Analytical representation of the solution of the space kinetic diffusion equation in a one-dimensional and homogeneous domain
Autor(a) principal: | |
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Data de Publicação: | 2019 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFRGS |
Texto Completo: | http://hdl.handle.net/10183/259737 |
Resumo: | In this work we solve the space kinetic diffusion equation in a one-dimensional geometry considering a homogeneous domain, for two energy groups and six groups of delayed neutron precursors. The proposed methodology makes use of a Taylor expansion in the space variable of the scalar neutron flux (fast and thermal) and the concentration of delayed neutron precursors, allocating the time dependence to the coefficients. Upon truncating the Taylor series at quadratic order, one obtains a set of recursive systems of ordinary differential equations, where a modified decomposition method is applied. The coefficient matrix is split into two, one constant diagonal matrix and the second one with the remaining time dependent and off-diagonal terms. Moreover, the equation system is reorganized such that the terms containing the latter matrix are treated as source terms. Note, that the homogeneous equation system has a well known solution, since the matrix is diagonal and constant. This solution plays the role of the recursion initialization of the decomposition method. The recursion scheme is set up in a fashion where the solutions of the previous recursion steps determine the source terms of the subsequent steps. A second feature of the method is the choice of the initial and boundary conditions, which are satisfied by the recursion initialization, while from the first recursion step onward the initial and boundary conditions are homogeneous. The recursion depth is then governed by a prescribed accuracy for the solution. |
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Tumelero, FernandaLapa, Celso Marcelo FranklinBodmann, Bardo Ernst JosefVilhena, Marco Tullio Menna Barreto de2023-07-01T03:40:10Z20192319-0612http://hdl.handle.net/10183/259737001168140In this work we solve the space kinetic diffusion equation in a one-dimensional geometry considering a homogeneous domain, for two energy groups and six groups of delayed neutron precursors. The proposed methodology makes use of a Taylor expansion in the space variable of the scalar neutron flux (fast and thermal) and the concentration of delayed neutron precursors, allocating the time dependence to the coefficients. Upon truncating the Taylor series at quadratic order, one obtains a set of recursive systems of ordinary differential equations, where a modified decomposition method is applied. The coefficient matrix is split into two, one constant diagonal matrix and the second one with the remaining time dependent and off-diagonal terms. Moreover, the equation system is reorganized such that the terms containing the latter matrix are treated as source terms. Note, that the homogeneous equation system has a well known solution, since the matrix is diagonal and constant. This solution plays the role of the recursion initialization of the decomposition method. The recursion scheme is set up in a fashion where the solutions of the previous recursion steps determine the source terms of the subsequent steps. A second feature of the method is the choice of the initial and boundary conditions, which are satisfied by the recursion initialization, while from the first recursion step onward the initial and boundary conditions are homogeneous. The recursion depth is then governed by a prescribed accuracy for the solution.application/pdfengBrazilian Journal of Radiation Sciences. Brazilian Radiation Protection Society - SBPR. Vol. 7, no. 2B (2019), p. 1-13Difusão de nêutronsMétodo da decomposição de AdomianNeutron diffusion equationTaylor seriesModified Adomian decomposition methodAnalytical representation of the solution of the space kinetic diffusion equation in a one-dimensional and homogeneous domainEstrangeiroinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFRGSinstname:Universidade Federal do Rio Grande do Sul (UFRGS)instacron:UFRGSTEXT001168140.pdf.txt001168140.pdf.txtExtracted Texttext/plain25934http://www.lume.ufrgs.br/bitstream/10183/259737/2/001168140.pdf.txt12ea78a18388cc7170179eaed03e18e0MD52ORIGINAL001168140.pdfTexto completo (inglês)application/pdf421770http://www.lume.ufrgs.br/bitstream/10183/259737/1/001168140.pdf126cab07dbc04afba279d1893bdacba7MD5110183/2597372023-07-02 03:41:57.26851oai:www.lume.ufrgs.br:10183/259737Repositório de PublicaçõesPUBhttps://lume.ufrgs.br/oai/requestopendoar:2023-07-02T06:41:57Repositório Institucional da UFRGS - Universidade Federal do Rio Grande do Sul (UFRGS)false |
