Unified Integral Transforms Algorithm for Solving Multidimensional Nonlinear Convection-Diffusion Problems
Autor(a) principal: | |
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Data de Publicação: | 2013 |
Outros Autores: | , , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFRJ |
Texto Completo: | http://hdl.handle.net/11422/8529 |
Resumo: | The present work summarizes the theory and describes the algorithm related to an open-source mixed symbolic-numerical computational code named unified integral transforms (UNIT) that provides a computational environment for finding hybrid numerical-analytical solutions of linear and nonlinear partial differential systems via integral transforms. The reported research was performed by employing the well-established methodology known as the generalized integral transform technique (GITT), together with the symbolic and numerical computation tools provided by the Mathematica system. The main purpose of this study is to illustrate the robust precision-controlled simulation of multidimensional nonlinear transient convection-diffusion problems, while providing a brief introduction of this open source implementation. Test cases are selected based on nonlinear multidimensional formulations of Burgers’ equation, with the establishment of reference results for specific numerical values of the governing parameters. Special aspects in the computational behavior of the algorithm are then discussed, demonstrating the implemented possibilities within the present version of the UNIT code, including the proposition of a progressive filtering strategy and a combined criteria reordering scheme, not previously discussed in related works, both aimed at convergence acceleration of the eigenfunction expansions. |
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Unified Integral Transforms Algorithm for Solving Multidimensional Nonlinear Convection-Diffusion ProblemsNumerical methodsConvection-diffusion problemsUnified integral transformsGeneralized integral transform techniqueCNPQ::CIENCIAS EXATAS E DA TERRA::FISICA::AREAS CLASSICAS DE FENOMENOLOGIA E SUAS APLICACOES::DINAMICA DOS FLUIDOSThe present work summarizes the theory and describes the algorithm related to an open-source mixed symbolic-numerical computational code named unified integral transforms (UNIT) that provides a computational environment for finding hybrid numerical-analytical solutions of linear and nonlinear partial differential systems via integral transforms. The reported research was performed by employing the well-established methodology known as the generalized integral transform technique (GITT), together with the symbolic and numerical computation tools provided by the Mathematica system. The main purpose of this study is to illustrate the robust precision-controlled simulation of multidimensional nonlinear transient convection-diffusion problems, while providing a brief introduction of this open source implementation. Test cases are selected based on nonlinear multidimensional formulations of Burgers’ equation, with the establishment of reference results for specific numerical values of the governing parameters. Special aspects in the computational behavior of the algorithm are then discussed, demonstrating the implemented possibilities within the present version of the UNIT code, including the proposition of a progressive filtering strategy and a combined criteria reordering scheme, not previously discussed in related works, both aimed at convergence acceleration of the eigenfunction expansions.Indisponível.Taylor & FrancisBrasilNúcleo Interdisciplinar de Dinâmica dos Fluidos2019-06-26T16:31:59Z2023-12-21T03:06:04Z2013-02-28info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article1040-7782http://hdl.handle.net/11422/852910.1080/10407782.2013.756763engNumerical Heat Transfer, Part A ApplicationsCotta, Renato MachadoKnupp, Diego CamposNaveira-Cotta, Carolina PalmaSphaier, Leandro AlcoforadoQuaresma, João Nazareno Nonatoinfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFRJinstname:Universidade Federal do Rio de Janeiro (UFRJ)instacron:UFRJ2023-12-21T03:06:04Zoai:pantheon.ufrj.br:11422/8529Repositório InstitucionalPUBhttp://www.pantheon.ufrj.br/oai/requestpantheon@sibi.ufrj.bropendoar:2023-12-21T03:06:04Repositório Institucional da UFRJ - Universidade Federal do Rio de Janeiro (UFRJ)false |
dc.title.none.fl_str_mv |
Unified Integral Transforms Algorithm for Solving Multidimensional Nonlinear Convection-Diffusion Problems |
title |
Unified Integral Transforms Algorithm for Solving Multidimensional Nonlinear Convection-Diffusion Problems |
spellingShingle |
