Homogenization of a spectral equation in neutron transport

Grégoire Allaire; Guillaume Bal

doi:10.1016/S0764-4442(97)89102-1

Homogenization of a spectral equation in neutron transport

Grégoire Allaire
, Guillaume Bal

Research output: Contribution to journal › Article › peer-review

Abstract

We study the homogenization of an eigenvalue problem for the neutron transport in a periodic heterogeneous domain. We prove that the neutronic flux can be factorized as a product of two terms, up to a remainder which converges strongly to zero with the period. The first term is the first eigenvector of the transport equation in the periodicity cell. The second term is the solution of an eigenvalue problem for a diffusion equation in the homogenized domain. This result justifies and improves the engineering procedure used in practice for nuclear reactor cores computations.

Translated title of the contribution	Homogénéisation d'une équation spectrale du transport neutronique
Original language	English
Pages (from-to)	1043-1048
Number of pages	6
Journal	Comptes Rendus de l'Academie des Sciences - Series I: Mathematics
Volume	325
Issue number	9
DOIs	https://doi.org/10.1016/S0764-4442(97)89102-1
Publication status	Published - 1 Jan 1997

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title = "Homogenization of a spectral equation in neutron transport",

abstract = "We study the homogenization of an eigenvalue problem for the neutron transport in a periodic heterogeneous domain. We prove that the neutronic flux can be factorized as a product of two terms, up to a remainder which converges strongly to zero with the period. The first term is the first eigenvector of the transport equation in the periodicity cell. The second term is the solution of an eigenvalue problem for a diffusion equation in the homogenized domain. This result justifies and improves the engineering procedure used in practice for nuclear reactor cores computations.",

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AU - Allaire, Grégoire

AU - Bal, Guillaume

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N2 - We study the homogenization of an eigenvalue problem for the neutron transport in a periodic heterogeneous domain. We prove that the neutronic flux can be factorized as a product of two terms, up to a remainder which converges strongly to zero with the period. The first term is the first eigenvector of the transport equation in the periodicity cell. The second term is the solution of an eigenvalue problem for a diffusion equation in the homogenized domain. This result justifies and improves the engineering procedure used in practice for nuclear reactor cores computations.

AB - We study the homogenization of an eigenvalue problem for the neutron transport in a periodic heterogeneous domain. We prove that the neutronic flux can be factorized as a product of two terms, up to a remainder which converges strongly to zero with the period. The first term is the first eigenvector of the transport equation in the periodicity cell. The second term is the solution of an eigenvalue problem for a diffusion equation in the homogenized domain. This result justifies and improves the engineering procedure used in practice for nuclear reactor cores computations.

U2 - 10.1016/S0764-4442(97)89102-1

DO - 10.1016/S0764-4442(97)89102-1

M3 - Article

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SN - 0764-4442

VL - 325

SP - 1043

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JO - Comptes Rendus de l'Academie des Sciences - Series I: Mathematics

JF - Comptes Rendus de l'Academie des Sciences - Series I: Mathematics

IS - 9

ER -

Homogenization of a spectral equation in neutron transport

Abstract

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