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Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects pp 97–105Cite as

Consistency Analysis of a 1D Finite Volume Scheme for Barotropic Euler Models

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 77))

Abstract

This work is concerned with the consistency study of a 1D (staggered kinetic) finite volume scheme for barotropic Euler models. We prove a Lax-Wendroff-like statement: the limit of a converging (and uniformly bounded) sequence of stepwise constant functions defined from the scheme is a weak entropic-solution of the system of conservation laws.

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References

  1. Berthelin, F., Goudon, T., Minjeaud, S.: Kinetic schemes on staggered grids for barotropic euler models: entropy-stability, analysis. Mathematics of Computation (2014)

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  2. Herbin, R., Latché, J.C., Nguyen, T.T.: Consistent explicit staggered schemes for compressible flows; part I: the barotropic Euler equations. Technical Report, LATP, University of Aix-Marseille & CNRS (2013)

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Author information

Authors and Affiliations

  1. INRIA Team COFFEE & University of Nice Sophia Antipolis, CNRS, LJAD, UMR 7351, Nice, France

    Florent Berthelin & Thierry Goudon

  2. INRIA Team CASTOR& University of Nice Sophia Antipolis, CNRS, LJAD, UMR 7351, Nice, France

    Sebastian Minjeaud

Authors
  1. Florent Berthelin
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  2. Thierry Goudon
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  3. Sebastian Minjeaud
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Corresponding author

Correspondence to Sebastian Minjeaud .

Editor information

Editors and Affiliations

  1. Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany

    Jürgen Fuhrmann

  2. Institute Comp. Applied Mathematics, University of Münster Center for Nonlinear Sciences (CeNoS ), Münster, Germany

    Mario Ohlberger

  3. Inst. Appl. Analysis and Num. Simulation, University of Stuttgart, Stuttgart, Germany

    Christian Rohde

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© 2014 Springer International Publishing Switzerland

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Berthelin, F., Goudon, T., Minjeaud, S. (2014). Consistency Analysis of a 1D Finite Volume Scheme for Barotropic Euler Models. In: Fuhrmann, J., Ohlberger, M., Rohde, C. (eds) Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects. Springer Proceedings in Mathematics & Statistics, vol 77. Springer, Cham. https://doi.org/10.1007/978-3-319-05684-5_8

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