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On the interface boundary condition of Beavers, Joseph, and Saffman. (English) Zbl 0969.76088
For a periodic porous medium, the authors consider the problem of effective boundary conditions on the interface between a porous medium and a free fluid. The results of homogenization theory are used to obtain a rigorous justification for the Saffman’s form of the Beavers and Joseph law. Some previous results of the authors are used to obtain interesting estimations of the velocity field. Finally, a comparison is made between classical Poiseuille flow and a Poiseuille flow with Beavers and Joseph condition.

MSC:
76S05 Flows in porous media; filtration; seepage
76M50 Homogenization applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
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