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

Grégoire Allaire; Zakaria Habibi

doi:10.3934/dcdsb.2013.18.1

Article Contents

2013, Volume 18, Issue 1: 1-36. Doi: 10.3934/dcdsb.2013.18.1

This issue Previous Article Next Article The basic reproduction number of discrete SIR and SEIS models with periodic parameters

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

Grégoire Allaire^1, and
Zakaria Habibi^2,

1.
CMAP, Ecole Polytechnique, 91128 Palaiseau, & DM2S, CEA Saclay, 91191 Gif sur Yvette
2.
DM2S/SFME/LTMF, CEA Saclay, 91191 Gif sur Yvette, & CMAP, Ecole Polytechnique, 91128 Palaiseau

Received: March 2012

Revised: July 2012

Published: January 2013

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Abstract

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.

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Mathematics Subject Classification: Primary: 35B27, 80M40; Secondary: 80A20.

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