Homogenization of an incompressible viscous flow in a porous medium with double porosity

We study the homogenization of an incompressible viscous flow in a porous medium with double porosity. We derive a macroscopic model with local Navier–Stokes system in the large cavities, Darcy law in the thinner porous rock, and a contact law between the two. We use Γ-convergence methods associated...

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Bibliographic Details
Published in:Zeitschrift für angewandte Mathematik und Physik 2010-12, Vol.61 (6), p.1053-1083
Main Author: Jarroudi, Mustapha El
Format: Article
Language:English
Subjects:
Engineering
Mathematical Methods in Physics
Theoretical and Applied Mechanics
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Summary:We study the homogenization of an incompressible viscous flow in a porous medium with double porosity. We derive a macroscopic model with local Navier–Stokes system in the large cavities, Darcy law in the thinner porous rock, and a contact law between the two. We use Γ-convergence methods associated with multi-scale convergence notions in order to get this limit law. We exhibit a critical ratio between the two scales of the pores.
ISSN:0044-2275
1420-9039
DOI:10.1007/s00033-010-0097-9