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International Conference on Finite Volumes for Complex Applications

FVCA 2017: Finite Volumes for Complex Applications VIII - Methods and Theoretical Aspects pp 255–263Cite as

Low Mach Number Limit of a Pressure Correction MAC Scheme for Compressible Barotropic Flows

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 199))

Abstract

We study the incompressible limit of a pressure correction MAC scheme (Herbin et al., Math. Model. Numer. Anal. 48, 1807–1857, 2013) [3] for the unstationary compressible barotropic Navier–Stokes equations. Provided the initial data are well-prepared, the solution of the numerical scheme converges, as the Mach number tends to zero, towards the solution of the classical pressure correction inf-sup stable MAC scheme for the incompressible Navier–Stokes equations.

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References

  1. Gallouët, T., Herbin, R., Latché, J.C., Mallem, K.: Convergence of the MAC scheme for the incompressible Navier–Stokes equations. Found. Comput. Math. (2016)

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  2. Grapsas, D., Herbin, R., Kheriji, W., Latché, J.C.: An unconditionally stable finite element-finite volume pressure correction scheme for the compressible Navier–Stokes equations (2015) (under revision)

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  3. Herbin, R., Kheriji, W., Latché, J.C.: On some implicit and semi-implicit staggered schemes for the shallow water and Euler equations. Math. Model. Numer. Anal. 48, 1807–1857 (2013)

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  4. Lions, P.L., Masmoudi, N.: Incompressible limit for a viscous compressible fluid. J. de Mathmatiques Pures et Appliquées 77, 585–627 (1998)

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Author information

Authors and Affiliations

  1. I2M UMR 7373, Aix-Marseille Université, CNRS, École Centrale de Marseille, 39 rue Joliot Curie, 13453, Marseille, France

    Raphaèle Herbin

  2. Institut de Radioprotection et de Sûreté Nucléaire (IRSN), 13115, Saint-Paul-lez-Durance, France

    Jean-Claude Latché

  3. Université de Lyon, CNRS UMR 5208, Université Lyon 1, Institut Camille Jordan, 43 Bd 11 Novembre 1918, F69622, Villeurbanne cedex, France

    Khaled Saleh

Authors
  1. Raphaèle Herbin
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  2. Jean-Claude Latché
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  3. Khaled Saleh
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Corresponding author

Correspondence to Khaled Saleh .

Editor information

Editors and Affiliations

  1. Equipe RAPSODI, Inria Lille - Nord Europe, Villeneuve-d’Ascq, France

    Clément Cancès

  2. Commissariat à l'énergie atomique et aux énergies alternatives, Centre de Saclay, Gif-sur-Yvette, France

    Pascal Omnes

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Herbin, R., Latché, JC., Saleh, K. (2017). Low Mach Number Limit of a Pressure Correction MAC Scheme for Compressible Barotropic Flows. In: Cancès, C., Omnes, P. (eds) Finite Volumes for Complex Applications VIII - Methods and Theoretical Aspects . FVCA 2017. Springer Proceedings in Mathematics & Statistics, vol 199. Springer, Cham. https://doi.org/10.1007/978-3-319-57397-7_18

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