Section: New Results

Modelling and simulation for underground nuclear waste storage

Participant : Grégoire Allaire.

Since its foundation in 2002 G. Allaire is a member of the GDR MOMAS (Groupement de Recherches du CNRS sur les MOdélisations MAthématiques et Simulations numériques liées aux problèmes de gestion des déchets nucléaires). The problem of nuclear waste storage is of paramount importance from the industrial, as well as environmental, points of view. In the framework of this GDR MOMAS we are working on three different topics: inverse problems (reconstructing porosity and permeability fields from measurements), multi-scale numerical methods, upscaling by homogenization (finding macroscopic models and effective coefficients).

Jointly with R. Brizzi, A. Mikelic et A. Piatnitski we studied reactive flows through porous media. We supposed dominant Peclet's number, dominant Damköhler's number and general linear reactions at the pore boundaries. Our goal was to obtain the dispersion tensor and the upscaled model. We introduce the multiple scale expansions with drift for the problem and use this technique to upscale the reactive flow equations. Our result was illustrated with numerical simulations for the dispersion tensor [5] , [2] .