Development of a Finite Volume Inter-cell Polynomial Expansion Method for the Neutron Diffusion Equation

Heterogeneous nuclear reactors require numerical methods to solve the neutron diffusion equation (NDE) to obtain the neutron flux distribution inside them, by discretizing the heterogeneous geometry in a set of homogeneous regions. This discretization requires additional equations at the inner faces...

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Autores: Bernal García, Álvaro, Jose E. Roman|||0000-0003-1144-6772, Miró Herrero, Rafael|||0000-0003-1012-0869, Ginestar Peiro, Damián|||0000-0003-1243-6648, Verdú Martín, Gumersindo Jesús|||0000-0001-5098-080X
Tipo de recurso: artículo
Fecha de publicación:2016
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/69282
Acceso en línea:https://riunet.upv.es/handle/10251/69282
Access Level:acceso abierto
Palabra clave:Neutron diffusion equation
Finite volume method
Polynomial expansion
Steady state
CIENCIAS DE LA COMPUTACION E INTELIGENCIA ARTIFICIAL
MATEMATICA APLICADA
INGENIERIA NUCLEAR
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dc.title.none.fl_str_mv Development of a Finite Volume Inter-cell Polynomial Expansion Method for the Neutron Diffusion Equation
title Development of a Finite Volume Inter-cell Polynomial Expansion Method for the Neutron Diffusion Equation
spellingShingle Development of a Finite Volume Inter-cell Polynomial Expansion Method for the Neutron Diffusion Equation
Bernal García, Álvaro
Neutron diffusion equation
Finite volume method
Polynomial expansion
Steady state
CIENCIAS DE LA COMPUTACION E INTELIGENCIA ARTIFICIAL
MATEMATICA APLICADA
INGENIERIA NUCLEAR
title_short Development of a Finite Volume Inter-cell Polynomial Expansion Method for the Neutron Diffusion Equation
title_full Development of a Finite Volume Inter-cell Polynomial Expansion Method for the Neutron Diffusion Equation
title_fullStr Development of a Finite Volume Inter-cell Polynomial Expansion Method for the Neutron Diffusion Equation
title_full_unstemmed Development of a Finite Volume Inter-cell Polynomial Expansion Method for the Neutron Diffusion Equation
title_sort Development of a Finite Volume Inter-cell Polynomial Expansion Method for the Neutron Diffusion Equation
dc.creator.none.fl_str_mv Bernal García, Álvaro
Jose E. Roman|||0000-0003-1144-6772
Miró Herrero, Rafael|||0000-0003-1012-0869
Ginestar Peiro, Damián|||0000-0003-1243-6648
Verdú Martín, Gumersindo Jesús|||0000-0001-5098-080X
author Bernal García, Álvaro
author_facet Bernal García, Álvaro
Jose E. Roman|||0000-0003-1144-6772
Miró Herrero, Rafael|||0000-0003-1012-0869
Ginestar Peiro, Damián|||0000-0003-1243-6648
Verdú Martín, Gumersindo Jesús|||0000-0001-5098-080X
author_role author
author2 Jose E. Roman|||0000-0003-1144-6772
Miró Herrero, Rafael|||0000-0003-1012-0869
Ginestar Peiro, Damián|||0000-0003-1243-6648
Verdú Martín, Gumersindo Jesús|||0000-0001-5098-080X
author2_role author
author
author
author
dc.contributor.none.fl_str_mv Departamento de Ingeniería Química y Nuclear
Departamento de Sistemas Informáticos y Computación
Departamento de Matemática Aplicada
Escuela Técnica Superior de Ingeniería Aeroespacial y Diseño Industrial
Instituto Universitario de Matemática Multidisciplinar
Escuela Técnica Superior de Ingeniería Industrial
Instituto Universitario de Seguridad Industrial, Radiofísica y Medioambiental
Escuela Técnica Superior de Ingeniería Informática
Ministerio de Educación, Cultura y Deporte
Generalitat Valenciana
Universitat Politècnica de València
Ministerio de Economía y Competitividad
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Neutron diffusion equation
Finite volume method
Polynomial expansion
Steady state
CIENCIAS DE LA COMPUTACION E INTELIGENCIA ARTIFICIAL
