Objectivity tests for Navier–Stokes simulations: The revealing of non-physical solutions produced by Laplace formulations

Autores
Limache, Alejandro Cesar; Sánchez, Pablo Javier; Dalcin, Lisandro Daniel; Idelsohn, Sergio Rodolfo
Año de publicación
2008
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Laplace formulations are weak formulations of the Navier–Stokes equations commonly used in computational fluid dynamics. In these schemes, the viscous terms are given as a function of the Laplace diffusion operator only. Despite their popularity, recently, it has been proven that they violate a fundamental principle of continuum mechanics, the principle of objectivity. It is remarkable that such flaw has not being noticed before, neither detected in numerical experiments. In this work, a series of objectivity tests have been designed with the purpose of revealing such problem in real numerical experiments. Through the tests it is shown how, for slip boundaries or free-surfaces, Laplace formulations generate non-physical solutions which widely depart from the real fluid dynamics. These tests can be easily reproduced, not requiring complex simulation tools. Furthermore, they can be used as benchmarks to check consistency of developed or commercial software. The article is closed with a discussion of the mathematical aspects involved, including the issues of boundary conditions and objectivity.
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: Sánchez, Pablo Javier. 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: Dalcin, Lisandro Daniel. 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. Centro Internacional de Métodos Numéricos en Ingeniería; España
Materia
Navierstokes Equations
Objectivity
Laplace Diffusion Operator
Annular Cavity
Free-Surfaces
Boundary Conditions
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:11336/25382
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Objectivity tests for Navier–Stokes simulations: The revealing of non-physical solutions produced by Laplace formulationsLimache, Alejandro CesarSánchez, Pablo JavierDalcin, Lisandro DanielIdelsohn, Sergio RodolfoNavierstokes EquationsObjectivityLaplace Diffusion OperatorAnnular CavityFree-SurfacesBoundary ConditionsLaplace formulations are weak formulations of the Navier–Stokes equations commonly used in computational fluid dynamics. In these schemes, the viscous terms are given as a function of the Laplace diffusion operator only. Despite their popularity, recently, it has been proven that they violate a fundamental principle of continuum mechanics, the principle of objectivity. It is remarkable that such flaw has not being noticed before, neither detected in numerical experiments. In this work, a series of objectivity tests have been designed with the purpose of revealing such problem in real numerical experiments. Through the tests it is shown how, for slip boundaries or free-surfaces, Laplace formulations generate non-physical solutions which widely depart from the real fluid dynamics. These tests can be easily reproduced, not requiring complex simulation tools. Furthermore, they can be used as benchmarks to check consistency of developed or commercial software. The article is closed with a discussion of the mathematical aspects involved, including the issues of boundary conditions and objectivity.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: Sánchez, Pablo Javier. 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: Dalcin, Lisandro Daniel. 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. Centro Internacional de Métodos Numéricos en Ingeniería; EspañaElsevier Science Sa2008-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/25382Limache, Alejandro Cesar; Sánchez, Pablo Javier; Dalcin, Lisandro Daniel; Idelsohn, Sergio Rodolfo; Objectivity tests for Navier–Stokes simulations: The revealing of non-physical solutions produced by Laplace formulations; Elsevier Science Sa; Computer Methods in Applied Mechanics and Engineering; 197; 49-50; 12-2008; 4180-41920045-7825CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.cma.2008.04.020info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0045782508001734info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:59:43Zoai:ri.conicet.gov.ar:11336/25382instacron: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:34982025-09-29 09:59:43.441CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Objectivity tests for Navier–Stokes simulations: The revealing of non-physical solutions produced by Laplace formulations
title Objectivity tests for Navier–Stokes simulations: The revealing of non-physical solutions produced by Laplace formulations
spellingShingle Objectivity tests for Navier–Stokes simulations: The revealing of non-physical solutions produced by Laplace formulations
Limache, Alejandro Cesar
Navierstokes Equations
Objectivity
Laplace Diffusion Operator
Annular Cavity
Free-Surfaces
Boundary Conditions
title_short Objectivity tests for Navier–Stokes simulations: The revealing of non-physical solutions produced by Laplace formulations
