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Homogenization of the criticality spectral equation in neutron transport

Published online by Cambridge University Press:  15 August 2002

Grégoire Allaire
Affiliation:
Laboratoire d'Analyse Numérique, Université Paris VI, 75252 Paris Cedex 5, France, and CEA Saclay, DRN/DMT/SERMA, 91191 Gif-sur-Yvette, France. allaire@ann.jussieu.fr.
Guillaume Bal
Affiliation:
Électricité de France DER/IMA/MMN, 92141 Clamart, France and LAN, Université Paris VI, 75252 Paris Cedex 5, France. : Stanford University, Department of Mathematics, CA 94305, USA. bal@math.Stanford.edu.
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Abstract

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 first eigenvector of a diffusion equation in the homogenized domain. Furthermore, the corresponding eigenvalue gives a second order corrector for the eigenvalue of the heterogeneous transport problem. This result justifies and improves the engineering procedure used in practice for nuclear reactor cores computations.

Type
Research Article
Copyright
© EDP Sciences, SMAI, 1999

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