A VMS–based fractional step technique for the compressible Navier–Stokes equations using conservative variables

In this paper we address the compressible Navier–Stokes equations written in the so-called conservative formulation. In particular, we focus on the possibility of uncoupling the computation of the problem unknowns, namely, density, linear momentum and total energy, a technique usually labeled as fra...

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Autores: Parada Bustelo, Samuel|||0000-0003-0185-350X, Codina, Ramon|||0000-0002-7412-778X, Baiges Aznar, Joan|||0000-0002-3940-5887
Tipo de recurso: artículo
Fecha de publicación:2022
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:2117/371375
Acceso en línea:https://hdl.handle.net/2117/371375
https://dx.doi.org/10.1016/j.jcp.2022.111137
Access Level:acceso abierto
Palabra clave:Navier-Stokes equations
Compressible flow
Variational Multiscale Method (VMS)
Fractional step schemes
Finite element method
Supersonic flows
Equacions de Navier-Stokes
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits
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spelling A VMS–based fractional step technique for the compressible Navier–Stokes equations using conservative variablesParada Bustelo, Samuel|||0000-0003-0185-350XCodina, Ramon|||0000-0002-7412-778XBaiges Aznar, Joan|||0000-0002-3940-5887Navier-Stokes equationsCompressible flowVariational Multiscale Method (VMS)Fractional step schemesFinite element methodSupersonic flowsEquacions de Navier-StokesÀrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finitsIn this paper we address the compressible Navier–Stokes equations written in the so-called conservative formulation. In particular, we focus on the possibility of uncoupling the computation of the problem unknowns, namely, density, linear momentum and total energy, a technique usually labeled as fractional step method, which allows to reduce the associated computational cost. The proposed methodology is a finite-element solver supplemented with a stabilization technique within the Variational Multi-Scale framework. In this regard, we consider orthogonal and dynamic definitions for the subscales. This discretization in space shows an adequate stability, permitting in particular the use of equal interpolation for all variables in play. However, we complement it with a shock-capturing operator in order to solve problems involving shocks. Several representative benchmark flow simulations are performed, which demonstrate the suitability of the proposed algorithm for a vast range of regimes.Samuel Parada gratefully acknowledges the support received from the Agència de Gestió d'Ajuts Universitaris i de Recerca through the predoctoral FI grant 2019-FI-B-00607. Joan Baiges gratefully acknowledges the support of the Spanish Government through the Ramón y Cajal grant RYC-2015-17367. Ramon Codina gratefully acknowledges the support received from the ICREA Acadèmia Research Program of the Catalan Government. This work was partially funded through the TOP-FSI: RTI2018-098276-B-I00 project of the Spanish Government. CIMNE is a recipient of a “Severo Ochoa Programme for Centers of Excellence in R&D” grant (CEX2018-000797-S) by the Spanish Government.Peer Reviewed20222022-06-0120222022-07-27journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/371375https://dx.doi.org/10.1016/j.jcp.2022.111137reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)InglésengAgencia Estatal de Investigación http://doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 RTI2018-098276-B-I00 OPTIMIZACION TOPOLOGICA DE ESTRUCTURAS SUJETAS A INTERACCION FLUIDO-ESTRUCTURAopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/3713752026-05-27T15:37:01Z
dc.title.none.fl_str_mv A VMS–based fractional step technique for the compressible Navier–Stokes equations using conservative variables
title A VMS–based fractional step technique for the compressible Navier–Stokes equations using conservative variables
spellingShingle A VMS–based fractional step technique for the compressible Navier–Stokes equations using conservative variables
Parada Bustelo, Samuel|||0000-0003-0185-350X
Navier-Stokes equations
Compressible flow
Variational Multiscale Method (VMS)
Fractional step schemes
Finite element method
Supersonic flows
Equacions de Navier-Stokes
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits
title_short A VMS–based fractional step technique for the compressible Navier–Stokes equations using conservative variables
title_full A VMS–based fractional step technique for the compressible Navier–Stokes equations using conservative variables
title_fullStr A VMS–based fractional step technique for the compressible Navier–Stokes equations using conservative variables
title_full_unstemmed A VMS–based fractional step technique for the compressible Navier–Stokes equations using conservative variables
title_sort A VMS–based fractional step technique for the compressible Navier–Stokes equations using conservative variables
dc.creator.none.fl_str_mv Parada Bustelo, Samuel|||0000-0003-0185-350X
Codina, Ramon|||0000-0002-7412-778X
Baiges Aznar, Joan|||0000-0002-3940-5887
author Parada Bustelo, Samuel|||0000-0003-0185-350X
author_facet Parada Bustelo, Samuel|||0000-0003-0185-350X
Codina, Ramon|||0000-0002-7412-778X
Baiges Aznar, Joan|||0000-0002-3940-5887
author_role author
author2 Codina, Ramon|||0000-0002-7412-778X
Baiges Aznar, Joan|||0000-0002-3940-5887
author2_role author
author
dc.subject.none.fl_str_mv Navier-Stokes equations
Compressible flow
Variational Multiscale Method (VMS)
Fractional step schemes
Finite element method
Supersonic flows
Equacions de Navier-Stokes
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits
topic Navier-Stokes equations
Compressible flow
Variational Multiscale Method (VMS)
Fractional step schemes
Finite element method
Supersonic flows
Equacions de Navier-Stokes
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits
description In this paper we address the compressible Navier–Stokes equations written in the so-called conservative formulation. In particular, we focus on the possibility of uncoupling the computation of the problem unknowns, namely, density, linear momentum and total energy, a technique usually labeled as fractional step method, which allows to reduce the associated computational cost. The proposed methodology is a finite-element solver supplemented with a stabilization technique within the Variational Multi-Scale framework. In this regard, we consider orthogonal and dynamic definitions for the subscales. This discretization in space shows an adequate stability, permitting in particular the use of equal interpolation for all variables in play. However, we complement it with a shock-capturing operator in order to solve problems involving shocks. Several representative benchmark flow simulations are performed, which demonstrate the suitability of the proposed algorithm for a vast range of regimes.
publishDate 2022
dc.date.none.fl_str_mv 2022
2022-06-01
2022
2022-07-27
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/2117/371375
https://dx.doi.org/10.1016/j.jcp.2022.111137
url https://hdl.handle.net/2117/371375
https://dx.doi.org/10.1016/j.jcp.2022.111137
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación http://doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 RTI2018-098276-B-I00 OPTIMIZACION TOPOLOGICA DE ESTRUCTURAS SUJETAS A INTERACCION FLUIDO-ESTRUCTURA
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
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-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
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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