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Numerical homogenization of a nonlinearly coupled elliptic-parabolic system, reduced basis method, and application to nuclear waste storage

Antoine Gloria 1, 2 Thierry Goudon 3, 4 Stella Krell 3, 4
1 SIMPAF - SImulations and Modeling for PArticles and Fluids
LPP - Laboratoire Paul Painlevé - UMR 8524, Inria Lille - Nord Europe
3 COFFEE - COmplex Flows For Energy and Environment
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR7351
Abstract : We consider the homogenization of a coupled system of PDEs describing flows in highly heterogeneous porous media. Due to the coupling, the effective coefficients always depend on the slow variable, even in the simple case when the porosity is taken purely periodic. Therefore the most important part of the computational time for the numerical simulation of such flows is dedicated to the determination of these coefficients. We propose a new numerical algorithm based on Reduced Basis techniques, which significantly improves the computational performances.
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Submitted on : Friday, February 22, 2013 - 10:22:02 AM
Last modification on : Monday, October 12, 2020 - 2:28:04 PM
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Antoine Gloria, Thierry Goudon, Stella Krell. Numerical homogenization of a nonlinearly coupled elliptic-parabolic system, reduced basis method, and application to nuclear waste storage. Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2013, 23 (13), pp.1-33. ⟨10.1142/S0218202513500395⟩. ⟨hal-00674519v2⟩

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