Unified Integral Transforms Algorithm for Solving Multidimensional Nonlinear Convection-Diffusion Problems Cotta, Renato Machado Numerical methods Convection-diffusion problems Unified integral transforms Generalized integral transform technique CNPQ::CIENCIAS EXATAS E DA TERRA::FISICA::AREAS CLASSICAS DE FENOMENOLOGIA E SUAS APLICACOES::DINAMICA DOS FLUIDOS |
title_short |
Unified Integral Transforms Algorithm for Solving Multidimensional Nonlinear Convection-Diffusion Problems |
title_full |
Unified Integral Transforms Algorithm for Solving Multidimensional Nonlinear Convection-Diffusion Problems |
title_fullStr |
Unified Integral Transforms Algorithm for Solving Multidimensional Nonlinear Convection-Diffusion Problems |
title_full_unstemmed |
Unified Integral Transforms Algorithm for Solving Multidimensional Nonlinear Convection-Diffusion Problems |
title_sort |
Unified Integral Transforms Algorithm for Solving Multidimensional Nonlinear Convection-Diffusion Problems |
author |
Cotta, Renato Machado |
author_facet |
Cotta, Renato Machado Knupp, Diego Campos Naveira-Cotta, Carolina Palma Sphaier, Leandro Alcoforado Quaresma, João Nazareno Nonato |
author_role |
author |
author2 |
Knupp, Diego Campos Naveira-Cotta, Carolina Palma Sphaier, Leandro Alcoforado Quaresma, João Nazareno Nonato |
author2_role |
author author author author |
dc.contributor.author.fl_str_mv |
Cotta, Renato Machado Knupp, Diego Campos Naveira-Cotta, Carolina Palma Sphaier, Leandro Alcoforado Quaresma, João Nazareno Nonato |
dc.subject.por.fl_str_mv |
Numerical methods Convection-diffusion problems Unified integral transforms Generalized integral transform technique CNPQ::CIENCIAS EXATAS E DA TERRA::FISICA::AREAS CLASSICAS DE FENOMENOLOGIA E SUAS APLICACOES::DINAMICA DOS FLUIDOS |
topic |
Numerical methods Convection-diffusion problems Unified integral transforms Generalized integral transform technique CNPQ::CIENCIAS EXATAS E DA TERRA::FISICA::AREAS CLASSICAS DE FENOMENOLOGIA E SUAS APLICACOES::DINAMICA DOS FLUIDOS |
description |
The present work summarizes the theory and describes the algorithm related to an open-source mixed symbolic-numerical computational code named unified integral transforms (UNIT) that provides a computational environment for finding hybrid numerical-analytical solutions of linear and nonlinear partial differential systems via integral transforms. The reported research was performed by employing the well-established methodology known as the generalized integral transform technique (GITT), together with the symbolic and numerical computation tools provided by the Mathematica system. The main purpose of this study is to illustrate the robust precision-controlled simulation of multidimensional nonlinear transient convection-diffusion problems, while providing a brief introduction of this open source implementation. Test cases are selected based on nonlinear multidimensional formulations of Burgers’ equation, with the establishment of reference results for specific numerical values of the governing parameters. Special aspects in the computational behavior of the algorithm are then discussed, demonstrating the implemented possibilities within the present version of the UNIT code, including the proposition of a progressive filtering strategy and a combined criteria reordering scheme, not previously discussed in related works, both aimed at convergence acceleration of the eigenfunction expansions. |
publishDate |
2013 |
dc.date.none.fl_str_mv |
2013-02-28 2019-06-26T16:31:59Z 2023-12-21T03:06:04Z |
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 |
1040-7782 http://hdl.handle.net/11422/8529 10.1080/10407782.2013.756763 |
identifier_str_mv |
1040-7782 10.1080/10407782.2013.756763 |
url |
http://hdl.handle.net/11422/8529 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Numerical Heat Transfer, Part A Applications |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Taylor & Francis Brasil Núcleo Interdisciplinar de Dinâmica dos Fluidos |
publisher.none.fl_str_mv |
Taylor & Francis Brasil Núcleo Interdisciplinar de Dinâmica dos Fluidos |
dc.source.none.fl_str_mv |
reponame:Repositório Institucional da UFRJ instname:Universidade Federal do Rio de Janeiro (UFRJ) instacron:UFRJ |
instname_str |
Universidade Federal do Rio de Janeiro (UFRJ) |
instacron_str |
UFRJ |
institution |
UFRJ |
reponame_str |
Repositório Institucional da UFRJ |
collection |
Repositório Institucional da UFRJ |
repository.name.fl_str_mv |
Repositório Institucional da UFRJ - Universidade Federal do Rio de Janeiro (UFRJ) |
repository.mail.fl_str_mv |
pantheon@sibi.ufrj.br |
_version_ |
1815455991196549120 |