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Interface Conditions for Arbitrary Flows in Coupled Porous-Medium and Free-Flow Systems

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Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples (FVCA 2020)

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Abstract

Physically consistent interface conditions are important for accurate mathematical modelling and numerical simulation of flow and transport processes in coupled free-flow and porous-medium systems. Traditional coupling concepts are valid for simplified cases only, such as flows parallel to the fluid-porous interface or very specific boundary value problems. This severely limits the range of applications that can be accurately modelled. Evidently, there is a need for more general interface conditions to couple free flow to porous-medium flow. In this paper, we propose new coupling conditions for arbitrary flow directions and periodic porous media. These conditions are derived by the theory of homogenisation and boundary layers and are applicable to general filtration problems. The derived set of coupling conditions are validated by comparison of pore-scale to macroscale numerical simulations.

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Acknowledgements

The work is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—Project Number 327154368—SFB 1313.

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Authors and Affiliations

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

    Elissa Eggenweiler & Iryna Rybak

Authors
  1. Elissa Eggenweiler
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  2. Iryna Rybak
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Corresponding author

Correspondence to Elissa Eggenweiler .

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Editors and Affiliations

  1. NORCE Norwegian Research Centre AS, Bergen, Norway

    Robert Klöfkorn

  2. Department of Mathematics, University of Bergen, Bergen, Norway

    Eirik Keilegavlen

  3. Department of Mathematics, University of Bergen, Bergen, Norway

    Florin A. Radu

  4. Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany

    Jürgen Fuhrmann

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Eggenweiler, E., Rybak, I. (2020). Interface Conditions for Arbitrary Flows in Coupled Porous-Medium and Free-Flow Systems. In: Klöfkorn, R., Keilegavlen, E., Radu, F.A., Fuhrmann, J. (eds) Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples. FVCA 2020. Springer Proceedings in Mathematics & Statistics, vol 323. Springer, Cham. https://doi.org/10.1007/978-3-030-43651-3_31

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