Second order corrector in the homogenization of a conductive-radiative heat transfer problem

Grégoire Allaire (1, 2) , Zakaria Habibi (1, 2)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 DM2S - Département de Modélisation des Systèmes et Structures

This paper focuses on the contribution of the so-called second order corrector in periodic homogenization applied to a conductive-radiative heat transfer problem. More precisely, heat is diffusing in a periodically perforated domain with a non-local boundary condition modelling the radiative transfer in each hole. If the source term is a periodically oscillating function (which is the case in our application to nuclear reactor physics), a strong gradient of the temperature takes place in each periodicity cell, corresponding to a large heat flux between the sources and the perforations. This effect cannot be taken into account by the homogenized model, neither by the first order corrector. We show that this local gradient effect can be reproduced if the second order corrector is added to the reconstructed solution.

Mots clés: Porous media; periodic homogenization; correctors; heat transfer; radiative transfer

Domaines: Analyse numérique [math.NA]

Grégoire Allaire, Zakaria Habibi. Second order corrector in the homogenization of a conductive-radiative heat transfer problem. Discrete and Continuous Dynamical Systems - Series B, 2013, 18 (1), pp.1-36. ⟨10.3934/dcdsb.2013.18.1⟩. ⟨hal-00932949⟩