SECOND-ORDER FINITE DIFFERENCE APPROXIMATIONS OF THE UPPER-CONVECTED TIME DERIVATIVE\ast

Detalhes bibliográficos
Autor(a) principal: Medeiros, Debora D.
Data de Publicação: 2021
Outros Autores: Notsu, Hirofumi, Oishi, Cassio M. [UNESP]
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1137/20M1364990
http://hdl.handle.net/11449/218786
Resumo: In this work, new finite difference schemes are presented for dealing with the upper convected time derivative in the context of the generalized Lie derivative. The upper-convected time derivative, which is usually encountered in the constitutive equation of the popular viscoelastic models, is reformulated in order to obtain approximations of second-order in time for solving a simplified constitutive equation in one and two dimensions. The theoretical analysis of the truncation errors of the methods takes into account the linear and quadratic interpolation operators based on a Lagrangian framework. Numerical experiments illustrating the theoretical results for the model equation defined in one and two dimensions are included. Finally, the finite difference approximations of second-order in time are also applied for solving a two-dimensional Oldroyd-B constitutive equation subjected to a prescribed velocity field at different Weissenberg numbers.
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spelling SECOND-ORDER FINITE DIFFERENCE APPROXIMATIONS OF THE UPPER-CONVECTED TIME DERIVATIVE\astgeneralized Lie derivativeLagrangian schemefinite difference methodIn this work, new finite difference schemes are presented for dealing with the upper convected time derivative in the context of the generalized Lie derivative. The upper-convected time derivative, which is usually encountered in the constitutive equation of the popular viscoelastic models, is reformulated in order to obtain approximations of second-order in time for solving a simplified constitutive equation in one and two dimensions. The theoretical analysis of the truncation errors of the methods takes into account the linear and quadratic interpolation operators based on a Lagrangian framework. Numerical experiments illustrating the theoretical results for the model equation defined in one and two dimensions are included. Finally, the finite difference approximations of second-order in time are also applied for solving a two-dimensional Oldroyd-B constitutive equation subjected to a prescribed velocity field at different Weissenberg numbers.Center of Mathematical Sciences Applied to Industry (Cepid-CeMEAI) grantFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)JSPS KAKENHIJST PRESTO grantJST CREST grantConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Univ Sao Paulo, Dept Matemat Aplicada & Estat, Inst Ciencias Matemat & Comp ICMC, Campus Sao Carlos, BR-1025480 Sao Paulo, SP, BrazilKanazawa Univ, Fac Math & Phys, Kanazawa, Ishikawa 9201192, JapanUniv Estadual Paulista, Dept Matemat & Comp, Fac Ciencias & Tecnol, BR-19060900 Presidente Prudente, SP, BrazilUniv Estadual Paulista, Dept Matemat & Comp, Fac Ciencias & Tecnol, BR-19060900 Presidente Prudente, SP, BrazilCenter of Mathematical Sciences Applied to Industry (Cepid-CeMEAI) grant: 2013/07375-0FAPESP: 2019/08742-2FAPESP: 2017/11428-2JSPS KAKENHI: JP18H01135JSPS KAKENHI: JP20H01823JSPS KAKENHI: JP20KK0058JSPS KAKENHI: JP21H04431JST PRESTO grant: JPMJPR16EAJST CREST grant: JPMJCR2014CNPq: 305383/2019-1FAPESP: 2013/07375-0Siam PublicationsUniversidade de São Paulo (USP)Kanazawa UnivUniversidade Estadual Paulista (UNESP)Medeiros, Debora D.Notsu, HirofumiOishi, Cassio M. [UNESP]2022-04-28T17:23:04Z2022-04-28T17:23:04Z2021-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article2955-2988http://dx.doi.org/10.1137/20M1364990Siam Journal On Numerical Analysis. Philadelphia: Siam Publications, v. 59, n. 6, p. 2955-2988, 2021.0036-1429http://hdl.handle.net/11449/21878610.1137/20M1364990WOS:000748784400007Web of Sciencereponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengSiam Journal On Numerical Analysisinfo:eu-repo/semantics/openAccess2024-06-19T14:32:06Zoai:repositorio.unesp.br:11449/218786Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T23:29:23.318789Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv SECOND-ORDER FINITE DIFFERENCE APPROXIMATIONS OF THE UPPER-CONVECTED TIME DERIVATIVE\ast
title SECOND-ORDER FINITE DIFFERENCE APPROXIMATIONS OF THE UPPER-CONVECTED TIME DERIVATIVE\ast
spellingShingle SECOND-ORDER FINITE DIFFERENCE APPROXIMATIONS OF THE UPPER-CONVECTED TIME DERIVATIVE\ast
Medeiros, Debora D.
