Topological optimization applied to a variable density and conductivity model of pollution in porous media

Abstract

This article deals with modeling and numerical study of pollutants transfer in porous media by topological optimization. Indeed we perform the modeling of pollution in porous media in non‐permanent cases by assuming the variability or not of some parameters such as the conductivity and the density. The model of pollutants transfer obtained in the case when the conductivity and the density are constant is similar to meadows of few coefficients to the one obtained by varying (with respect to the space) only the conductivity. By taking into account the space variability of density, conductivity, and diffusion under some assumptions we obtain a more realistic model of pollutants transfer. Topological optimization applied to these models allows reaching numerically the optimal design of a least squared functional. In fact, topological derivatives are used as descent direction and permit to creation of circular or cylindrical holes in order to decrease the considered cost function. Numerical results obtained are presented for Neumann and Dirichlet conditions on the boundary of the holes for 2 and 3 dimensions in nonpermanent cases of pollutants transfer.