Stokes–Darcy coupling for periodically curved interfaces

Sören Dobberschütz

doi:10.1016/j.crme.2013.12.003

Stokes–Darcy coupling for periodically curved interfaces

Sören Dobberschütz ¹

¹ Nano-Science Center, University of Copenhagen, Universitetsparken 5, 2100 København, Denmark

Comptes Rendus. Mécanique, Volume 342 (2014) no. 2, pp. 73-78.

Abstract
Résumé

We investigate the boundary condition between a free fluid and a porous medium, where the interface between the two is given as a periodically curved structure. Using a coordinate transformation, we can employ methods of periodic homogenisation to derive effective boundary conditions for the transformed system. In the porous medium, the fluid velocity is given by Darcy's law with a non-constant permeability matrix. In tangential direction as well as for the pressure, a jump appears. Its magnitudes can be calculated with the help of a generalised boundary layer function. The results can be interpreted as a generalised law of Beavers and Joseph for curved interfaces.

On considère le comportement d'un fluide libre au-dessus d'un milieu poreux avec une interface courbée périodique. Utilisant une transformation des coordonnées, on peut utiliser des méthodes d'homogénéisation périodique pour la dérivation des conditions aux limites. Le comportement du fluide en milieu poreux est donné par une loi de Darcy avec une matrice de perméabilité non constante. Ensuite, on obtient le comportement du fluide à l'interface. Une discontinuité apparaît pour la pression ainsi que pour la vitesse tangentielle. L'amplitude des discontinuités peut être calculée par une fonction de couche limite généralisée. Ainsi, les résultats donnent une loi généralisée de Beavers et Joseph pour des interfaces courbées.

Received: 2013-11-01
Accepted: 2013-12-13
Published online: 2014-01-24

DOI: 10.1016/j.crme.2013.12.003

Keywords: Fluid mechanics, Homogenisation, Interfacial exchange, Porous media
Mots-clés : Mécanique des fluides, Homogénéisation, Transport de masse à travers une surface de séparation, Milieux poreux

Author's affiliations:

Sören Dobberschütz ¹

¹ Nano-Science Center, University of Copenhagen, Universitetsparken 5, 2100 København, Denmark

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     title = {Stokes{\textendash}Darcy coupling for periodically curved interfaces},
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Sören Dobberschütz. Stokes–Darcy coupling for periodically curved interfaces. Comptes Rendus. Mécanique, Volume 342 (2014) no. 2, pp. 73-78. doi : 10.1016/j.crme.2013.12.003. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2013.12.003/

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