MATEMATICA APLICADA
INGENIERIA NUCLEAR
topic Neutron diffusion equation
Finite volume method
Polynomial expansion
Steady state
CIENCIAS DE LA COMPUTACION E INTELIGENCIA ARTIFICIAL
MATEMATICA APLICADA
INGENIERIA NUCLEAR
description Heterogeneous nuclear reactors require numerical methods to solve the neutron diffusion equation (NDE) to obtain the neutron flux distribution inside them, by discretizing the heterogeneous geometry in a set of homogeneous regions. This discretization requires additional equations at the inner faces of two adjacent cells: neutron flux and current continuity, which imply an excess of equations. The finite volume method (FVM) is suitable to be applied to NDE, because it can be easily applied to any mesh and it is typically used in the transport equations due to the conservation of the transported quantity within the volume. However, the gradient and face-averaged values in the FVM are typically calculated as a function of the cell-averaged values of adjacent cells. So, if the materials of the adjacent cells are different, the neutron current condition could not be accomplished. Therefore, a polynomial expansion of the neutron flux is developed in each cell for assuring the accomplishment of the flux and current continuity and calculating both analytically. In this polynomial expansion, the polynomial terms for each cell were assigned previously and the constant coefficients are determined by solving the eigenvalue problem with SLEPc. A sensitivity analysis for determining the best set of polynomial terms is performed.
publishDate 2016
dc.date.none.fl_str_mv 2016
2016-01-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://riunet.upv.es/handle/10251/69282
url https://riunet.upv.es/handle/10251/69282
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Educación y Cultura http://dx.doi.org/10.13039/501100003176 FPU13%2F01009 FPU13%2F01009
Ministerio de Economía y Competitividad http://dx.doi.org/10.13039/501100003329 ENE2014-59442-P DESARROLLO DE NUEVOS MODELOS Y CAPACIDADES EN EL SISTEMA DE CODIGOS ACOPLADO VALKIN%2FTH-3D. VERIFICACION, VALIDACION Y CUANTIFICACION DE INCERTIDUMBRES
Ministerio de Economía y Competitividad http://dx.doi.org/10.13039/501100003329 ENE2012-34585 Desarrollo de una plataforma multifísica de altas prestaciones para simulaciones Termohidráulico-Neutrónicas en ingeniería nuclear
Generalitat Valenciana https://doi.org/10.13039/501100003359 PROMETEOII%2F2014%2F008 New improved capacities in 3d-VALKIN (Valencian Neutronic Kinetisc). N3D-VALKIN
Universitat Politècnica de València https://doi.org/10.13039/501100004233 UPPTE%2F2012%2F118
Ministerio de Economía y Competitividad http://dx.doi.org/10.13039/501100003329 TIN2013-41049-P EXTENSION DE LA LIBRERIA SLEPC PARA POLINOMIOS MATRICIALES, FUNCIONES MATRICIALES Y ECUACIONES MATRICIALES EN PLATAFORMAS DE COMPUTACION EMERGENTES
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Taylor & Francis
publisher.none.fl_str_mv Taylor & Francis
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
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spelling Development of a Finite Volume Inter-cell Polynomial Expansion Method for the Neutron Diffusion EquationBernal García, ÁlvaroJose E. Roman|||0000-0003-1144-6772Miró Herrero, Rafael|||0000-0003-1012-0869Ginestar Peiro, Damián|||0000-0003-1243-6648Verdú Martín, Gumersindo Jesús|||0000-0001-5098-080XNeutron diffusion equationFinite volume methodPolynomial expansionSteady stateCIENCIAS DE LA COMPUTACION E INTELIGENCIA ARTIFICIALMATEMATICA APLICADAINGENIERIA NUCLEARHeterogeneous nuclear reactors require numerical methods to solve the neutron diffusion equation (NDE) to obtain the neutron flux distribution inside them, by discretizing