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Vietnam Journal of Mathematics

, Volume 44, Issue 3, pp 557–586 | Cite as

The Generalized Finite Volume SUSHI Scheme for the Discretization of Richards Equation

  • Konstantin Brenner
  • Danielle HilhorstEmail author
  • Huy-Cuong Vu-Do
Article
  • 94 Downloads

Abstract

In this article, we apply the generalized finite volume method SUSHI to the discretization of Richards equation, an elliptic-parabolic equation modeling groundwater flow, where the diffusion term can be anisotropic and heterogeneous. This class of locally conservative methods can be applied to a wide range of unstructured possibly non-matching polyhedral meshes in arbitrary space dimension. As is needed for Richards equation, the time discretization is fully implicit. We obtain a convergence result based upon a priori estimates and the application of the Fréchet–Kolmogorov compactness theorem. We implement the scheme and present numerical tests.

Keywords

Richards equation Finite volume scheme SUSHI scheme 

Mathematics Subject Classification (2010)

35K15 35K65 65M08 65M12 76S05 

Notes

Acknowledgments

We thank Professor Pascal Omnès as well as the referees for a careful rereading of our manuscript which has led to many improvements. This work was supported by the ITN Marie Curie Network FIRST and Fondation Jacques Hadamard.

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Copyright information

© Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2015

Authors and Affiliations

  • Konstantin Brenner
    • 1
  • Danielle Hilhorst
    • 2
    Email author
  • Huy-Cuong Vu-Do
    • 3
  1. 1.LJAD University Nice Sophia-Antipolis & Coffee team Inria Sophia-AntipolisMéditerranéeFrance
  2. 2.Laboratoire de MathématiquesCNRS et Université de Paris-SudOrsayFrance
  3. 3.Faculty of Mathematics and Computer ScienceUniversity of SciencesHo Chi MinhVietnam

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