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On the Conditions for Coupling Free Flow and Porous-Medium Flow in a Finite Volume Framework

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Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems (FVCA 2017)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 200))

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Abstract

This article presents model concepts for the coupling of one-phase compositional non-isothermal Navier-Stokes flow to two-phase compositional non-isothermal Darcy flow in a finite volume framework. The focus of the presented coupling conditions is on defining appropriate conditions for momentum transfer without introducing additional degrees of freedom at the interface. Four different methods are presented and compared with the help of numerical simulations of flow around an evaporating porous medium. The results show that simply assigning the porous medium gas pressure as the gas pressure at the interface (CM1) leads to high, non-physical velocities in cells at the corner of the porous medium. This effect can be weakened by recalculating the interface gas pressure with the help of the total mass balance and additional assumptions concerning the state at the interface (CM2). Allowing only momentum transfer between the gas phases (CM3) leads to an increase of the resistance against inflow, if the porous medium is filled with water. However, in order to minimize the assumptions made, an additional system of equations can be introduced and solved to recalculate the pressure at the interface (CM4). This method is computationally more expensive but shows the expected physical behavior regarding the velocity profile.

The original version of the book was revised: Missed out corrections have been updated. The erratum to the book is available at https://doi.org/10.1007/978-3-319-57394-6_58

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Authors and Affiliations

  1. Universität Stuttgart, Pfaffenwaldring 61, 70569, Stuttgart, Germany

    Thomas Fetzer, Christoph Grüninger, Bernd Flemisch & Rainer Helmig

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  1. Thomas Fetzer
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  2. Christoph Grüninger
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  3. Bernd Flemisch
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  4. Rainer Helmig
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Correspondence to Thomas Fetzer .

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Editors and Affiliations

  1. Equipe RAPSODI, Inria Lille - Nord Europe, Villeneuve-d’Ascq, France

    Clément Cancès

  2. Commissariat à l'énergie atomique et aux énergies alternatives, Centre de Saclay, Gif-sur-Yvette, France

    Pascal Omnes

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Fetzer, T., Grüninger, C., Flemisch, B., Helmig, R. (2017). On the Conditions for Coupling Free Flow and Porous-Medium Flow in a Finite Volume Framework. In: Cancès, C., Omnes, P. (eds) Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems. FVCA 2017. Springer Proceedings in Mathematics & Statistics, vol 200. Springer, Cham. https://doi.org/10.1007/978-3-319-57394-6_37

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