Homogenization of fluid–porous interface coupling in a biconnected fractured media

Abstract

The modelization of mass transfer through biconnected fractured porous media is studied by homogenizing the coupling between the Darcyan percolation and the viscous Stokes flow on their interface governed by the Beavers–Joseph law. The case of high transmission coefficients is considered. The asymptotic behaviour is completely described with the help of the solutions of some specific local problems and of a nonhomogeneous Neumann problem defined by the effective permeability tensor.

Keywords:

• fractured porous media
• Stokes flow
• Beavers–Joseph interface
• homogenization
• two-scale convergence

AMS Subject Classifications:

• 35B27
• 76M50
• 76S05

Acknowledgements

This work has been accomplished during the visit of D. Polişevschi at the I.R.M.A.R.’s Department of Mechanics (University of Rennes 1), whose support is gratefully acknowledged.