On the boundary conditions at the contact interface between a porous medium and a free fluid

Abstract

. We consider a slow viscous flow in a two--dimensional domain consisting of a porous medium and a free fluid domain. At the boundaries of the solid part of porous medium we suppose the no--slip boundary condition. Supposing a periodic porous medium with period proportional to the characteristic pore size and a fixed porosity and using the homogenization, we find conditions on the interface linking pressures and velocities. Furthermore, we estimate the L 2 --norm of the difference between the solution for some pores size " and the combination of solutions of the limit problems and show the convergence as " tends to zero. We distinguish a) the balanced flow in free fluid domain and in porous medium and b) the small flow in porous medium caused by the flow in free fluid domain. In the case a) we obtain continuity of the normal velocities at the interface and the value of Darcy's pressure at the interface is equal to zero. In b) at the interface difference between the Darcy pressure and...