Affiliations: Université Lyon 1 – UCB, Équipe MCS, Bât. ISTIL, 15, Bld. Latarjet, 69622 Villeurbanne cedex, France E‐mail: [email protected]‐lyon1.fr | Laboratoire d'Analyse Numérique, tour 55–65 – 5ème étage, Université Pierre et Marie Curie, 4, place Jussieu, 75252 Paris cedex 05, France | Mathematical Division, Institute for Low Temperature Physics and Engineering, 47, Lenin ave., 61164 Kharkov, Ukraine E‐mail: [email protected], [email protected] | Russian Academy of Sciences, Oil & Gas Research Institute, 63, Leninski prospect, 117917 Moscow, Russia E‐mail: [email protected]
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.
