Homogenization of heat diffusion in a cracked medium

Xavier Blanc (1) , Benjamin-Edouard Peigney (2)

1 LJLL - Laboratoire Jacques-Louis Lions
2 DAM/DIF - DAM Île-de-France

We develop in this note a homogenization method to tackle the problem of a diffusion process through a cracked medium. We show that the cracked surface of the domain induces a source term in the homogenized equation. We assume that the cracks are orthogonal to the surface of the material, where an incoming heat flux is applied. The cracks are supposed to be of depth 1, of small width, and periodically arranged.

Mots clés: homogenization; diffusion process; heterogeneous media; cracked media

Domaines: Equations aux dérivées partielles [math.AP]; Thermique [physics.class-ph]

Xavier Blanc, Benjamin-Edouard Peigney. Homogenization of heat diffusion in a cracked medium. Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 2014, ⟨10.1137/13092191X⟩. ⟨hal-01438671⟩