An overview of the boltzmann transport equation solution for neutrons, photons and electrons in cartesian geometry
Autor(a) principal: | |
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Data de Publicação: | 2009 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da FURG (RI FURG) |
Texto Completo: | http://repositorio.furg.br/handle/1/872 |
Resumo: | Questions regarding accuracy and efficiency of deterministic transport methods are still on our mind today, even with modern supercomputers. The most versatile and widely used deterministic methods are the PN approximation, the SN method (discrete ordinates method) and their variants. In the discrete ordinates (SN) formulations of the transport equation, it is assumed that the linearized Boltzmann equation only holds for a set of distinct numerical values of the direction-of-motion variables. In this work, looking forward to confirm the capabilities of deterministic methods in obtaining accurate results, we present a general overview of deterministic methods to solve the Boltzmann transport equation for neutral and charged particles. First, we describe a review in the Laplace transform technique applied to SN two dimensional transport equation in a rectangular domain considering Compton scattering. Next, we solved the Fokker-Planck (FP) equation, an alternative approach for the Boltzmann transport equation, assuming a monoenergetic electron beam in a rectangular domain. The main idea relies on applying the PN approximation, a recent advance in the class of deterministic methods, in the angular variable, to the two dimensional Fokker-Planck equation and then applying the Laplace Transform in the spatial x-variable. Numerical results are given to illustrate the accuracy of deterministic methods presented. |
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An overview of the boltzmann transport equation solution for neutrons, photons and electrons in cartesian geometryQuestions regarding accuracy and efficiency of deterministic transport methods are still on our mind today, even with modern supercomputers. The most versatile and widely used deterministic methods are the PN approximation, the SN method (discrete ordinates method) and their variants. In the discrete ordinates (SN) formulations of the transport equation, it is assumed that the linearized Boltzmann equation only holds for a set of distinct numerical values of the direction-of-motion variables. In this work, looking forward to confirm the capabilities of deterministic methods in obtaining accurate results, we present a general overview of deterministic methods to solve the Boltzmann transport equation for neutral and charged particles. First, we describe a review in the Laplace transform technique applied to SN two dimensional transport equation in a rectangular domain considering Compton scattering. Next, we solved the Fokker-Planck (FP) equation, an alternative approach for the Boltzmann transport equation, assuming a monoenergetic electron beam in a rectangular domain. The main idea relies on applying the PN approximation, a recent advance in the class of deterministic methods, in the angular variable, to the two dimensional Fokker-Planck equation and then applying the Laplace Transform in the spatial x-variable. Numerical results are given to illustrate the accuracy of deterministic methods presented.2011-08-17T23:35:39Z2011-08-17T23:35:39Z2009info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfRODRIGUEZ, Bárbara D. do Amaral ; VILHENA, Marco Tullio. A solution for the two-dimensional transport equation for photons and electrons in a rectangular domain by the Laplace transform technique. International Journal of Nuclear Energy, Science and Technology, v. 5, p. 25-40, 2010. Disponível em: <http://www.iaea.org/inis/collection/NCLCollectionStore/_Public/41/115/41115759.pdf>. Acesso em: 16 ago. 2011978-85-99141-03-8http://repositorio.furg.br/handle/1/872engRodriguez, Bárbara Denicol do AmaralVilhena, Marco Túllio Menna Barreto deinfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da FURG (RI FURG)instname:Universidade Federal do Rio Grande (FURG)instacron:FURG2011-09-19T20:31:37Zoai:repositorio.furg.br:1/872Repositório InstitucionalPUBhttps://repositorio.furg.br/oai/request || http://200.19.254.174/oai/requestopendoar:2011-09-19T20:31:37Repositório Institucional da FURG (RI FURG) - Universidade Federal do Rio Grande (FURG)false |
dc.title.none.fl_str_mv |
An overview of the boltzmann transport equation solution for neutrons, photons and electrons in cartesian geometry |
title |