generalized Lie derivative
Lagrangian scheme
finite difference method
title_short SECOND-ORDER FINITE DIFFERENCE APPROXIMATIONS OF THE UPPER-CONVECTED TIME DERIVATIVE\ast
title_full SECOND-ORDER FINITE DIFFERENCE APPROXIMATIONS OF THE UPPER-CONVECTED TIME DERIVATIVE\ast
title_fullStr SECOND-ORDER FINITE DIFFERENCE APPROXIMATIONS OF THE UPPER-CONVECTED TIME DERIVATIVE\ast
title_full_unstemmed SECOND-ORDER FINITE DIFFERENCE APPROXIMATIONS OF THE UPPER-CONVECTED TIME DERIVATIVE\ast
title_sort SECOND-ORDER FINITE DIFFERENCE APPROXIMATIONS OF THE UPPER-CONVECTED TIME DERIVATIVE\ast
author Medeiros, Debora D.
author_facet Medeiros, Debora D.
Notsu, Hirofumi
Oishi, Cassio M. [UNESP]
author_role author
author2 Notsu, Hirofumi
Oishi, Cassio M. [UNESP]
author2_role author
author
dc.contributor.none.fl_str_mv Universidade de São Paulo (USP)
Kanazawa Univ
Universidade Estadual Paulista (UNESP)
dc.contributor.author.fl_str_mv Medeiros, Debora D.
Notsu, Hirofumi
Oishi, Cassio M. [UNESP]
dc.subject.por.fl_str_mv generalized Lie derivative
Lagrangian scheme
finite difference method
topic generalized Lie derivative
Lagrangian scheme
finite difference method
description In this work, new finite difference schemes are presented for dealing with the upper convected time derivative in the context of the generalized Lie derivative. The upper-convected time derivative, which is usually encountered in the constitutive equation of the popular viscoelastic models, is reformulated in order to obtain approximations of second-order in time for solving a simplified constitutive equation in one and two dimensions. The theoretical analysis of the truncation errors of the methods takes into account the linear and quadratic interpolation operators based on a Lagrangian framework. Numerical experiments illustrating the theoretical results for the model equation defined in one and two dimensions are included. Finally, the finite difference approximations of second-order in time are also applied for solving a two-dimensional Oldroyd-B constitutive equation subjected to a prescribed velocity field at different Weissenberg numbers.
publishDate 2021
dc.date.none.fl_str_mv 2021-01-01
2022-04-28T17:23:04Z
2022-04-28T17:23:04Z
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 http://dx.doi.org/10.1137/20M1364990
Siam Journal On Numerical Analysis. Philadelphia: Siam Publications, v. 59, n. 6, p. 2955-2988, 2021.
0036-1429
http://hdl.handle.net/11449/218786
10.1137/20M1364990
WOS:000748784400007
url http://dx.doi.org/10.1137/20M1364990
http://hdl.handle.net/11449/218786
identifier_str_mv Siam Journal On Numerical Analysis. Philadelphia: Siam Publications, v. 59, n. 6, p. 2955-2988, 2021.
0036-1429
10.1137/20M1364990
WOS:000748784400007
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Siam Journal On Numerical Analysis
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 2955-2988
dc.publisher.none.fl_str_mv Siam Publications
publisher.none.fl_str_mv Siam Publications
dc.source.none.fl_str_mv Web of Science
reponame:Repositório Institucional da UNESP
instname:Universidade Estadual Paulista (UNESP)
instacron:UNESP
instname_str Universidade Estadual Paulista (UNESP)
instacron_str UNESP
institution UNESP
reponame_str Repositório Institucional da UNESP
collection Repositório Institucional da UNESP
repository.name.fl_str_mv Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)
repository.mail.fl_str_mv
_version_ 1808129525061517312

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