The Violation of Objectivity in Laplace Formulations of the Navier-Stokes Equations

Autores
Limache, Alejandro Cesar; Idelsohn, Sergio Rodolfo; Rossi, R.; Oñate, E.
Año de publicación
2007
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The Navier–Stokes equations written in Laplace form are often the starting point of many numerical methods for the simulation of viscous flows. Imposing the natural boundary conditions of the Laplace form or neglecting the viscous contributions on free surfaces are traditionally considered reasonable and harmless assumptions. With these boundary conditions any formulation derived from integral methods (like finite elements or finite volumes) recovers the pure Laplacian aspect of the strong form of the equations. This approach has also the advantage of being convenient in terms of computational effort and, as a consequence, it is used extensively. However, we have recently discovered that these resulting Laplacian formulations violate a basic axiom of continuum mechanics: the principle of objectivity. In the present article we give an accurate account about these topics. We also show that unexpected differences may sometimes arise between Laplace discretizations and divergence discretizations.
Fil: Limache, Alejandro Cesar. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; Argentina
Fil: Idelsohn, Sergio Rodolfo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; Argentina. International Center for Numerical Methods in Engineering; España
Fil: Rossi, R.. International Center for Numerical Methods in Engineering; España
Fil: Oñate, E.. International Center for Numerical Methods in Engineering; España
Materia
Navier-Stokes Equations
Objectivity
Laplace Diffusion Operator
Annular Cavity
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/20794
Acceder
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network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling The Violation of Objectivity in Laplace Formulations of the Navier-Stokes EquationsLimache, Alejandro CesarIdelsohn, Sergio RodolfoRossi, R.Oñate, E.Navier-Stokes EquationsObjectivityLaplace Diffusion OperatorAnnular Cavityhttps://purl.org/becyt/ford/2.11https://purl.org/becyt/ford/2The Navier–Stokes equations written in Laplace form are often the starting point of many numerical methods for the simulation of viscous flows. Imposing the natural boundary conditions of the Laplace form or neglecting the viscous contributions on free surfaces are traditionally considered reasonable and harmless assumptions. With these boundary conditions any formulation derived from integral methods (like finite elements or finite volumes) recovers the pure Laplacian aspect of the strong form of the equations. This approach has also the advantage of being convenient in terms of computational effort and, as a consequence, it is used extensively. However, we have recently discovered that these resulting Laplacian formulations violate a basic axiom of continuum mechanics: the principle of objectivity. In the present article we give an accurate account about these topics. We also show that unexpected differences may sometimes arise between Laplace discretizations and divergence discretizations.Fil: Limache, Alejandro Cesar. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; ArgentinaFil: Idelsohn, Sergio Rodolfo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; Argentina. International Center for Numerical Methods in Engineering; EspañaFil: Rossi, R.. International Center for Numerical Methods in Engineering; EspañaFil: Oñate, E.. International Center for Numerical Methods in Engineering; EspañaJohn Wiley & Sons Ltd2007-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/20794Limache, Alejandro Cesar; Idelsohn, Sergio Rodolfo; Rossi, R.; Oñate, E.; The Violation of Objectivity in Laplace Formulations of the Navier-Stokes Equations; John Wiley & Sons Ltd; International Journal For Numerical Methods In Fluids; 54; 6-8; 12-2007; 639-6640271-2091CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://onlinelibrary.wiley.com/doi/10.1002/fld.1480/abstractinfo:eu-repo/semantics/altIdentifier/doi/10.1002/fld.1480info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:09:02Zoai:ri.conicet.gov.ar:11336/20794instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-10 13:09:03.01CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The Violation of Objectivity in Laplace Formulations of the Navier-Stokes Equations
title The Violation of Objectivity in Laplace Formulations of the Navier-Stokes Equations
spellingShingle The Violation of Objectivity in Laplace Formulations of the Navier-Stokes Equations
Limache, Alejandro Cesar
Navier-Stokes Equations
Objectivity
Laplace Diffusion Operator
Annular Cavity
title_short The Violation of Objectivity in Laplace Formulations of the Navier-Stokes Equations
title_full The Violation of Objectivity in Laplace Formulations of the Navier-Stokes Equations
title_fullStr The Violation of Objectivity in Laplace Formulations of the Navier-Stokes Equations
title_full_unstemmed The Violation of Objectivity in Laplace Formulations of the Navier-Stokes Equations
title_sort The Violation of Objectivity in Laplace Formulations of the Navier-Stokes Equations
dc.creator.none.fl_str_mv Limache, Alejandro Cesar
Idelsohn, Sergio Rodolfo
Rossi, R.
