Two Asymptotic Models for Arrays of Underground Waste Containers

Grégoire Allaire (1, 2) , M. Briane , R. Brizzi (1) , Y. Capdeboscq

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 DeFI - Shape reconstruction and identification

We study the homogenization of two models of an underground nuclear waste repository. The nuclear waste cells are periodically stored in the middle of a geological layer and are the only source terms in a parabolic evolution problem. The diffusion constants have a very large contrast between the fuel repository and the soil. It is thus a combined problem of homogenization and singular perturbation. For two different asymptotic contrasts we give the homogenized limit problem which is rigorously justified by using two-scale convergence. Eventually we perform 2-d numerical computations to show the effectiveness of using the limit model instead of the original one.

Domaines: Analyse numérique [cs.NA]

Grégoire Allaire, M. Briane, R. Brizzi, Y. Capdeboscq. Two Asymptotic Models for Arrays of Underground Waste Containers. Applicable Analysis, 2009, 88, pp.1445-1467. ⟨hal-00784062⟩