An overview of the boltzmann transport equation solution for neutrons, photons and electrons in cartesian geometry |
spellingShingle |
An overview of the boltzmann transport equation solution for neutrons, photons and electrons in cartesian geometry Rodriguez, Bárbara Denicol do Amaral |
title_short |
An overview of the boltzmann transport equation solution for neutrons, photons and electrons in cartesian geometry |
title_full |
An overview of the boltzmann transport equation solution for neutrons, photons and electrons in cartesian geometry |
title_fullStr |
An overview of the boltzmann transport equation solution for neutrons, photons and electrons in cartesian geometry |
title_full_unstemmed |
An overview of the boltzmann transport equation solution for neutrons, photons and electrons in cartesian geometry |
title_sort |
An overview of the boltzmann transport equation solution for neutrons, photons and electrons in cartesian geometry |
author |
Rodriguez, Bárbara Denicol do Amaral |
author_facet |
Rodriguez, Bárbara Denicol do Amaral Vilhena, Marco Túllio Menna Barreto de |
author_role |
author |
author2 |
Vilhena, Marco Túllio Menna Barreto de |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Rodriguez, Bárbara Denicol do Amaral Vilhena, Marco Túllio Menna Barreto de |
description |
Questions regarding accuracy and efficiency of deterministic transport methods are still on our mind today, even with modern supercomputers. The most versatile and widely used deterministic methods are the PN approximation, the SN method (discrete ordinates method) and their variants. In the discrete ordinates (SN) formulations of the transport equation, it is assumed that the linearized Boltzmann equation only holds for a set of distinct numerical values of the direction-of-motion variables. In this work, looking forward to confirm the capabilities of deterministic methods in obtaining accurate results, we present a general overview of deterministic methods to solve the Boltzmann transport equation for neutral and charged particles. First, we describe a review in the Laplace transform technique applied to SN two dimensional transport equation in a rectangular domain considering Compton scattering. Next, we solved the Fokker-Planck (FP) equation, an alternative approach for the Boltzmann transport equation, assuming a monoenergetic electron beam in a rectangular domain. The main idea relies on applying the PN approximation, a recent advance in the class of deterministic methods, in the angular variable, to the two dimensional Fokker-Planck equation and then applying the Laplace Transform in the spatial x-variable. Numerical results are given to illustrate the accuracy of deterministic methods presented. |
publishDate |
2009 |
dc.date.none.fl_str_mv |
2009 2011-08-17T23:35:39Z 2011-08-17T23:35:39Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
RODRIGUEZ, Bárbara D. do Amaral ; VILHENA, Marco Tullio. A solution for the two-dimensional transport equation for photons and electrons in a rectangular domain by the Laplace transform technique. International Journal of Nuclear Energy, Science and Technology, v. 5, p. 25-40, 2010. Disponível em: <http://www.iaea.org/inis/collection/NCLCollectionStore/_Public/41/115/41115759.pdf>. Acesso em: 16 ago. 2011 978-85-99141-03-8 http://repositorio.furg.br/handle/1/872 |
identifier_str_mv |
RODRIGUEZ, Bárbara D. do Amaral ; VILHENA, Marco Tullio. A solution for the two-dimensional transport equation for photons and electrons in a rectangular domain by the Laplace transform technique. International Journal of Nuclear Energy, Science and Technology, v. 5, p. 25-40, 2010. Disponível em: <http://www.iaea.org/inis/collection/NCLCollectionStore/_Public/41/115/41115759.pdf>. Acesso em: 16 ago. 2011 978-85-99141-03-8 |
url |
http://repositorio.furg.br/handle/1/872 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
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reponame:Repositório Institucional da FURG (RI FURG) instname:Universidade Federal do Rio Grande (FURG) instacron:FURG |
instname_str |
Universidade Federal do Rio Grande (FURG) |
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FURG |
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FURG |
reponame_str |
Repositório Institucional da FURG (RI FURG) |
collection |
Repositório Institucional da FURG (RI FURG) |
repository.name.fl_str_mv |
Repositório Institucional da FURG (RI FURG) - Universidade Federal do Rio Grande (FURG) |
repository.mail.fl_str_mv |
|
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1807384388488396800 |