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Homogenisation of the Stokes problem with a pure non-homogeneous slip boundary condition by the periodic unfolding method

Published online by Cambridge University Press:  21 February 2011

ANCA CAPATINA  and
HORIA ENE
ANCA CAPATINA
Affiliation:
Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, RO-70700 Bucharest, Romania email: anca.capatina@imar.ro
HORIA ENE
Affiliation:
Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, RO-70700 Bucharest, Romania email: anca.capatina@imar.ro University of Piteşti, Department of Mathematics, 110040 Piteşti, România email: horia.ene@imar.ro
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Abstract

We study the homogenisation of the Stokes system with a non-homogeneous Fourier boundary condition on the boundary of the holes, depending on a parameter γ. Such systems arise in the modelling of the flow of an incompressible viscous fluid through a porous medium under the influence of body forces. At the limit, by using the periodic unfolding method in perforated domains, we obtain, following the values of γ, different Darcy's laws of type Mu = −N∇p + F with suitable matrices M and N with F depending on the right-hand side in the bulk term and in the boundary condition.

Keywords

HomogenisationPeriodic unfoldingStokes systemNon-homogeneous Fourier boundary condition
Type
Papers
Information
European Journal of Applied Mathematics , Volume 22 , Issue 4 , August 2011 , pp. 333 - 345
Copyright
Copyright © Cambridge University Press 2011

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