It is generally accepted that the effective velocity of a viscous flow over a porous bed satisfies the Beavers-Joseph slip law. To the contrary, the interface law for the effective stress has been a subject of controversy. Recently, a pressure jump interface law has been rigourously derived by Marciniak-Czochra and Mikelić. In this paper, we provide a confirmation of the analytical result using direct numerical simulation of the flow at the microscopic level. To the best of the authors' knowledge, this is the first numerical confirmation of the pressure interface law in the literature.

It is generally accepted that the effective velocity of a viscous flow over a porous bed satisfies the Beavers-Joseph slip law. To the contrary, in the case of a forced infiltration of a viscous fluid into a porous medium the interface law has been a subject of controversy. In this paper, we prove rigorously that the effective interface conditions are: (i) the continuity of the normal effective velocities; (ii) zero Darcy's pressure and (iii) a given slip velocity. The effective tangential slip velocity is calculated from the boundary layer and depends only on the pore geometry. In the next order of approximation, we derive a pressure slip law. An independent confirmation of the analytical results using direct numerical simulation of the flow at the microscopic level is given, as well.

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