The effective permeability of fractured porous media subject to the Beavers-Joseph contact law

Isabelle Gruais (1) , Dan Polisevski (2) , Florentina-Alina Stanescu (2)

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

We are interested in the asymptotic behaviour of a fluid flow contained in a microscopic periodic distribution of fissures perturbating a porous medium where the Darcy law is valid, when the coupling between both systems is modeled by the Beavers-Joseph interface condition. As the small period of the distribution tends to zero, the interface condition is preserved on a microscopic scale under the additional assumption that the permeability coefficients behave like the squared period of the distribution which is also the squared size of the fissures. Moreover, the resulting pressure is purely macroscopic unlike the velocity field which also depends on the microscopic variable.

Mots clés: Two-scale convergence; Fractured porous media; Homogenization; Stokes flow \sep Beavers-Joseph interface

Domaines: Equations aux dérivées partielles [math.AP]

Isabelle Gruais, Dan Polisevski, Florentina-Alina Stanescu. The effective permeability of fractured porous media subject to the Beavers-Joseph contact law. Asymptotic Analysis, 2014, 90 (3-4), pp.267-280. ⟨10.3233/ASY-141248⟩. ⟨hal-00904846⟩