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Gradient discretization of hybrid dimensional Darcy flows in fractured porous media

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Abstract

This article deals with the discretization of hybrid dimensional Darcy flows in fractured porous media. These models couple the flow in the fractures represented as 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 scheme and the hybrid finite volume scheme are extended to such models and are shown to verify the gradient scheme framework. Our theoretical results are confirmed by numerical experiments performed on tetrahedral, Cartesian and hexahedral meshes in heterogeneous isotropic and anisotropic porous media.

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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 7351 CNRS, University Nice Sophia Antipolis, Parc Valrose, 06108, Nice Cedex 02, France

    Konstantin Brenner, Mayya Groza, Gilles Lebeau & Roland Masson

  2. Team COFFEE, INRIA Sophia Antipolis Méditerranée, Parc Valrose, 06108, Nice Cedex 02, France

    Konstantin Brenner, Mayya Groza & Roland Masson

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

    Cindy Guichard

  4. INRIA, ANGE Project-Team, Rocquencourt, B.P. 105, 78153, Le Chesnay Cedex, France

    Cindy Guichard

  5. CEREMA, ANGE Project-Team, 134 rue de Beauvais, 60280, Margny-Lès-Compiègne, France

    Cindy Guichard

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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Correspondence to Roland Masson.

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Brenner, K., Groza, M., Guichard, C. et al. Gradient discretization of hybrid dimensional Darcy flows in fractured porous media. Numer. Math. 134, 569–609 (2016). https://doi.org/10.1007/s00211-015-0782-x

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  • DOI: https://doi.org/10.1007/s00211-015-0782-x

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