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Two asymptotic models for arrays of underground waste containers

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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 2D numerical computations to show the effectiveness of using the limit model instead of the original one.

Keywords: diffusion; homogenization; porous media

Document Type: Research Article

DOI: https://doi.org/10.1080/00036810902922590

Affiliations: 1: Centre de Mathematiques Appliquees, Ecole Polytechnique, 91128 Palaiseau, France 2: Centre de Mathematiques, INSA de Rennes et IRMAR, 35043 Rennes, France 3: Mathematical Institute, University of Oxford, Oxford OX1 3LB, UK

Publication date: 2009-10-01

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