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An Asymptotic-Preserving Scheme for Systems of Conservation Laws with Source Terms on 2D Unstructured Meshes

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Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects

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

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Abstract

A finite volumes numerical scheme is here proposed for hyperbolic systems of conservation laws with source terms which degenerate into parabolic systems in large times when the source terms become stiff. In this framework, it is crucial that the numerical schemes are asymptotic-preserving i.e. that they degenerate accordingly . Here, an asymptotic-preserving numerical scheme is designed for any system within the aforementioned class on 2D unstructured meshes. This scheme is proved to be consistent and stable under a suitable CFL condition. Moreover, we show that it is also possible to prove that it preserves the set of (physically) admissible states under a geometrical property on the mesh. Finally, numerical examples are given to illustrate its behavior.

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Acknowledgments

This work was supported by ANR-12-IS01-0004-01 GEONUM.

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Authors and Affiliations

  1. Laboratoire de Mathématiques Jean Leray, Université de Nantes, 2 rue de la Houssinière, 44322, Nantes Cedex 3, France

    C. Berthon, G. Moebs & R. Turpault

Authors
  1. C. Berthon
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  2. G. Moebs
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  3. R. Turpault
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Corresponding author

Correspondence to R. Turpault .

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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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Berthon, C., Moebs, G., Turpault, R. (2014). An Asymptotic-Preserving Scheme for Systems of Conservation Laws with Source Terms on 2D Unstructured Meshes. 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_9

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