Seepage through a strongly heterogeneous material, consisting of open saturated pores, is modeled as a Stokes flow contained in a rigid matrix. Through homogenization of the problem, a two-scale formulation is derived. The subscale problem is that of a Stokes flow whereas the macroscale problem pertains to a Darcy flow. The prolongation of the macroscale Darcy flow fulfills the variational consistent macrohomogeniety condition and is valid for both linear and nonlinear subscale flows. The subscale problem is solved using the finite element method. Numerical results concerning both linear and nonlinear flow are presented.
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Univ Clermont Ferrand, CNRS, UMR 6620, Math Lab, F-63177 Clermont Ferrand, FranceUniv Clermont Ferrand, CNRS, UMR 6620, Math Lab, F-63177 Clermont Ferrand, France
Amirat, Youcef
Shelukhin, Vladimir
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MA Lavrentyev Hydrodynam Inst, Novosibirsk 630090, RussiaUniv Clermont Ferrand, CNRS, UMR 6620, Math Lab, F-63177 Clermont Ferrand, France
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Univ Pau & Pays Adour, UMR 5142, Lab Math & Leurs Applicat IPRA, CNRS, Av Univ, F-64000 Pau, FranceUniv Pau & Pays Adour, UMR 5142, Lab Math & Leurs Applicat IPRA, CNRS, Av Univ, F-64000 Pau, France
Amaziane, Brahim
Pankratov, Leonid
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Univ Pau & Pays Adour, UMR 5142, Lab Math & Leurs Applicat IPRA, CNRS, Av Univ, F-64000 Pau, France
Moscow Inst Phys & Technol, Lab Fluid Dynam & Seism, 9 Inst Skiy, Dolgoprudnyi 141700, Moscow Region, RussiaUniv Pau & Pays Adour, UMR 5142, Lab Math & Leurs Applicat IPRA, CNRS, Av Univ, F-64000 Pau, France
Pankratov, Leonid
Piatnitski, Andrey
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Univ Tromso, Campus Narvik,Postbox 385, N-8505 Narvik, Norway
Inst Informat Transmiss Problems RAS, Bolshoy Karetny 19, Moscow 127051, RussiaUniv Pau & Pays Adour, UMR 5142, Lab Math & Leurs Applicat IPRA, CNRS, Av Univ, F-64000 Pau, France