Study of the double porosity model versus the fissures thickness

Abstract

We study by homogenization the various macroscopic models associated to the diffusion through a fissured media, i.e., a set of low conductivity blocks crossed by a net of highly conducting fissures. According to the fissure thickness, δε, range we obtain different models. For this, first we homogenize by seeking the limit when ε, the small parameter associated to the blocks size, goes to zero and then we study the limit when δ goes to zero. In each situation we prove the convergence to the corresponding macroscopic model.