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Homogenization of a spectral problem in neutronic multigroup diffusion

✍ Scribed by Grégoire Allaire; Yves Capdeboscq

Book ID
104268215
Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
292 KB
Volume
187
Category
Article
ISSN
0045-7825

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✦ Synopsis

This paper is concerned with the homogenization of an eigenvalue problem in a periodic heterogeneous domain for the multigroup neutron diusion system. Such a model is used for studying the criticality of nuclear reactor cores. We prove that the ®rst eigenvector of the multigroup system in the periodicity cell controls the oscillatory behaviour of the solutions, whereas the global trend is asymptotically given by a homogenized diusion eigenvalue problem. The neutron ¯ux, corresponding to the ®rst eigenvector of the multigroup system, tends to the product of the ®rst periodic and homogenized eigenvectors. This result justi®es and improves the engineering procedure used in practice for nuclear reactor core computation.

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