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Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems pp 527–535Cite as

Gradient Discretization of Hybrid Dimensional Darcy Flows in Fractured Porous Media

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 78))

Abstract

This article deals with the discretization of hybrid dimensional model of Darcy flow in fractured porous media. These models couple the flow in the fractures represented as the surfaces of codimension one with the flow in the surrounding matrix. The convergence analysis is carried out in the framework of Gradient schemes which accounts for a large family of conforming and nonconforming discretizations. The Vertex Approximate Gradient (VAG) scheme and the Hybrid Finite Volume (HFV) scheme are applied to such models and are shown to verify the Gradient scheme framework. Our theoretical results are confirmed by a few numerical experiments performed both on tetrahedral and hexahedral meshes in heterogeneous isotropic and anisotropic media.

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References

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Acknowledgments

The authors would like to thank GDFSuez EP and Storengy for partially supporting this work, and Robert Eymard for fruitful discussions during the elaboration of this work.

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Authors and Affiliations

  1. Laboratoire de Mathématiques J.A. Dieudonné UMR CNRS 7251 and Team COFFEE, University Nice Sophia Antipolis, CNRS and INRIA Sophia Antipolis Méditerranée, Nice, France

    Konstantin Brenner, Mayya Groza & Roland Masson

  2. Laboratoire Jacques-Louis Lions, CNRS, UMR 7598, Sorbonne Universités, UPMC Univ Paris 06, F-75005, Paris, France

    Cindy Guichard

  3. Laboratoire de Mathématiques J.A. Dieudonné UMR CNRS 7251, University Nice Sophia Antipolis and CNRS, Nice, France

    Gilles Lebeau

Authors
  1. Konstantin Brenner
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  2. Mayya Groza
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  3. Cindy Guichard
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  4. Gilles Lebeau
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  5. Roland Masson
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Corresponding author

Correspondence to Cindy Guichard .

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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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© 2014 Springer International Publishing Switzerland

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Brenner, K., Groza, M., Guichard, C., Lebeau, G., Masson, R. (2014). Gradient Discretization of Hybrid Dimensional Darcy Flows in Fractured Porous Media. In: Fuhrmann, J., Ohlberger, M., Rohde, C. (eds) Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems. Springer Proceedings in Mathematics & Statistics, vol 78. Springer, Cham. https://doi.org/10.1007/978-3-319-05591-6_52

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