Effective pressure boundary condition for the filtration through porous medium via homogenization
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 bounda...
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| Main Authors: | , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
26 May 2018
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| In: |
Nonlinear analysis. Real world applications
Year: 2018, Volume: 44, Pages: 149-172 |
| DOI: | 10.1016/j.nonrwa.2018.04.008 |
| Online Access: | Resolving-System, Volltext: http://dx.doi.org/10.1016/j.nonrwa.2018.04.008 Verlag, Volltext: http://www.sciencedirect.com/science/article/pii/S1468121818304036 
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| Author Notes: | Thomas Carraro, Eduard Marušić-Paloka, Andro Mikelić |
| Summary: | 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. |
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| Item Description: | Gesehen am 08.03.2019 |
| Physical Description: | Online Resource |
| DOI: | 10.1016/j.nonrwa.2018.04.008 |