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Stokes–Brinkman–Darcy Models for Coupled Free-Flow and Porous-Medium Systems

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Finite Volumes for Complex Applications X—Volume 1, Elliptic and Parabolic Problems (FVCA 2023)

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Abstract

Coupled systems involving free flow and porous medium have gained significant attention in recent years due to their prevalence in environment and industry. Most of the coupling approaches are suitable only for flows parallel to the fluid–porous interface, and a generalization of the coupling concept is required. In this work, we consider a thin transition region between the free-flow and porous-medium domains, which stores and transports mass, momentum, and energy. The flow system of interest is incompressible and single-phase. The model comprises the Stokes equations in the free-flow domain, the Brinkman equations in the transition region, and Darcy’s law in the porous medium. These models are coupled through suitable interface conditions. Numerical simulation results for the coupled full-dimensional Stokes–Brinkman–Darcy model are provided. A dimensionally reduced formulation for the coupled model is proposed in the case of a thin transition region. This model consists of the averaged Brinkman equations of co-dimension one, which are coupled to the full-dimensional Stokes and Darcy’s equations in the free flow and porous medium, respectively.

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Acknowledgements

The work is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - Project Number 490872182.

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Authors and Affiliations

  1. Institute of Applied Analysis and Numerical Simulation, University of Stuttgart, Pfaffenwaldring 57, 70569, Stuttgart, Germany

    Linheng Ruan & Iryna Rybak

Authors
  1. Linheng Ruan
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  2. Iryna Rybak
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Correspondence to Linheng Ruan .

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Editors and Affiliations

  1. IRMA, Strasbourg, France

    Emmanuel Franck

  2. Weierstrass Institute, Berlin, Germany

    Jürgen Fuhrmann

  3. IRMA, Strasbourg, France

    Victor Michel-Dansac

  4. IRMA, Strasbourg, France

    Laurent Navoret

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Ruan, L., Rybak, I. (2023). Stokes–Brinkman–Darcy Models for Coupled Free-Flow and Porous-Medium Systems. In: Franck, E., Fuhrmann, J., Michel-Dansac, V., Navoret, L. (eds) Finite Volumes for Complex Applications X—Volume 1, Elliptic and Parabolic Problems. FVCA 2023. Springer Proceedings in Mathematics & Statistics, vol 432. Springer, Cham. https://doi.org/10.1007/978-3-031-40864-9_31

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