A FFT-based method to compute the permeability induced by a Stokes slip flow through a porous medium

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. To cite this article: V. Monchiet et al., C.R. Mecanique 337 (2009). (C) 2009 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.