Comptes Rendus
no. 4
A FFT-based method to compute the permeability induced by a Stokes slip flow through a porous medium
[Détermination de la perméabilité d'un milieu poreux périodique pour un écoulement de Stokes avec glissement par une méthode basée sur la FFT]

Présenté par : Jean-Baptiste Leblond

Vincent Monchiet1  ; Guy Bonnet1 ; Guy Lauriat1
1 Université Paris-Est, Laboratoire modélisation et simulation multi echelle, LMSME FRE3160 CNRS, 5, boulevard Descartes, 77454 Marne la Vallée, France
Comptes Rendus. Mécanique, Volume 337 (2009) no. 4, pp. 192-197.

Cette Note présente une méthode basée sur la FFT pour la détermination de la perméabilité d'un milieu poreux périodique. Le milieu poreux est constitué d'une matrice solide indéformable saturée par un fluide visqueux. L'écoulement obéit aux équations de Stokes et une condition de glissement sur la surface du squelette solide est également considérée. La perméabilité est alors obtenue en résolvant les équations issues de l'homogénéisation de milieux périodiques et par une extension de la méthode FFT utilisée pour les matériaux composites élastiques périodiques. La prise en compte de la condition de glissement est effectuée en introduisant une interphase entre le fluide visqueux et le solide. La méthode repose sur une représentation du champ de vitesses en séries de Fourier et sur l'expression explicite du tenseur de Green dans l'espace de Fourier.

This Note presents a FFT based-method for obtaining the permeability of a periodic micro-porous medium. The periodic medium is constituted of a rigid solid matrix saturated by a viscous fluid. The flow obeys the Stokes equations and a slip condition at the surface of the rigid skeleton is considered. The permeability is obtained from the homogenization of periodic media and an extension of the FFT method used for composite elastic media. The incorporation of the slip condition is made through the introduction of an interphase between the fluid and the solid. The method of solution uses the classical expansion along Neumann series of the velocity field of the periodic problem and Green's tensor in Fourier space.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2009.04.003
Keywords: Porous media, Homogenization, Effective properties, Permeability, Viscous fluid
Mots-clés : Milieux poreux, Homogénéisation, Propriétés effectives, Perméabilité, Fluide visqueux

Vincent Monchiet 1 ; Guy Bonnet 1 ; Guy Lauriat 1

1 Université Paris-Est, Laboratoire modélisation et simulation multi echelle, LMSME FRE3160 CNRS, 5, boulevard Descartes, 77454 Marne la Vallée, France 
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Vincent Monchiet; Guy Bonnet; Guy Lauriat. A FFT-based method to compute the permeability induced by a Stokes slip flow through a porous medium. Comptes Rendus. Mécanique, Volume 337 (2009) no. 4, pp. 192-197. doi : 10.1016/j.crme.2009.04.003. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2009.04.003/

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