On the interface boundary condition of Beavers, Joseph, and Saffman. (English) Zbl 0969.76088

Jäger, Willi; Mikelic, Andro

SIAM J. Appl. Math. 60, No. 4, 1111-1127 (2000).

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.

Reviewer: Gelu Paşa (Bucureşti)

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

Keywords:

effective interface law; Saffman-Beavers-Joseph law; velocity estimates; periodic porous medium; homogenization; Poiseuille flow