Log-conformation representation of hiperbolic conservation laws with source term

Detalhes bibliográficos
Autor(a) principal: Bielça, L.a. [UNESP]
Data de Publicação: 2014
Outros Autores: Meneguette, M. [UNESP]
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1590/S2179-84512014000300006
http://hdl.handle.net/11449/212205
Resumo: The objective of this work is to study, through a simple equation, the statement that the numerical instability associated to the high Weissenberg number in equations with source term can be resolved by the use of the so called logarithmic conformation representation. We will focus on hyperbolic conservation laws, but more specifically on the advection equation with a source term. The source term imposes a necessity of an elastic balance, as well as the CFL convective balance for stability. Will be seen that the representation of such equation by the log-conformation removes the restriction of stability inherent to the elastic balance pointed out by Fattal & Kupferman [3] as the cause of the high Weissenberg number problem (HWNP).
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spelling Log-conformation representation of hiperbolic conservation laws with source termsource termlog-conformation representation (LCR)high Weissenberg number problem (HWNP)termo fonterepresentação por conformação logarítmicaproblema do alto número de WeissenbergThe objective of this work is to study, through a simple equation, the statement that the numerical instability associated to the high Weissenberg number in equations with source term can be resolved by the use of the so called logarithmic conformation representation. We will focus on hyperbolic conservation laws, but more specifically on the advection equation with a source term. The source term imposes a necessity of an elastic balance, as well as the CFL convective balance for stability. Will be seen that the representation of such equation by the log-conformation removes the restriction of stability inherent to the elastic balance pointed out by Fattal & Kupferman [3] as the cause of the high Weissenberg number problem (HWNP).O objetivo deste trabalho é estudar, por meio de uma equação simples, a afirmação de que a instabilidade numérica associada ao elevado número Weissenberg em equações com termo fonte, pode ser resolvida pela utilização da denominada representação por conformação logarítmica. Vamos nos concentrar nas leis de conservação hiperbólicas, mas mais especificamente na equação de advecção com termo fonte. O termo fonte impõe a necessidade de um equilíbrio elástico, tanto quanto um equilíbrio convectivo (CFL), para a estabilidade. Será visto que a representação de tal equação pela conformação logarítmica remove a restrição de estabilidade inerente para o equilíbrio elástico apontado por Fattal & Kupferman [3] como causa do problema do alto número de Weissenberg.Universidade Estadual Paulista, FCTUniversidade Estadual Paulista, FCTSociedade Brasileira de Matemática Aplicada e ComputacionalUniversidade Estadual Paulista (Unesp)Bielça, L.a. [UNESP]Meneguette, M. [UNESP]2021-07-14T10:36:19Z2021-07-14T10:36:19Z2014-12info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article293-299application/pdfhttp://dx.doi.org/10.1590/S2179-84512014000300006TEMA (São Carlos). São Carlos, SP, Brazil: Sociedade Brasileira de Matemática Aplicada e Computacional, v. 15, n. 3, p. 293-299, 2014.1677-19662179-8451http://hdl.handle.net/11449/21220510.1590/S2179-84512014000300006S2179-84512014000300006S2179-84512014000300006.pdfSciELOreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengTEMA (São Carlos)info:eu-repo/semantics/openAccess2024-01-02T06:17:25Zoai:repositorio.unesp.br:11449/212205Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T21:54:43.833369Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Log-conformation representation of hiperbolic conservation laws with source term
title Log-conformation representation of hiperbolic conservation laws with source term
spellingShingle Log-conformation representation of hiperbolic conservation laws with source term
Bielça, L.a. [UNESP]
source term
log-conformation representation (LCR)
high Weissenberg number problem (HWNP)
termo fonte
representação por conformação logarítmica
problema do alto número de Weissenberg
title_short Log-conformation representation of hiperbolic conservation laws with source term
title_full Log-conformation representation of hiperbolic conservation laws with source term
title_fullStr Log-conformation representation of hiperbolic conservation laws with source term
title_full_unstemmed Log-conformation representation of hiperbolic conservation laws with source term
title_sort Log-conformation representation of hiperbolic conservation laws with source term
author Bielça, L.a. [UNESP]
author_facet Bielça, L.a. [UNESP]
Meneguette, M. [UNESP]
author_role author
author2 Meneguette, M. [UNESP]
author2_role author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (Unesp)
dc.contributor.author.fl_str_mv Bielça, L.a. [UNESP]
Meneguette, M. [UNESP]
dc.subject.por.fl_str_mv source term
log-conformation representation (LCR)
high Weissenberg number problem (HWNP)
termo fonte
representação por conformação logarítmica
problema do alto número de Weissenberg
topic source term
log-conformation representation (LCR)
high Weissenberg number problem (HWNP)
termo fonte
representação por conformação logarítmica
problema do alto número de Weissenberg
description The objective of this work is to study, through a simple equation, the statement that the numerical instability associated to the high Weissenberg number in equations with source term can be resolved by the use of the so called logarithmic conformation representation. We will focus on hyperbolic conservation laws, but more specifically on the advection equation with a source term. The source term imposes a necessity of an elastic balance, as well as the CFL convective balance for stability. Will be seen that the representation of such equation by the log-conformation removes the restriction of stability inherent to the elastic balance pointed out by Fattal & Kupferman [3] as the cause of the high Weissenberg number problem (HWNP).
publishDate 2014
dc.date.none.fl_str_mv 2014-12
2021-07-14T10:36:19Z
2021-07-14T10:36:19Z
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/10.1590/S2179-84512014000300006
TEMA (São Carlos). São Carlos, SP, Brazil: Sociedade Brasileira de Matemática Aplicada e Computacional, v. 15, n. 3, p. 293-299, 2014.
1677-1966
2179-8451
http://hdl.handle.net/11449/212205
10.1590/S2179-84512014000300006
S2179-84512014000300006
S2179-84512014000300006.pdf
url http://dx.doi.org/10.1590/S2179-84512014000300006
http://hdl.handle.net/11449/212205
identifier_str_mv TEMA (São Carlos). São Carlos, SP, Brazil: Sociedade Brasileira de Matemática Aplicada e Computacional, v. 15, n. 3, p. 293-299, 2014.
1677-1966
2179-8451
10.1590/S2179-84512014000300006
S2179-84512014000300006
S2179-84512014000300006.pdf
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv TEMA (São Carlos)
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 293-299
application/pdf
dc.publisher.none.fl_str_mv Sociedade Brasileira de Matemática Aplicada e Computacional
publisher.none.fl_str_mv Sociedade Brasileira de Matemática Aplicada e Computacional
dc.source.none.fl_str_mv SciELO
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_ 1808129372708667392