Homogenization of a neutronic critical diffusion problem with drift

In this paper we study the homogenization of an eigenvalue problem for a cooperative system of weakly coupled elliptic partial differential equations, called the neutronic multigroup diffusion model, in a periodic heterogeneous domain. Such a model is used for studying the criticality of nuclear rea...

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Váldodahkki: Capdeboscq, Y
Materiálatiipa: Journal article
Giella:English
Almmustuhtton: 2002
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author Capdeboscq, Y
author_facet Capdeboscq, Y
author_sort Capdeboscq, Y
collection OXFORD
description In this paper we study the homogenization of an eigenvalue problem for a cooperative system of weakly coupled elliptic partial differential equations, called the neutronic multigroup diffusion model, in a periodic heterogeneous domain. Such a model is used for studying the criticality of nuclear reactor cores. In a recent work in collaboration with Grégoire Allaire, it is proved that, under a symmetry assumption, the first 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 diffusion eigenvalue problem. It is shown here that when this symmetry condition is not fulfilled, the asymptotic behaviour of the neutron flux, corresponding to the first eigenvector of the multigroup system, is dramatically different. This result enables to consider new types of geometrical configurations in practical nuclear reactor core computations.
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spelling oxford-uuid:67b46234-662d-4c3f-9ea6-93a94f1e65f52022-03-26T18:40:01ZHomogenization of a neutronic critical diffusion problem with driftJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:67b46234-662d-4c3f-9ea6-93a94f1e65f5EnglishSymplectic Elements at Oxford2002Capdeboscq, YIn this paper we study the homogenization of an eigenvalue problem for a cooperative system of weakly coupled elliptic partial differential equations, called the neutronic multigroup diffusion model, in a periodic heterogeneous domain. Such a model is used for studying the criticality of nuclear reactor cores. In a recent work in collaboration with Grégoire Allaire, it is proved that, under a symmetry assumption, the first 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 diffusion eigenvalue problem. It is shown here that when this symmetry condition is not fulfilled, the asymptotic behaviour of the neutron flux, corresponding to the first eigenvector of the multigroup system, is dramatically different. This result enables to consider new types of geometrical configurations in practical nuclear reactor core computations.
spellingShingle Capdeboscq, Y
Homogenization of a neutronic critical diffusion problem with drift
title Homogenization of a neutronic critical diffusion problem with drift
title_full Homogenization of a neutronic critical diffusion problem with drift
title_fullStr Homogenization of a neutronic critical diffusion problem with drift
title_full_unstemmed Homogenization of a neutronic critical diffusion problem with drift
title_short Homogenization of a neutronic critical diffusion problem with drift
title_sort homogenization of a neutronic critical diffusion problem with drift
work_keys_str_mv AT capdeboscqy homogenizationofaneutroniccriticaldiffusionproblemwithdrift