Asymptotic analysis of the laminar viscous flow over a porous bed

We consider the laminar viscous channel flow over a porous surface. The siz e of the pores is much smaller than the size of the channel, and it is impo rtant to determine the effective boundary conditions at the porous surface. We study the corresponding boundary layers, and, by a rigorous asymptotic expansion, we obtain Saffman's modification of the interface condition obse rved by Beavers and Joseph. The effective coefficient in the law is determi ned through an auxiliary boundary-layer type problem, whose computational a nd modeling aspects are discussed in detail. Furthermore, the approximation errors for the velocity and for the effective mass flow are given as power s of the characteristic pore size. Finally, we give the interface condition linking the effective pressure fields in the porous medium and in the chan nel, and we determine the jump of the effective pressures explicitly.