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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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Hauptverfasser: Carraro, Thomas (VerfasserIn) , Marušić-Paloka, Eduard (VerfasserIn) , Mikelić, Andro (VerfasserIn)
Dokumenttyp: Article (Journal)
Sprache:Englisch
Veröffentlicht: 26 May 2018
In: Nonlinear analysis. Real world applications
Year: 2018, Jahrgang: 44, Pages: 149-172
DOI:10.1016/j.nonrwa.2018.04.008
Online-Zugang:Resolving-System, Volltext: http://dx.doi.org/10.1016/j.nonrwa.2018.04.008
Verlag, Volltext: http://www.sciencedirect.com/science/article/pii/S1468121818304036
Volltext
Verfasserangaben:Thomas Carraro, Eduard Marušić-Paloka, Andro Mikelić

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520 |a 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. 
650 4 |a Effective tangential velocity jump 
650 4 |a Homogenization 
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650 4 |a Stationary Navier-Stokes equations 
650 4 |a Stress boundary conditions 
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