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Homogenization of heat diffusion in a cracked medium

By Xavier Blanc and Benjamin-Edouard Peigney

Abstract

International audienceWe 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

Topics: cracked media, heterogeneous media, homogenization, diffusion process, [ MATH.MATH-AP ] Mathematics [math]/Analysis of PDEs [math.AP], [ PHYS.MECA.THER ] Physics [physics]/Mechanics [physics]/Thermics [physics.class-ph]
Publisher: Society for Industrial and Applied Mathematics
Year: 2014
DOI identifier: 10.1137/13092191X
OAI identifier: oai:HAL:hal-01438671v1
Provided by: Hal-Diderot
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