Homogenization of a spectral problem in neutronic multigroup diffusion
This paper is concerned with the homogenization of an eigenvalue problem in a periodic heterogeneous domain for the multigroup neutron diffusion system. Such a model is used for studying the criticality of nuclear reactor cores. We prove that the first eigenvector of the multigroup system in the per...
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| Format: | Journal article |
| Language: | English |
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2000
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| _version_ | 1797060404825817088 |
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| author | Allaire, G Capdeboscq, Y |
| author_facet | Allaire, G Capdeboscq, Y |
| author_sort | Allaire, G |
| collection | OXFORD |
| description | This paper is concerned with the homogenization of an eigenvalue problem in a periodic heterogeneous domain for the multigroup neutron diffusion system. Such a model is used for studying the criticality of nuclear reactor cores. We prove that 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. The neutron flux, corresponding to the first eigenvector of the multigroup system, tends to the product of the first periodic and homogenized eigenvectors. This result justifies and improves the engineering procedure used in practice for nuclear reactor core computation. © 2000 Elsevier Science S.A. |
| first_indexed | 2024-03-06T20:16:39Z |
| format | Journal article |
| id | oxford-uuid:2c5ab73f-1517-44e7-b75d-c712d0d9ccd7 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T20:16:39Z |
| publishDate | 2000 |
| record_format | dspace |
| spelling | oxford-uuid:2c5ab73f-1517-44e7-b75d-c712d0d9ccd72022-03-26T12:36:36ZHomogenization of a spectral problem in neutronic multigroup diffusionJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:2c5ab73f-1517-44e7-b75d-c712d0d9ccd7EnglishSymplectic Elements at Oxford2000Allaire, GCapdeboscq, YThis paper is concerned with the homogenization of an eigenvalue problem in a periodic heterogeneous domain for the multigroup neutron diffusion system. Such a model is used for studying the criticality of nuclear reactor cores. We prove that 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. The neutron flux, corresponding to the first eigenvector of the multigroup system, tends to the product of the first periodic and homogenized eigenvectors. This result justifies and improves the engineering procedure used in practice for nuclear reactor core computation. © 2000 Elsevier Science S.A. |
| spellingShingle | Allaire, G Capdeboscq, Y Homogenization of a spectral problem in neutronic multigroup diffusion |
| title | Homogenization of a spectral problem in neutronic multigroup diffusion |
| title_full | Homogenization of a spectral problem in neutronic multigroup diffusion |
| title_fullStr | Homogenization of a spectral problem in neutronic multigroup diffusion |
| title_full_unstemmed | Homogenization of a spectral problem in neutronic multigroup diffusion |
| title_short | Homogenization of a spectral problem in neutronic multigroup diffusion |
| title_sort | homogenization of a spectral problem in neutronic multigroup diffusion |
| work_keys_str_mv | AT allaireg homogenizationofaspectralprobleminneutronicmultigroupdiffusion AT capdeboscqy homogenizationofaspectralprobleminneutronicmultigroupdiffusion |