# 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

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topAllaire, 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

top- Guillaume Bal, Homogenization of a spectral equation with drift in linear transport
- Guillaume Bal, Homogenization of a spectral equation with drift in linear transport
- Guillaume Bal, Yvon Maday, Coupling of transport and diffusion models in linear transport theory
- Grégoire Allaire, Guillaume Bal, Vincent Siess, Homogenization and localization in locally periodic transport
- Grégoire Allaire, Guillaume Bal, Vincent Siess, Homogenization and localization in locally periodic transport
- Guillaume Bal, Yvon Maday, Coupling of transport and diffusion models in linear transport theory
- Grégoire Allaire, Homogénéisation et limite de diffusion pour une équation de transport
- Thierry Goudon, Antoine Mellet, Homogenization and Diffusion Asymptotics of the Linear Boltzmann Equation
- Thierry Goudon, Antoine Mellet, Homogenization and diffusion asymptotics of the linear Boltzmann equation

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