Homogenizing the Darcy-Stokes couplingReport as inadecuate

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1 IRMAR - Institut de Recherche Mathématique de Rennes 2 IMAR -Simion Stoilow- Institute of Mathematics

Abstract : We study a fluid flow traversing a porous medium and obeying the Darcy-s law in the case when this medium is fractured by a periodical distribution of fissures filled with a Stokes fluid. These two flows are coupled by a Beavers-Joseph type interface condition. As the small period of the distribution shrinks to zero, the resulting asymptotic behaviour is implicitely described by two underlying macroscopic quantities: the limit of the Stokes velocity and the limit of the Darcy pressure, solutions of a new coupled system obtained by homogenization. The behaviour of the macroscopic two-scale limit of the filtration velocity is given by an explicit two-scale Darcy type law, presenting coupling terms with the gradient of the limit of the Darcy pressure and with the limit of the Stokes velocity.

Keywords : Fractured porous media Stokes flow Beavers-Joseph interface Homogenization Two-scale convergence

Author: Isabelle Gruais - Dan Polisevski -

Source: https://hal.archives-ouvertes.fr/


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