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Etude de quelques problèmes d'écoulement dans les milieux poreux

Abstract : The aim of this thesis is the study of two problems of flow through porous media. In the first and the second chapter we study in the general framework of the homogenization method the flow of a viscous fluid through an elastic thin porous media. After the proof of the convergence of the homogenization process by using the two-scale convergence method it is possible to take the limit as the second small parameter (who caracterize the thickness of the solid part) tends to zero. We obtain a viscoelastic media with fading memory. We consider the two classical cases, when we have a Stokes flow in the fluid part and when we have a Navier-Stokes flow in the fluid part. In the third chapter we study a double porosity model in a double periodicity media. From a mechanical point of view this model represents a fracturated porous media. From a mathematical point of view we study a Neumann problem with double periodicity. We prove existence and unicity for such a problem and using the three-scale convergence method we obtain the homogenized equation and the homogenized coefficients. The result we obtain is a Darcy law at the macroscale and this show us that, at least in the steady case, both the double periodicity model and the double porosity model are the same
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  • HAL Id : tel-01777102, version 1



Ioana-Andreea Ene. Etude de quelques problèmes d'écoulement dans les milieux poreux. Mathématiques générales [math.GM]. Université Paul Verlaine - Metz, 1995. Français. ⟨NNT : 1995METZ053S⟩. ⟨tel-01777102⟩



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