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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Homogenization of the inviscid incompressible fluid flow through a 2D porous medium


Authors: Andro Mikelic and Laetitia Paoli
Journal: Proc. Amer. Math. Soc. 127 (1999), 2019-2028
MSC (1991): Primary 35B27, 76C05, 76S05
Published electronically: February 26, 1999
MathSciNet review: 1626446
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Abstract | References | Similar Articles | Additional Information

Abstract: We consider the non-stationary incompressible Euler equations in a 2D porous medium. We suppose a periodic porous medium, with the period proportional to the characteristic pore size $\varepsilon$ and with connected fluid part. The flow is subject to an external force, corresponding to an inflow. We start from an initial irrotational velocity and prove that the effective filtration velocity satisfies a transient filtration law. It has similarities with Darcy's law, but it now connects the time derivative of the filtration velocity with the pressure gradient. The viscosity does not appear in the filtration law any more and the permeability tensor is determined through auxiliary problems of decomposition type. Using the limit problem, we construct the correction for the fluid velocity and prove that $C^1 ( [0,T]; L^2(\Omega)^2 )$-norm of the error is of order $\varepsilon$. Similarly, we estimate the difference between the fluid pressure and its correction in $C ( [0,T]; L^1(\Omega) )$ as $C \varepsilon$.


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Additional Information

Andro Mikelic
Affiliation: Equipe d’Analyse Numérique Lyon-Saint Etienne, UMR 5585 CNRS, Université Lyon 1, 43 boulevard du 11 novembre 1918, 69622 Villeurbanne Cedex, France
Email: andro@iris.univ-lyon1.fr

Laetitia Paoli
Affiliation: Equipe d’Analyse Numérique Lyon-Saint Etienne, UMR 5585 CNRS, Université de Saint Etienne, 23 rue du Docteur P.Michelon, 42023 Saint Etienne Cedex, France
Email: paoli@anumsun1.univ-st-etienne.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05062-5
PII: S 0002-9939(99)05062-5
Received by editor(s): September 15, 1997
Published electronically: February 26, 1999
Communicated by: James Glimm
Article copyright: © Copyright 1999 American Mathematical Society



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