dc.title.pt_BR.fl_str_mv |
Analytical representation of the solution of the space kinetic diffusion equation in a one-dimensional and homogeneous domain |
title |
Analytical representation of the solution of the space kinetic diffusion equation in a one-dimensional and homogeneous domain |
spellingShingle |
Analytical representation of the solution of the space kinetic diffusion equation in a one-dimensional and homogeneous domain Tumelero, Fernanda Difusão de nêutrons Método da decomposição de Adomian Neutron diffusion equation Taylor series Modified Adomian decomposition method |
title_short |
Analytical representation of the solution of the space kinetic diffusion equation in a one-dimensional and homogeneous domain |
title_full |
Analytical representation of the solution of the space kinetic diffusion equation in a one-dimensional and homogeneous domain |
title_fullStr |
Analytical representation of the solution of the space kinetic diffusion equation in a one-dimensional and homogeneous domain |
title_full_unstemmed |
Analytical representation of the solution of the space kinetic diffusion equation in a one-dimensional and homogeneous domain |
title_sort |
Analytical representation of the solution of the space kinetic diffusion equation in a one-dimensional and homogeneous domain |
author |
Tumelero, Fernanda |
author_facet |
Tumelero, Fernanda Lapa, Celso Marcelo Franklin Bodmann, Bardo Ernst Josef Vilhena, Marco Tullio Menna Barreto de |
author_role |
author |
author2 |
Lapa, Celso Marcelo Franklin Bodmann, Bardo Ernst Josef Vilhena, Marco Tullio Menna Barreto de |
author2_role |
author author author |
dc.contributor.author.fl_str_mv |
Tumelero, Fernanda Lapa, Celso Marcelo Franklin Bodmann, Bardo Ernst Josef Vilhena, Marco Tullio Menna Barreto de |
dc.subject.por.fl_str_mv |
Difusão de nêutrons Método da decomposição de Adomian |
topic |
Difusão de nêutrons Método da decomposição de Adomian Neutron diffusion equation Taylor series Modified Adomian decomposition method |
dc.subject.eng.fl_str_mv |
Neutron diffusion equation Taylor series Modified Adomian decomposition method |
description |
In this work we solve the space kinetic diffusion equation in a one-dimensional geometry considering a homogeneous domain, for two energy groups and six groups of delayed neutron precursors. The proposed methodology makes use of a Taylor expansion in the space variable of the scalar neutron flux (fast and thermal) and the concentration of delayed neutron precursors, allocating the time dependence to the coefficients. Upon truncating the Taylor series at quadratic order, one obtains a set of recursive systems of ordinary differential equations, where a modified decomposition method is applied. The coefficient matrix is split into two, one constant diagonal matrix and the second one with the remaining time dependent and off-diagonal terms. Moreover, the equation system is reorganized such that the terms containing the latter matrix are treated as source terms. Note, that the homogeneous equation system has a well known solution, since the matrix is diagonal and constant. This solution plays the role of the recursion initialization of the decomposition method. The recursion scheme is set up in a fashion where the solutions of the previous recursion steps determine the source terms of the subsequent steps. A second feature of the method is the choice of the initial and boundary conditions, which are satisfied by the recursion initialization, while from the first recursion step onward the initial and boundary conditions are homogeneous. The recursion depth is then governed by a prescribed accuracy for the solution. |
publishDate |
2019 |
dc.date.issued.fl_str_mv |
2019 |
dc.date.accessioned.fl_str_mv |
2023-07-01T03:40:10Z |
dc.type.driver.fl_str_mv |
Estrangeiro info:eu-repo/semantics/article |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10183/259737 |
dc.identifier.issn.pt_BR.fl_str_mv |
2319-0612 |
dc.identifier.nrb.pt_BR.fl_str_mv |
001168140 |
identifier_str_mv |
2319-0612 001168140 |
url |
http://hdl.handle.net/10183/259737 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.ispartof.pt_BR.fl_str_mv |
Brazilian Journal of Radiation Sciences. Brazilian Radiation Protection Society - SBPR. Vol. 7, no. 2B (2019), p. 1-13 |
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info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
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application/pdf |
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Repositório Institucional da UFRGS |
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