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Two Asymptotic Models for Arrays of Underground Waste Containers

Grégoire Allaire 1, 2 M. Briane R. Brizzi 1 Y. Capdeboscq 
2 DeFI - Shape reconstruction and identification
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
Abstract : 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.
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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⟩

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