Homogenization of the criticality spectral equation in neutron transport

Grégoire Allaire; Guillaume Bal

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 33, Issue: 4, page 721-746
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Allaire, Grégoire, and Bal, Guillaume. " Homogenization of the criticality spectral equation in neutron transport ." ESAIM: Mathematical Modelling and Numerical Analysis 33.4 (2010): 721-746. <http://eudml.org/doc/197480>.

@article{Allaire2010,
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. },
author = {Allaire, Grégoire, Bal, Guillaume},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Homogenization; transport equations.; eigenvalue problem; periodic heterogeneous domain; nuclear reactor cores computations},
language = {eng},
month = {3},
number = {4},
pages = {721-746},
publisher = {EDP Sciences},
title = { Homogenization of the criticality spectral equation in neutron transport },
url = {http://eudml.org/doc/197480},
volume = {33},
year = {2010},
}

TY - JOUR
AU - Allaire, Grégoire
AU - Bal, Guillaume
TI - Homogenization of the criticality spectral equation in neutron transport
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 33
IS - 4
SP - 721
EP - 746
AB - 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.
LA - eng
KW - Homogenization; transport equations.; eigenvalue problem; periodic heterogeneous domain; nuclear reactor cores computations
UR - http://eudml.org/doc/197480
ER -

Citations in EuDML Documents

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  1. Guillaume Bal, Homogenization of a spectral equation with drift in linear transport
  2. Guillaume Bal, Homogenization of a spectral equation with drift in linear transport
  3. Guillaume Bal, Yvon Maday, Coupling of transport and diffusion models in linear transport theory
  4. Grégoire Allaire, Guillaume Bal, Vincent Siess, Homogenization and localization in locally periodic transport
  5. Grégoire Allaire, Guillaume Bal, Vincent Siess, Homogenization and localization in locally periodic transport
  6. Guillaume Bal, Yvon Maday, Coupling of transport and diffusion models in linear transport theory
  7. Grégoire Allaire, Homogénéisation et limite de diffusion pour une équation de transport
  8. Thierry Goudon, Antoine Mellet, Homogenization and Diffusion Asymptotics of the Linear Boltzmann Equation
  9. Thierry Goudon, Antoine Mellet, Homogenization and diffusion asymptotics of the linear Boltzmann equation

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