Nonlinear eigenvalue problem in the integral transforms solution of convection-diffusion with nonlinear boundary conditions

Detalhes bibliográficos
Autor(a) principal: Cotta, Renato Machado
Data de Publicação: 2015
Outros Autores: Naveira-Cotta, Carolina Palma, Knupp, Diego Campos
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UFRJ
Texto Completo: http://hdl.handle.net/11422/8423
Resumo: Indisponível.
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spelling Cotta, Renato MachadoNaveira-Cotta, Carolina PalmaKnupp, Diego Campos2019-06-11T17:03:34Z2023-11-30T03:03:31Z2015-10-150961-5539http://hdl.handle.net/11422/842310.1108/HFF-08-2015-0309Indisponível.The purpose of this paper is to propose the generalized integral transform technique (GITT) to the solution of convection-diffusion problems with nonlinear boundary conditions by employing the corresponding nonlinear eigenvalue problem in the construction of the expansion basis. The original nonlinear boundary condition coefficients in the problem formulation are all incorporated into the adopted eigenvalue problem, which may be itself integral transformed through a representative linear auxiliary problem, yielding a nonlinear algebraic eigenvalue problem for the associated eigenvalues and eigenvectors, to be solved along with the transformed ordinary differential system. The nonlinear eigenvalues computation may also be accomplished by rewriting the corresponding transcendental equation as an ordinary differential system for the eigenvalues, which is then simultaneously solved with the transformed potentials. An application on one-dimensional transient diffusion with nonlinear boundary condition coefficients is selected for illustrating some important computational aspects and the convergence behavior of the proposed eigenfunction expansions. For comparison purposes, an alternative solution with a linear eigenvalue problem basis is also presented and implemented. This novel approach can be further extended to various classes of nonlinear convection-diffusion problems, either already solved by the GITT with a linear coefficients basis, or new challenging applications with more involved nonlinearities.Submitted by Jairo Amaro (jairo.amaro@sibi.ufrj.br) on 2019-06-11T17:03:34Z No. of bitstreams: 1 6-2016_Nonlinear-eigenvalue-in-the-integral-transforms-min.pdf: 297586 bytes, checksum: 6411212be810b69e20b986e1c6cea711 (MD5)Made available in DSpace on 2019-06-11T17:03:34Z (GMT). No. of bitstreams: 1 6-2016_Nonlinear-eigenvalue-in-the-integral-transforms-min.pdf: 297586 bytes, checksum: 6411212be810b69e20b986e1c6cea711 (MD5) Previous issue date: 2015-10-15engEmeraldBrasilNúcleo Interdisciplinar de Dinâmica dos FluidosInternational Journal of Numerical Methods for Heat and Fluid FlowCNPQ::CIENCIAS EXATAS E DA TERRA::FISICA::AREAS CLASSICAS DE FENOMENOLOGIA E SUAS APLICACOES::DINAMICA DOS FLUIDOSDiffusionHybrid methodsIntegral transformsEigenvalue problemNonlinear boundary conditionsNonlinear problemsNonlinear eigenvalue problem in the integral transforms solution of convection-diffusion with nonlinear boundary conditionsinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article263767789abertoinfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFRJinstname:Universidade Federal do Rio de Janeiro (UFRJ)instacron:UFRJORIGINAL6-2016_Nonlinear-eigenvalue-in-the-integral-transforms-min.pdf6-2016_Nonlinear-eigenvalue-in-the-integral-transforms-min.pdfapplication/pdf297586http://pantheon.ufrj.br:80/bitstream/11422/8423/1/6-2016_Nonlinear-eigenvalue-in-the-integral-transforms-min.pdf6411212be810b69e20b986e1c6cea711MD51LICENSElicense.txtlicense.txttext/plain; charset=utf-81853http://pantheon.ufrj.br:80/bitstream/11422/8423/2/license.txtdd32849f2bfb22da963c3aac6e26e255MD5211422/84232023-11-30 00:03:31.597oai:pantheon.ufrj.br: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Repositório de PublicaçõesPUBhttp://www.pantheon.ufrj.br/oai/requestopendoar:2023-11-30T03:03:31Repositório Institucional da UFRJ - Universidade Federal do Rio de Janeiro (UFRJ)false
