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On the Coupling of Incompressible Stokes or Navier–Stokes and Darcy Flows Through Porous Media

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Book cover Modelling and Simulation in Fluid Dynamics in Porous Media

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 28))

Abstract

In this chapter, we present the theoretical analysis of coupled incompressible Navier–Stokes (or Stokes) flows and Darcy flows with the Beavers–Joseph–Saffman interface condition. We discuss alternative interface and porous media models. We review some finite element methods used by several authors in this coupling and present numerical experiments.

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Acknowledgements

The first author acknowledges support from the UT Austin/Portugal Collaboration, Project: UT Austin/MAT/0066/2008 “Reaction-Diffusion in Porous Media.” The second author acknowledges support by NSF grant no. DMS–0810387 and by KAUST award no. KUS-C1-016-04. The third author acknowledges support from NSF with the grant DMS 0810422.

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Authors and Affiliations

  1. UPMC–Paris 6 and CNRS, UMR 7598, F-75230, Paris Cedex 05, France

    V. Girault

  2. Department of Mathematics, Texas A&M University, College Station, TX, 77843, USA

    V. Girault & G. Kanschat

  3. Department of Computational and Applied Mathematics, Rice University, Houston, TX, 77005, USA

    B. Rivière

Authors
  1. V. Girault
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  2. G. Kanschat
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  3. B. Rivière
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Correspondence to V. Girault .

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Editors and Affiliations

  1. , Department of Mathematics, University of Coimbra, EC Santa Cruz, Coimbra, 3001-501, Portugal

    José A. Ferreira

  2. , Department of Mathematics, University of Coimbra, EC Santa Cruz, Coimbra, 3001-501, Portugal

    Sílvia Barbeiro

  3. , Department of Mathematics, University of Coimbra, EC Santa Cruz, Coimbra, 3001-501, Portugal

    Gonçalo Pena

  4. Inst. Computational Engineering &, Sciences (ICES), University of Texas, Austin, Austin, 78712, Texas, USA

    Mary F. Wheeler

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Girault, V., Kanschat, G., Rivière, B. (2013). On the Coupling of Incompressible Stokes or Navier–Stokes and Darcy Flows Through Porous Media. In: Ferreira, J., Barbeiro, S., Pena, G., Wheeler, M. (eds) Modelling and Simulation in Fluid Dynamics in Porous Media. Springer Proceedings in Mathematics & Statistics, vol 28. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5055-9_1

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