute for Theoretical StudiesHeidelbergGermany

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