Effective pressure boundary condition for the filtration through porous medium via homogenization. (December 2018)

• Record Type: Journal Article
• Authors: Carraro, Thomas; Marušić-Paloka, Eduard; Mikelić, Andro
• Is Part Of: Nonlinear analysis. Volume 44(2018)
• Page Start: 149
• Page End: 172
• Publication Date: 2018-12
• Subjects: Homogenization -- Stationary Navier–Stokes equations -- Stress boundary conditions -- Effective tangential velocity jump -- Porous media; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2018.04.008
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We present homogenization of the viscous incompressible porous media flows under stress boundary conditions at the outer boundary. In addition to Darcy's law describing filtration in the interior of the porous medium, we derive rigorously the effective pressure boundary condition at the outer boundary. It is a linear combination of the outside pressure and the applied shear stress. We use the two-scale convergence in the sense of boundary layers, introduced by Allaire and Conca (1997) to obtain the boundary layer structure next to the outer boundary. The approach allows establishing the strong L 2 -convergence of the velocity corrector and identification of the effective boundary velocity slip jump. The theoretical results are confirmed through numerical experiments.