Homogenization of a convection–diffusion model with reaction in a porous medium
Grégoire Allaire, Anne-Lise Raphael · Comptes Rendus Mathématique · 2007
We study the homogenization of a convection–diffusion equation with reaction in a porous medium when both the Péclet and Damkohler numbers are large. We prove that, up to a large drift, the homogenized equation is a diffusion equation. Our method is based on a factorization principle and two-scale convergence. The main consequence is that we obtain rigorous definitions of homogenized coefficients which justify heuristic arguments in the method of volume averaging. We perform 2-d numerical computations of the diffusion–dispersion homogenized coefficient which are in very good agreement with previous results obtained by the method of volume averaging.