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Homogenization of the criticality spectral equation in neutron transport

Grégoire Allaire, Guillaume Bal (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We address the homogenization of an eigenvalue problem for the neutron transport equation in a periodic heterogeneous domain, modeling the criticality study of nuclear reactor cores. We prove that the neutron flux, corresponding to the first and unique positive eigenvector, can be factorized in the product of two terms, up to a remainder which goes strongly to zero with the period. One term is the first eigenvector of the transport equation in the periodicity cell. The other term is the...

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