dc.title.en.fl_str_mv Nonlinear eigenvalue problem in the integral transforms solution of convection-diffusion with nonlinear boundary conditions
title Nonlinear eigenvalue problem in the integral transforms solution of convection-diffusion with nonlinear boundary conditions
spellingShingle Nonlinear eigenvalue problem in the integral transforms solution of convection-diffusion with nonlinear boundary conditions
Cotta, Renato Machado
CNPQ::CIENCIAS EXATAS E DA TERRA::FISICA::AREAS CLASSICAS DE FENOMENOLOGIA E SUAS APLICACOES::DINAMICA DOS FLUIDOS
Diffusion
Hybrid methods
Integral transforms
Eigenvalue problem
Nonlinear boundary conditions
Nonlinear problems
title_short Nonlinear eigenvalue problem in the integral transforms solution of convection-diffusion with nonlinear boundary conditions
title_full Nonlinear eigenvalue problem in the integral transforms solution of convection-diffusion with nonlinear boundary conditions
title_fullStr Nonlinear eigenvalue problem in the integral transforms solution of convection-diffusion with nonlinear boundary conditions
title_full_unstemmed Nonlinear eigenvalue problem in the integral transforms solution of convection-diffusion with nonlinear boundary conditions
title_sort Nonlinear eigenvalue problem in the integral transforms solution of convection-diffusion with nonlinear boundary conditions
author Cotta, Renato Machado
author_facet Cotta, Renato Machado
Naveira-Cotta, Carolina Palma
Knupp, Diego Campos
author_role author
author2 Naveira-Cotta, Carolina Palma
Knupp, Diego Campos
author2_role author
author
dc.contributor.author.fl_str_mv Cotta, Renato Machado
Naveira-Cotta, Carolina Palma
Knupp, Diego Campos
dc.subject.cnpq.fl_str_mv CNPQ::CIENCIAS EXATAS E DA TERRA::FISICA::AREAS CLASSICAS DE FENOMENOLOGIA E SUAS APLICACOES::DINAMICA DOS FLUIDOS
topic CNPQ::CIENCIAS EXATAS E DA TERRA::FISICA::AREAS CLASSICAS DE FENOMENOLOGIA E SUAS APLICACOES::DINAMICA DOS FLUIDOS
Diffusion
Hybrid methods
Integral transforms
Eigenvalue problem
Nonlinear boundary conditions
Nonlinear problems
dc.subject.eng.fl_str_mv Diffusion
Hybrid methods
Integral transforms
Eigenvalue problem
Nonlinear boundary conditions
Nonlinear problems
description Indisponível.
publishDate 2015
dc.date.issued.fl_str_mv 2015-10-15
dc.date.accessioned.fl_str_mv 2019-06-11T17:03:34Z
dc.date.available.fl_str_mv 2023-11-30T03:03:31Z
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 http://hdl.handle.net/11422/8423
dc.identifier.issn.pt_BR.fl_str_mv 0961-5539
dc.identifier.doi.pt_BR.fl_str_mv 10.1108/HFF-08-2015-0309
identifier_str_mv 0961-5539
10.1108/HFF-08-2015-0309
url http://hdl.handle.net/11422/8423
dc.language.iso.fl_str_mv eng
language eng
dc.relation.ispartof.en.fl_str_mv International Journal of Numerical Methods for Heat and Fluid Flow
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Emerald
dc.publisher.country.fl_str_mv Brasil
dc.publisher.department.fl_str_mv Núcleo Interdisciplinar de Dinâmica dos Fluidos
publisher.none.fl_str_mv Emerald
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
bitstream.url.fl_str_mv http://pantheon.ufrj.br:80/bitstream/11422/8423/1/6-2016_Nonlinear-eigenvalue-in-the-integral-transforms-min.pdf
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