Oñate, E.
author Limache, Alejandro Cesar
author_facet Limache, Alejandro Cesar
Idelsohn, Sergio Rodolfo
Rossi, R.
Oñate, E.
author_role author
author2 Idelsohn, Sergio Rodolfo
Rossi, R.
Oñate, E.
author2_role author
author
author
dc.subject.none.fl_str_mv Navier-Stokes Equations
Objectivity
Laplace Diffusion Operator
Annular Cavity
topic Navier-Stokes Equations
Objectivity
Laplace Diffusion Operator
Annular Cavity
purl_subject.fl_str_mv https://purl.org/becyt/ford/2.11
https://purl.org/becyt/ford/2
dc.description.none.fl_txt_mv The Navier–Stokes equations written in Laplace form are often the starting point of many numerical methods for the simulation of viscous flows. Imposing the natural boundary conditions of the Laplace form or neglecting the viscous contributions on free surfaces are traditionally considered reasonable and harmless assumptions. With these boundary conditions any formulation derived from integral methods (like finite elements or finite volumes) recovers the pure Laplacian aspect of the strong form of the equations. This approach has also the advantage of being convenient in terms of computational effort and, as a consequence, it is used extensively. However, we have recently discovered that these resulting Laplacian formulations violate a basic axiom of continuum mechanics: the principle of objectivity. In the present article we give an accurate account about these topics. We also show that unexpected differences may sometimes arise between Laplace discretizations and divergence discretizations.
Fil: Limache, Alejandro Cesar. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; Argentina
Fil: Idelsohn, Sergio Rodolfo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; Argentina. International Center for Numerical Methods in Engineering; España
Fil: Rossi, R.. International Center for Numerical Methods in Engineering; España
Fil: Oñate, E.. International Center for Numerical Methods in Engineering; España
description The Navier–Stokes equations written in Laplace form are often the starting point of many numerical methods for the simulation of viscous flows. Imposing the natural boundary conditions of the Laplace form or neglecting the viscous contributions on free surfaces are traditionally considered reasonable and harmless assumptions. With these boundary conditions any formulation derived from integral methods (like finite elements or finite volumes) recovers the pure Laplacian aspect of the strong form of the equations. This approach has also the advantage of being convenient in terms of computational effort and, as a consequence, it is used extensively. However, we have recently discovered that these resulting Laplacian formulations violate a basic axiom of continuum mechanics: the principle of objectivity. In the present article we give an accurate account about these topics. We also show that unexpected differences may sometimes arise between Laplace discretizations and divergence discretizations.
publishDate 2007
dc.date.none.fl_str_mv 2007-12
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/20794
Limache, Alejandro Cesar; Idelsohn, Sergio Rodolfo; Rossi, R.; Oñate, E.; The Violation of Objectivity in Laplace Formulations of the Navier-Stokes Equations; John Wiley & Sons Ltd; International Journal For Numerical Methods In Fluids; 54; 6-8; 12-2007; 639-664
0271-2091
CONICET Digital
CONICET
url http://hdl.handle.net/11336/20794
identifier_str_mv Limache, Alejandro Cesar; Idelsohn, Sergio Rodolfo; Rossi, R.; Oñate, E.; The Violation of Objectivity in Laplace Formulations of the Navier-Stokes Equations; John Wiley & Sons Ltd; International Journal For Numerical Methods In Fluids; 54; 6-8; 12-2007; 639-664
0271-2091
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://onlinelibrary.wiley.com/doi/10.1002/fld.1480/abstract
info:eu-repo/semantics/altIdentifier/doi/10.1002/fld.1480
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv John Wiley & Sons Ltd
publisher.none.fl_str_mv John Wiley & Sons Ltd
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 12.993085

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