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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.
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Acknowledgements
This work has been supported by the Groupement de Recherches MoMaS sponsored by ANDRA, BRGM, CEA, CNRS, EDF and IRSN. G. Allaire is a member of the DEFI project at INRIA Saclay Ile de France and is partly supported by the Chair ‘Mathematical modelling and numerical simulation, F-EADS Ecole Polytechnique INRIA’.
Notes
Note
1. The research group MoMaS (Mathematical Modelling and Numerical Simulation for Nuclear Waste Management Problems) is part of the PACE Research Federation. MoMaS's sponsors are: ANDRA (National Radioactive Waste Management Agency), BRGM (Bureau des recherches géologiques et minières), CEA (Atomic Energy Commission), CNRS (National Center for Scientific Research), EDF (Électricité de France), IRSN (Institute for Radiological Protection and Nuclear Safety).