## Fluid structure interaction problems in deformable porous media: Toward permeability of deformable porous media

• In this work the problem of fluid flow in deformable porous media is studied. First, the stationary fluid-structure interaction (FSI) problem is formulated in terms of incompressible Newtonian fluid and a linearized elastic solid. The flow is assumed to be characterized by very low Reynolds number and is described by the Stokes equations. The strains in the solid are small allowing for the solid to be described by the Lame equations, but no restrictions are applied on the magnitude of the displacements leading to strongly coupled, nonlinear fluid-structure problem. The FSI problem is then solved numerically by an iterative procedure which solves sequentially fluid and solid subproblems. Each of the two subproblems is discretized by finite elements and the fluid-structure coupling is reduced to an interface boundary condition. Several numerical examples are presented and the results from the numerical computations are used to perform permeability computations for different geometries.

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Author: O. Iliev, A. Mikelic, P. Popov urn:nbn:de:hbz:386-kluedo-13493 Berichte des Fraunhofer-Instituts für Techno- und Wirtschaftsmathematik (ITWM Report) (65) Report English 2004 2004 Fraunhofer-Institut für Techno- und Wirtschaftsmathematik 2004/10/27 deformable porous media; finite elements; fluid-structure interaction; linear elasticity; stokes; upscaling Fraunhofer (ITWM) 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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