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Theses

Modèles couplés en milieux poreux : transport réactif et fractures

Abstract : This thesis deals with numerical simulation of coupled models for flow and transport in porous media. We present a new method for coupling chemical reactions and transport by using a Newton-Krylov method, and we also present a model of flow in fractured media, based on a domain decomposition method that takes into account the case of intersecting fractures. This study is composed of three parts: the first part contains an analysis, and implementation, of various numerical methods for discretizing advection-diffusion problems, in particular by using operator splitting methods.
The second part is concerned with a fully coupled method for modeling transport and chemistry problems. The coupled transport-chemistry model is described, after discretization in time, by a system of nonlinear equations. The size of the system, namely the number of grid points times the number a chemical species, precludes a direct solution of the linear system. To alleviate this difficulty, we solve the system by a Newton-Krylov method, so as to avoid forming and factoring the Jacobian matrix.
In the last part, we present a model of flow in 3D for intersecting fractures, by using a domain decomposition method. The fractures are treated as interfaces between subdomains. We show existence and uniqueness of the solution, and we validate the model by numerical tests.
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https://tel.archives-ouvertes.fr/tel-00373688
Contributor : Laila Amir <>
Submitted on : Tuesday, April 7, 2009 - 1:39:00 AM
Last modification on : Friday, May 25, 2018 - 12:02:03 PM
Long-term archiving on: : Thursday, June 10, 2010 - 7:54:51 PM

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  • HAL Id : tel-00373688, version 1

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Laila Amir. Modèles couplés en milieux poreux : transport réactif et fractures. Mathématiques [math]. Université Paris Dauphine - Paris IX, 2008. Français. ⟨tel-00373688⟩

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