Second order corrector in the homogenization of a conductive-radiative heat transfer problem
Grégoire Allaire, Zakaria Habibi · Discrete and Continuous Dynamical Systems - B · 2012
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 conditionmodelling the radiative transfer in each hole. If the source term is a periodically oscillatingfunction (which is the case in our application to nuclear reactor physics), a strong gradientof the temperature takes place in each periodicity cell, corresponding to a large heat fluxbetween the sources and the perforations. This effect cannot be taken into account by thehomogenized model, neither by the first order corrector. We show that this local gradienteffect can be reproduced if the second order corrector is added to the reconstructed solution.