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Grid Orientation Effect and MultiPoint Flux Approximation

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Finite Volumes for Complex Applications VI Problems & Perspectives

Part of the book series: Springer Proceedings in Mathematics ((PROM,volume 4))

Abstract

Some cases of nonlinear coupling between a diffusion equation, related to the computation of a pressure field within a porous medium, and a convection equation, related to the conservation of a species, lead to the apparition of the so-called grid orientation effect. We propose in this paper a new procedure to eliminate this Grid Orientation Effect, only based on the modification of the stencil of the discrete version of the convection equation. Numerical results show the efficiency and the accuracy of the method.

MSC2010: 76S05, 65M08, 76E06

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Author information

Authors and Affiliations

  1. Université Paris-Est, Paris, France

    Robert Eymard

  2. Université Paris-Est and IFP Energies nouvelles, Paris, France

    Cindy Guichard

  3. IFP Energies nouvelles, Paris, France

    Roland Masson

Authors
  1. Robert Eymard
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  2. Cindy Guichard
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  3. Roland Masson
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Corresponding author

Correspondence to Robert Eymard .

Editor information

Editors and Affiliations

  1. , Faculty of Mechanical Engineering, Czech Technical University, Karlovo náměstí 13, Prague, Czech Republic

    Jaroslav Fořt

  2. , Faculty of Mechanical Engineering, Czech Technical University, Karlovo náměstí 13, Prague, Czech Republic

    Jiří Fürst

  3. , Faculty of Mechanical Engineering, Czech Technical University, Karlovo náměstí 13, Prague, Czech Republic

    Jan Halama

  4. LATP, Laboratoire d'Analyse, Probabilités et Topologie, Université Aix-Marseille, rue Joliot Curie 39, Marseille, 13453, France

    Raphaèle Herbin

  5. LATP, Laboratoire d'Analyse, Probabilités et Topologie, Université Aix-Marseille, rue Joliot Curie 39, Marseille, 13453, France

    Florence Hubert

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Eymard, R., Guichard, C., Masson, R. (2011). Grid Orientation Effect and MultiPoint Flux Approximation. In: Fořt, J., Fürst, J., Halama, J., Herbin, R., Hubert, F. (eds) Finite Volumes for Complex Applications VI Problems & Perspectives. Springer Proceedings in Mathematics, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20671-9_44

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