Discrete energy-conservation properties in the numerical simulation of the navier–stokes equations

Nonlinear convective terms pose the most critical issues when a numerical discretization of the Navier–Stokes equations is performed, especially at high Reynolds numbers. They are indeed responsible for a nonlinear instability arising from the amplification of aliasing errors that come from the eval...

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Autores: Coppola, Gennaro, Capuano, Francesco|||0000-0003-0274-5260
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:2117/365098
Acceso en línea:https://hdl.handle.net/2117/365098
https://dx.doi.org/10.1115/1.4042820
Access Level:acceso abierto
Palabra clave:Fluid mechanics
Mecànica de fluids
Àrees temàtiques de la UPC::Enginyeria mecànica::Mecànica de fluids
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spelling Discrete energy-conservation properties in the numerical simulation of the navier–stokes equationsCoppola, GennaroCapuano, Francesco|||0000-0003-0274-5260Fluid mechanicsMecànica de fluidsÀrees temàtiques de la UPC::Enginyeria mecànica::Mecànica de fluidsNonlinear convective terms pose the most critical issues when a numerical discretization of the Navier–Stokes equations is performed, especially at high Reynolds numbers. They are indeed responsible for a nonlinear instability arising from the amplification of aliasing errors that come from the evaluation of the products of two or more variables on a finite grid. The classical remedy to this difficulty has been the construction of difference schemes able to reproduce at a discrete level some of the fundamental symmetry properties of the Navier–Stokes equations. The invariant character of quadratic quantities such as global kinetic energy in inviscid incompressible flows is a particular symmetry, whose enforcement typically guarantees a sufficient control of aliasing errors that allows the fulfillment of long-time integration. In this paper, a survey of the most successful approaches developed in this field is presented. The incompressible and compressible cases are both covered, and treated separately, and the topics of spatial and temporal energy conservation are discussed. The theory and the ideas are exposed with full details in classical simplified numerical settings, and the extensions to more complex situations are also reviewed. The effectiveness of the illustrated approaches is documented by numerical simulations of canonical flows and by industrial flow computations taken from the literature.20192019-01-0120222022-03-31journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/365098https://dx.doi.org/10.1115/1.4042820reponame: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:2117/3650982026-05-27T15:37:01Z
dc.title.none.fl_str_mv Discrete energy-conservation properties in the numerical simulation of the navier–stokes equations
title Discrete energy-conservation properties in the numerical simulation of the navier–stokes equations
spellingShingle Discrete energy-conservation properties in the numerical simulation of the navier–stokes equations
Coppola, Gennaro
Fluid mechanics
Mecànica de fluids
Àrees temàtiques de la UPC::Enginyeria mecànica::Mecànica de fluids
title_short Discrete energy-conservation properties in the numerical simulation of the navier–stokes equations
title_full Discrete energy-conservation properties in the numerical simulation of the navier–stokes equations
title_fullStr Discrete energy-conservation properties in the numerical simulation of the navier–stokes equations
title_full_unstemmed Discrete energy-conservation properties in the numerical simulation of the navier–stokes equations
title_sort Discrete energy-conservation properties in the numerical simulation of the navier–stokes equations
dc.creator.none.fl_str_mv Coppola, Gennaro
Capuano, Francesco|||0000-0003-0274-5260
author Coppola, Gennaro
author_facet Coppola, Gennaro
Capuano, Francesco|||0000-0003-0274-5260
author_role author
author2 Capuano, Francesco|||0000-0003-0274-5260
author2_role author
dc.subject.none.fl_str_mv Fluid mechanics
Mecànica de fluids
Àrees temàtiques de la UPC::Enginyeria mecànica::Mecànica de fluids
topic Fluid mechanics
Mecànica de fluids
Àrees temàtiques de la UPC::Enginyeria mecànica::Mecànica de fluids
description Nonlinear convective terms pose the most critical issues when a numerical discretization of the Navier–Stokes equations is performed, especially at high Reynolds numbers. They are indeed responsible for a nonlinear instability arising from the amplification of aliasing errors that come from the evaluation of the products of two or more variables on a finite grid. The classical remedy to this difficulty has been the construction of difference schemes able to reproduce at a discrete level some of the fundamental symmetry properties of the Navier–Stokes equations. The invariant character of quadratic quantities such as global kinetic energy in inviscid incompressible flows is a particular symmetry, whose enforcement typically guarantees a sufficient control of aliasing errors that allows the fulfillment of long-time integration. In this paper, a survey of the most successful approaches developed in this field is presented. The incompressible and compressible cases are both covered, and treated separately, and the topics of spatial and temporal energy conservation are discussed. The theory and the ideas are exposed with full details in classical simplified numerical settings, and the extensions to more complex situations are also reviewed. The effectiveness of the illustrated approaches is documented by numerical simulations of canonical flows and by industrial flow computations taken from the literature.
publishDate 2019
dc.date.none.fl_str_mv 2019
2019-01-01
2022
2022-03-31
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/365098
https://dx.doi.org/10.1115/1.4042820
url https://hdl.handle.net/2117/365098
https://dx.doi.org/10.1115/1.4042820
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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