Dynamic term-by-term stabilized finite element formulation using orthogonal subgrid-scales for the incompressible Navier–Stokes problem

In this paper, we propose and analyze the stability and the dissipative structure of a new dynamic term-by-term stabilized finite element formulation for the Navier–Stokes problem that can be viewed as a variational multiscale (VMS) method under some assumptions. The essential point of the formulati...

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Autores: Castillo, Ernesto, Codina, Ramon|||0000-0002-7412-778X
Tipo de recurso: artículo
Fecha de publicación:2019
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/131121
Acceso en línea:https://hdl.handle.net/2117/131121
https://dx.doi.org/10.1016/j.cma.2019.02.041
Access Level:acceso abierto
Palabra clave:Navier-Stokes equations
Stabilized finite element methods Variational multiscale Dynamic subscales Term-by-term stabilization
Equacions de Navier-Stokes -- Mètodes numèrics
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits
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spelling Dynamic term-by-term stabilized finite element formulation using orthogonal subgrid-scales for the incompressible Navier–Stokes problemCastillo, ErnestoCodina, Ramon|||0000-0002-7412-778XNavier-Stokes equationsStabilized finite element methods Variational multiscale Dynamic subscales Term-by-term stabilizationEquacions de Navier-Stokes -- Mètodes numèricsÀrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finitsIn this paper, we propose and analyze the stability and the dissipative structure of a new dynamic term-by-term stabilized finite element formulation for the Navier–Stokes problem that can be viewed as a variational multiscale (VMS) method under some assumptions. The essential point of the formulation is the time dependent nature of the subscales and, contrary to residual-based formulations, the introduction of two velocity subscale components. They represent the components of the convective and the pressure gradient terms, respectively, of the momentum equation that cannot be captured by the finite element mesh. A key idea of the proposed method is that the convective subscale is close to a solenoidal field and the pressure gradient subscale is close to a potential field. The method ensures stability in anisotropic space–time discretizations, which is proved using numerical analysis for a linearized problem and demonstrated in classical numerical tests. The work includes a detailed description of the proposed formulation and several numerical examples that serve to justify our claims.Peer Reviewed20192019-06-0120192019-04-02journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/131121https://dx.doi.org/10.1016/j.cma.2019.02.041reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivs 3.0 Spainhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/1311212026-05-27T15:37:01Z
dc.title.none.fl_str_mv Dynamic term-by-term stabilized finite element formulation using orthogonal subgrid-scales for the incompressible Navier–Stokes problem
title Dynamic term-by-term stabilized finite element formulation using orthogonal subgrid-scales for the incompressible Navier–Stokes problem
spellingShingle Dynamic term-by-term stabilized finite element formulation using orthogonal subgrid-scales for the incompressible Navier–Stokes problem
Castillo, Ernesto
Navier-Stokes equations
Stabilized finite element methods Variational multiscale Dynamic subscales Term-by-term stabilization
Equacions de Navier-Stokes -- Mètodes numèrics
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits
title_short Dynamic term-by-term stabilized finite element formulation using orthogonal subgrid-scales for the incompressible Navier–Stokes problem
title_full Dynamic term-by-term stabilized finite element formulation using orthogonal subgrid-scales for the incompressible Navier–Stokes problem
title_fullStr Dynamic term-by-term stabilized finite element formulation using orthogonal subgrid-scales for the incompressible Navier–Stokes problem
title_full_unstemmed Dynamic term-by-term stabilized finite element formulation using orthogonal subgrid-scales for the incompressible Navier–Stokes problem
title_sort Dynamic term-by-term stabilized finite element formulation using orthogonal subgrid-scales for the incompressible Navier–Stokes problem
dc.creator.none.fl_str_mv Castillo, Ernesto
Codina, Ramon|||0000-0002-7412-778X
author Castillo, Ernesto
author_facet Castillo, Ernesto
Codina, Ramon|||0000-0002-7412-778X
author_role author
author2 Codina, Ramon|||0000-0002-7412-778X
author2_role author
dc.subject.none.fl_str_mv Navier-Stokes equations
Stabilized finite element methods Variational multiscale Dynamic subscales Term-by-term stabilization
Equacions de Navier-Stokes -- Mètodes numèrics
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits
topic Navier-Stokes equations
Stabilized finite element methods Variational multiscale Dynamic subscales Term-by-term stabilization
Equacions de Navier-Stokes -- Mètodes numèrics
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits
description In this paper, we propose and analyze the stability and the dissipative structure of a new dynamic term-by-term stabilized finite element formulation for the Navier–Stokes problem that can be viewed as a variational multiscale (VMS) method under some assumptions. The essential point of the formulation is the time dependent nature of the subscales and, contrary to residual-based formulations, the introduction of two velocity subscale components. They represent the components of the convective and the pressure gradient terms, respectively, of the momentum equation that cannot be captured by the finite element mesh. A key idea of the proposed method is that the convective subscale is close to a solenoidal field and the pressure gradient subscale is close to a potential field. The method ensures stability in anisotropic space–time discretizations, which is proved using numerical analysis for a linearized problem and demonstrated in classical numerical tests. The work includes a detailed description of the proposed formulation and several numerical examples that serve to justify our claims.
publishDate 2019
dc.date.none.fl_str_mv 2019
2019-06-01
2019
2019-04-02
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/131121
https://dx.doi.org/10.1016/j.cma.2019.02.041
url https://hdl.handle.net/2117/131121
https://dx.doi.org/10.1016/j.cma.2019.02.041
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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