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 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. We show that the cracked surface of the domain induces a volume source term in the homogenized equation.

Domaines: Modélisation et simulation; Equations aux dérivées partielles [math.AP]

Xavier Blanc, Benjamin-Edouard Peigney. Homogenization of heat diffusion in a cracked medium. Comptes Rendus. Mathématique, 2014, 352 (5), pp.405-409. ⟨10.1016/j.crma.2014.03.003⟩. ⟨hal-01007668⟩