Comptes Rendus
A transformation approach for the derivation of boundary conditions between a curved porous medium and a free fluid
Comptes Rendus. Mécanique, Volume 338 (2010) no. 2, pp. 71-77.

The behaviour of a free fluid flow above a porous medium, both separated by a curved interface, is investigated. By carrying out a coordinate transformation, we obtain the description of the flow in a domain with a straight interface. Using periodic homogenisation, the effective behaviour of the transformed partial differential equations in the porous part is given by a Darcy law with non-constant permeability matrix. Then the fluid behaviour at the porous-liquid interface is obtained with the help of generalised boundary-layer functions: Whereas the velocity in normal direction is continuous across the interface, a jump appears in tangential direction. Its magnitude seems to be related to the slope of the interface. Therefore the results indicate a generalised law of Beavers and Joseph.

On considère le comportement d'un fluid libre au-dessus d'un milieu poreux avec une interface courbée. Utilisant une transformation des coordonnées, on obtient la description de l'écoulement dans un domaine avec une frontière plane. En limite à deux échelles, le comportement du fluid en milieu poreux est donné par une loi de Darcy avec une matrice de perméabilité non-constante. Ensuite, on obtient le comportement du fluid à l'interface : La vitesse est continue à travers l'interface dans le sens normal, mais une discontinuité apparaît en sens tangentiel. Par conséquent, les résultats indiquent une loi généralisée de Beavers et Joseph.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crme.2010.02.001
Keywords: Fluid mechanics, Homogenisation, Interfacial exchange, Porous media
Mot clés : Mécanique des fluides, Homogénéisation, Transport de masse à travers une surface de séparation, Milieux poreux

Sören Dobberschütz 1; Michael Böhm 1

1 Centre for Industrial Mathematics, FB 3, University of Bremen, Postfach 330 440, 28334 Bremen, Germany
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Sören Dobberschütz; Michael Böhm. A transformation approach for the derivation of boundary conditions between a curved porous medium and a free fluid. Comptes Rendus. Mécanique, Volume 338 (2010) no. 2, pp. 71-77. doi : 10.1016/j.crme.2010.02.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2010.02.001/

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