the heterogeneous geometry in a set of homogeneous regions. This discretization requires additional equations at the inner faces of two adjacent cells: neutron flux and current continuity, which imply an excess of equations. The finite volume method (FVM) is suitable to be applied to NDE, because it can be easily applied to any mesh and it is typically used in the transport equations due to the conservation of the transported quantity within the volume. However, the gradient and face-averaged values in the FVM are typically calculated as a function of the cell-averaged values of adjacent cells. So, if the materials of the adjacent cells are different, the neutron current condition could not be accomplished. Therefore, a polynomial expansion of the neutron flux is developed in each cell for assuring the accomplishment of the flux and current continuity and calculating both analytically. In this polynomial expansion, the polynomial terms for each cell were assigned previously and the constant coefficients are determined by solving the eigenvalue problem with SLEPc. A sensitivity analysis for determining the best set of polynomial terms is performed.This work has been partially supported by the Spanish Ministerio de Eduacion Cultura y Deporte [grant number FPU13/01009]; the Spanish Ministerio de Ciencia e Innovacion [project number ENE2014-59442-P], [project number ENE2012-34585]; the Generalitat Valenciana [project number PROMETEOII/2014/008]; the Universitat Politecnica de Valencia [project number UPPTE/2012/118]; and the Spanish Ministerio de Economia y Competitividad [project number TIN2013-41049-P].Taylor & FrancisDepartamento de Ingeniería Química y NuclearDepartamento de Sistemas Informáticos y ComputaciónDepartamento de Matemática AplicadaEscuela Técnica Superior de Ingeniería Aeroespacial y Diseño IndustrialInstituto Universitario de Matemática MultidisciplinarEscuela Técnica Superior de Ingeniería IndustrialInstituto Universitario de Seguridad Industrial, Radiofísica y MedioambientalEscuela Técnica Superior de Ingeniería InformáticaMinisterio de Educación, Cultura y DeporteGeneralitat ValencianaUniversitat Politècnica de ValènciaMinisterio de Economía y CompetitividadRepositorio Institucional de la Universitat Politècnica de València Riunet20162016-01-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://riunet.upv.es/handle/10251/69282reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengMinisterio de Educación y Cultura http://dx.doi.org/10.13039/501100003176 FPU13%2F01009 FPU13%2F01009Ministerio de Economía y Competitividad http://dx.doi.org/10.13039/501100003329 ENE2014-59442-P DESARROLLO DE NUEVOS MODELOS Y CAPACIDADES EN EL SISTEMA DE CODIGOS ACOPLADO VALKIN%2FTH-3D. VERIFICACION, VALIDACION Y CUANTIFICACION DE INCERTIDUMBRESMinisterio de Economía y Competitividad http://dx.doi.org/10.13039/501100003329 ENE2012-34585 Desarrollo de una plataforma multifísica de altas prestaciones para simulaciones Termohidráulico-Neutrónicas en ingeniería nuclearGeneralitat Valenciana https://doi.org/10.13039/501100003359 PROMETEOII%2F2014%2F008 New improved capacities in 3d-VALKIN (Valencian Neutronic Kinetisc). N3D-VALKINUniversitat Politècnica de València https://doi.org/10.13039/501100004233 UPPTE%2F2012%2F118Ministerio de Economía y Competitividad http://dx.doi.org/10.13039/501100003329 TIN2013-41049-P EXTENSION DE LA LIBRERIA SLEPC PARA POLINOMIOS MATRICIALES, FUNCIONES MATRICIALES Y ECUACIONES MATRICIALES EN PLATAFORMAS DE COMPUTACION EMERGENTESopen accesshttp://purl.org/coar/access_right/c_abf2Reserva de todos los derechoshttp://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/692822026-06-13T07:49:27Z
score 15.301603

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