Affiliations: URA 740, Equipe d'Analyse Numérique, Université de Saint-Etienne, 23, rue Dr. P. Michelon, 42023 Saint Etienne, France | Department of Mathematics, University of Zagreb, Bijenička 30, 41000 Zagreb, Croatia | URA 740, Laboratoire d'Analyse Numérique, Université Lyon 1, Bât 101, 43, bd. du onze novembre, 69622 Villeurbanne Cedex, France
Note: [] Correspondence to: A. Bourgeat, URA 740 Equipe d'Analyse Numérique, Université de Saint-Etienne 23 rue Dr. P. Michelon, 42023 Saint Etienne, France.
Abstract: We consider the behavior of the solution to Stokes system in porous medium, with characteristic size of the pores ε and containing a thin fissure {0≤xn≤η}, of width η. The limit when ε and η tend to zero gives the effective (or homogenized) behavior for the flow. Depending on the comparison between ε and η we obtain three possible limits: – When η<κε2/3 the fissure is not giving any contribution, i.e., the effective fluid flow is governed by the Darcy law. – When η~κε2/3 the coupling effect appears and the effective flow behaves like Darcy flow in the porous medium coupled with the tangential flow on the surface {xn = 0}. Compared to the previous case η<ε2/3, the effective velocity has now an additional tangential component concentrated on {xn = 0}. – When η>κε2/3 the fissure is dominant and the tangential flow at {xn = 0} is dominant. Meanwhile in the other part of the porous medium the effective velocity is equal to zero.
