期刊
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
卷 44, 期 -, 页码 149-172出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.nonrwa.2018.04.008
关键词
Homogenization; Stationary Navier-Stokes equations; Stress boundary conditions; Effective tangential velocity jump; Porous media
资金
- German Research Council (DFG) through project Multiscale modeling and numerical simulations of Lithium ion battery electrodes using real microstructures [CA 633/2-1]
- Croatian science foundation [3955]
- LABEX MILYON of Universite de Lyon, within the program Investissements d'Avenir [ANR-10-LABX-0070, ANR-11-IDEX-0007]
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. (C) 2018 Elsevier Ltd. All rights reserved.
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