title_full Objectivity tests for Navier–Stokes simulations: The revealing of non-physical solutions produced by Laplace formulations
title_fullStr Objectivity tests for Navier–Stokes simulations: The revealing of non-physical solutions produced by Laplace formulations
title_full_unstemmed Objectivity tests for Navier–Stokes simulations: The revealing of non-physical solutions produced by Laplace formulations
title_sort Objectivity tests for Navier–Stokes simulations: The revealing of non-physical solutions produced by Laplace formulations
dc.creator.none.fl_str_mv Limache, Alejandro Cesar
Sánchez, Pablo Javier
Dalcin, Lisandro Daniel
Idelsohn, Sergio Rodolfo
author Limache, Alejandro Cesar
author_facet Limache, Alejandro Cesar
Sánchez, Pablo Javier
Dalcin, Lisandro Daniel
Idelsohn, Sergio Rodolfo
author_role author
author2 Sánchez, Pablo Javier
Dalcin, Lisandro Daniel
Idelsohn, Sergio Rodolfo
author2_role author
author
author
dc.subject.none.fl_str_mv Navierstokes Equations
Objectivity
Laplace Diffusion Operator
Annular Cavity
Free-Surfaces
Boundary Conditions
topic Navierstokes Equations
Objectivity
Laplace Diffusion Operator
Annular Cavity
Free-Surfaces
Boundary Conditions
dc.description.none.fl_txt_mv Laplace formulations are weak formulations of the Navier–Stokes equations commonly used in computational fluid dynamics. In these schemes, the viscous terms are given as a function of the Laplace diffusion operator only. Despite their popularity, recently, it has been proven that they violate a fundamental principle of continuum mechanics, the principle of objectivity. It is remarkable that such flaw has not being noticed before, neither detected in numerical experiments. In this work, a series of objectivity tests have been designed with the purpose of revealing such problem in real numerical experiments. Through the tests it is shown how, for slip boundaries or free-surfaces, Laplace formulations generate non-physical solutions which widely depart from the real fluid dynamics. These tests can be easily reproduced, not requiring complex simulation tools. Furthermore, they can be used as benchmarks to check consistency of developed or commercial software. The article is closed with a discussion of the mathematical aspects involved, including the issues of boundary conditions and objectivity.
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: Sánchez, Pablo Javier. 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: Dalcin, Lisandro Daniel. 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. Centro Internacional de Métodos Numéricos en Ingeniería; España
description Laplace formulations are weak formulations of the Navier–Stokes equations commonly used in computational fluid dynamics. In these schemes, the viscous terms are given as a function of the Laplace diffusion operator only. Despite their popularity, recently, it has been proven that they violate a fundamental principle of continuum mechanics, the principle of objectivity. It is remarkable that such flaw has not being noticed before, neither detected in numerical experiments. In this work, a series of objectivity tests have been designed with the purpose of revealing such problem in real numerical experiments. Through the tests it is shown how, for slip boundaries or free-surfaces, Laplace formulations generate non-physical solutions which widely depart from the real fluid dynamics. These tests can be easily reproduced, not requiring complex simulation tools. Furthermore, they can be used as benchmarks to check consistency of developed or commercial software. The article is closed with a discussion of the mathematical aspects involved, including the issues of boundary conditions and objectivity.
publishDate 2008
dc.date.none.fl_str_mv 2008-12
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/11336/25382
Limache, Alejandro Cesar; Sánchez, Pablo Javier; Dalcin, Lisandro Daniel; Idelsohn, Sergio Rodolfo; Objectivity tests for Navier–Stokes simulations: The revealing of non-physical solutions produced by Laplace formulations; Elsevier Science Sa; Computer Methods in Applied Mechanics and Engineering; 197; 49-50; 12-2008; 4180-4192
0045-7825
CONICET Digital
CONICET
url http://hdl.handle.net/11336/25382
identifier_str_mv Limache, Alejandro Cesar; Sánchez, Pablo Javier; Dalcin, Lisandro Daniel; Idelsohn, Sergio Rodolfo; Objectivity tests for Navier–Stokes simulations: The revealing of non-physical solutions produced by Laplace formulations; Elsevier Science Sa; Computer Methods in Applied Mechanics and Engineering; 197; 49-50; 12-2008; 4180-4192
0045-7825
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.cma.2008.04.020
info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0045782508001734
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
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier Science Sa
publisher.none.fl_str_mv Elsevier Science Sa
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 13.070432

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