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

• Verfasst von: Carraro, Thomas [VerfasserIn]
• Verfasst von: Marušić-Paloka, Eduard [VerfasserIn]
• Verfasst von: Mikelić, Andro [VerfasserIn]
• Titel: Effective pressure boundary condition for the filtration through porous medium via homogenization
• Verf.angabe: Thomas Carraro, Eduard Marušić-Paloka, Andro Mikelić
• Umfang: 24 S.
• Fussnoten: Gesehen am 08.03.2019
• Titel Quelle: Enthalten in: Nonlinear analysis / Real world applications
• Jahr Quelle: 2018
• Band/Heft Quelle: 44(2018), S. 149-172
• DOI: doi:10.1016/j.nonrwa.2018.04.008
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1588483614

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 L2-convergence of the velocity corrector and identification of the effective boundary velocity slip jump. The theoretical results are confirmed through numerical experiments.