Asymptotic Analysis of the Laminar Viscous Flow Over a Porous Bed

Abstract

We consider the laminar viscous channel ow over a porous surface. The size of the pores is much smaller than the size of the channel and it is important to determine the e ective boundary conditions at the porous surface. After studying the corresponding boundary layers, we obtain by a rigorous asymptotic expansion Sa man's modi cation of the interface condition observed by Beavers and Joseph. The e ective coe cient in the law is determined through an auxiliary boundary-layer type problem, whose computational and modeling aspects are discussed in detail. Furthermore, the approximation errors for the velocity and for the e ective mass ow are given as powers of the characteristic pore size ". Finally, the interface condition linking the e ective pressure elds, in the porous medium and in the channel, is given and the jump of the e ective pressures is explicitly determined.

Effective pressure boundary condition for the filtration through porous medium via homogenization

“…We start by proving that problem (4)-(6) admits at least one solution satisfying estimates (18)- (20).…”

“…Absence of the statistical homogeneity does not allow direct use of the homogenization techniques. Examples of situations where the 20 presence of an interface breaks the statistical homogeneity are…”

Approximate transmission conditions through a rough thin layer: The case of periodic roughness

“…Several papers are devoted to rough boundaries and derivations of equivalent boundary conditions [1,2,3,6]. In a recent article Basson and Gérard-Varet [4] derive approximate boundary condition for a boundary with random roughness.…”

Navier–Stokes/Forchheimer models for filtration through porous media

“…This condition was later derived mathematically by homogenization by Jäger and Mikelić [36][37][38].…”

“…Starting from the original experimental works of Beavers and Joseph on the coupling conditions between a fluid and a porous medium, mathematical investigations have been carried out in [22,[36][37][38]41,42]. Under those conditions, the analysis of a coupled Stokes/Darcy problem has been studied in [10,17,19,20,28,29,26,27,30,40,48] in the steady case, and in [12,53] in the time-dependent case.…”