Transiente diffusion equation: an alternative finite difference approach

Detalhes bibliográficos
Autor(a) principal: Oliveira, Marcelo Franco de
Data de Publicação: 2020
Tipo de documento: Artigo
Idioma: eng
Título da fonte: The Journal of Engineering and Exact Sciences
Texto Completo: https://periodicos.ufv.br/jcec/article/view/11755
Resumo: This work is concerned with development of an alternative finite difference method approach to the solution of the transient diffusion equation. In this approach is assumed that the potential function has a linear variation in some time interval. Thus an integral with respect to time is carried out in the initial diffusion equation. A constant time weighting function is adopted. The time integration reduces the order of the time derivative that appears in the initial equation. Two numerical examples are presented to verify the accuracy and applicability of the proposed approaches. The results are compared with the standard corresponding analytical solutions.
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spelling Transiente diffusion equation: an alternative finite difference approachEquação da difusão transiente: uma aproximação alternativa para diferenças finitasFinite Difference MethodDiffusion EquationTime IntervalMétodo das Diferenças FinitasEquação da DifusãoIntervalo de TempoThis work is concerned with development of an alternative finite difference method approach to the solution of the transient diffusion equation. In this approach is assumed that the potential function has a linear variation in some time interval. Thus an integral with respect to time is carried out in the initial diffusion equation. A constant time weighting function is adopted. The time integration reduces the order of the time derivative that appears in the initial equation. Two numerical examples are presented to verify the accuracy and applicability of the proposed approaches. The results are compared with the standard corresponding analytical solutions.Esse trabalho foi desenvolvido com uma aproximação alternativa para o Método das Diferenças Finitas (MDF) para solução da equação da difusão transiente. Nessa aproximação, considera-se que a função potencial tem uma variação linear em um dado intervalo de tempo. Assim uma integral em relação ao tempo é aplicada na equação inicial da difusão. Uma função de ponderação constante no tempo é adotada. A integração no tempo reduz a ordem da derivada temporal da equação inicial. Dois exemplos numéricos serão apresentados para verificar a acurácia e a aplicabilidade da aproximação proposta. Os resultados são comparados com a formulação tradicional do MEF e com a solução analítica.Universidade Federal de Viçosa - UFV2020-12-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://periodicos.ufv.br/jcec/article/view/1175510.18540/jcecvl6iss5pp0765-0769The Journal of Engineering and Exact Sciences; Vol. 6 No. 5 (2020); 0765-0769The Journal of Engineering and Exact Sciences; Vol. 6 Núm. 5 (2020); 0765-0769The Journal of Engineering and Exact Sciences; v. 6 n. 5 (2020); 0765-07692527-1075reponame:The Journal of Engineering and Exact Sciencesinstname:Universidade Federal de Viçosa (UFV)instacron:UFVenghttps://periodicos.ufv.br/jcec/article/view/11755/6410Copyright (c) 2020 The Journal of Engineering and Exact Scienceshttps://creativecommons.org/licenses/by/4.0info:eu-repo/semantics/openAccessOliveira, Marcelo Franco de2021-05-31T12:54:03Zoai:ojs.periodicos.ufv.br:article/11755Revistahttp://www.seer.ufv.br/seer/rbeq2/index.php/req2/oai2527-10752527-1075opendoar:2021-05-31T12:54:03The Journal of Engineering and Exact Sciences - Universidade Federal de Viçosa (UFV)false
dc.title.none.fl_str_mv Transiente diffusion equation: an alternative finite difference approach
Equação da difusão transiente: uma aproximação alternativa para diferenças finitas
title Transiente diffusion equation: an alternative finite difference approach
spellingShingle Transiente diffusion equation: an alternative finite difference approach
Oliveira, Marcelo Franco de
Finite Difference Method
Diffusion Equation
Time Interval
Método das Diferenças Finitas
Equação da Difusão
Intervalo de Tempo
title_short Transiente diffusion equation: an alternative finite difference approach
title_full Transiente diffusion equation: an alternative finite difference approach
title_fullStr Transiente diffusion equation: an alternative finite difference approach
title_full_unstemmed Transiente diffusion equation: an alternative finite difference approach
title_sort Transiente diffusion equation: an alternative finite difference approach
author Oliveira, Marcelo Franco de
author_facet Oliveira, Marcelo Franco de
author_role author
dc.contributor.author.fl_str_mv Oliveira, Marcelo Franco de
dc.subject.por.fl_str_mv Finite Difference Method
Diffusion Equation
Time Interval
Método das Diferenças Finitas
Equação da Difusão
Intervalo de Tempo
topic Finite Difference Method
Diffusion Equation
Time Interval
Método das Diferenças Finitas
Equação da Difusão
Intervalo de Tempo
description This work is concerned with development of an alternative finite difference method approach to the solution of the transient diffusion equation. In this approach is assumed that the potential function has a linear variation in some time interval. Thus an integral with respect to time is carried out in the initial diffusion equation. A constant time weighting function is adopted. The time integration reduces the order of the time derivative that appears in the initial equation. Two numerical examples are presented to verify the accuracy and applicability of the proposed approaches. The results are compared with the standard corresponding analytical solutions.
publishDate 2020
dc.date.none.fl_str_mv 2020-12-12
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv https://periodicos.ufv.br/jcec/article/view/11755
10.18540/jcecvl6iss5pp0765-0769
url https://periodicos.ufv.br/jcec/article/view/11755
identifier_str_mv 10.18540/jcecvl6iss5pp0765-0769
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv https://periodicos.ufv.br/jcec/article/view/11755/6410
dc.rights.driver.fl_str_mv Copyright (c) 2020 The Journal of Engineering and Exact Sciences
https://creativecommons.org/licenses/by/4.0
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Copyright (c) 2020 The Journal of Engineering and Exact Sciences
https://creativecommons.org/licenses/by/4.0
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Universidade Federal de Viçosa - UFV
publisher.none.fl_str_mv Universidade Federal de Viçosa - UFV
dc.source.none.fl_str_mv The Journal of Engineering and Exact Sciences; Vol. 6 No. 5 (2020); 0765-0769
The Journal of Engineering and Exact Sciences; Vol. 6 Núm. 5 (2020); 0765-0769
The Journal of Engineering and Exact Sciences; v. 6 n. 5 (2020); 0765-0769
2527-1075
reponame:The Journal of Engineering and Exact Sciences
instname:Universidade Federal de Viçosa (UFV)
instacron:UFV
instname_str Universidade Federal de Viçosa (UFV)
instacron_str UFV
institution UFV
reponame_str The Journal of Engineering and Exact Sciences
collection The Journal of Engineering and Exact Sciences
repository.name.fl_str_mv The Journal of Engineering and Exact Sciences - Universidade Federal de Viçosa (UFV)
repository.mail.fl_str_mv
_version_ 1808845246100930560

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