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
2 ULB - Département de Mathématique [Bruxelles]
3 COFFEE - COmplex Flows For Energy and Environment
4 JAD - Laboratoire Jean Alexandre Dieudonné

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.

Mots clés: reduced basis method; porous media; homogenization; reduced basis method.

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]; Bibliothèque électronique [cs.DL]

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, 2013, 23 (13), pp.1-33. ⟨10.1142/S0218202513500395⟩. ⟨hal-00674519v2⟩