Numerical Analysis of a Projection-Based Stabilized POD-ROM for Incompressible Flows

In this paper, we propose a new stabilized projection-based proper orthogonal de-composition reduced order model (POD-ROM) for the numerical simulation of incompressible flows.The new method draws inspiration from successful numerical stabilization techniques used in thecontext of finite element (FE...

Descripción completa

Detalles Bibliográficos
Autor: Rubino, Samuele
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2020
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/138505
Acceso en línea:https://hdl.handle.net/11441/138505
https://doi.org/10.1137/19M1276686
Access Level:acceso abierto
Palabra clave:Navier--Stokes equations
projection stabilization
proper orthogonal decomposition
reduced order models
incompressible flows
numerical analysis
id ES_e55d44eb93e1989fdab6cd3c4cb3d4a0
oai_identifier_str oai:idus.us.es:11441/138505
network_acronym_str ES
network_name_str España
repository_id_str
spelling Numerical Analysis of a Projection-Based Stabilized POD-ROM for Incompressible FlowsRubino, SamueleNavier--Stokes equationsprojection stabilizationproper orthogonal decompositionreduced order modelsincompressible flowsnumerical analysisIn this paper, we propose a new stabilized projection-based proper orthogonal de-composition reduced order model (POD-ROM) for the numerical simulation of incompressible flows.The new method draws inspiration from successful numerical stabilization techniques used in thecontext of finite element (FE) methods, such as local projection stabilization (LPS). In particular,the new LPS-ROM is a velocity-pressure ROM that uses pressure modes as well to compute thereduced order pressure needed for instance in the computation of relevant quantities, such as dragand lift forces on bodies in the flow. The new LPS-ROM circumvents the standard discrete inf-supcondition for the POD velocity-pressure spaces, whose fulfillment can be rather expensive in realisticapplications in computational fluid dynamics (CFD). Also, the velocity modes do not have to beeither strongly or weakly divergence-free, which allows the use of snapshots generated, for instance,with penalty or projection-based stabilized methods. The numerical analysis of the fully Navier--Stokes discretization for the new LPS-ROM is presented by mainly deriving the corresponding errorestimates. Numerical studies are performed to discuss the accuracy and performance of the newLPS-ROM on a two-dimensional laminar unsteady flow past a circular obstacle.SIAMEcuaciones Diferenciales y Análisis NuméricoFQM120: Modelado Matemático y Simulación de Sistemas Medioambientales2020info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdftext/htmlhttps://hdl.handle.net/11441/138505https://doi.org/10.1137/19M1276686reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésSIAM journal on numerical analysis, 58 (4), 2019-2058.http://doi.org/10.1137/19M1276686info:eu-repo/semantics/openAccessoai:idus.us.es:11441/1385052026-06-17T12:51:07Z
dc.title.none.fl_str_mv Numerical Analysis of a Projection-Based Stabilized POD-ROM for Incompressible Flows
title Numerical Analysis of a Projection-Based Stabilized POD-ROM for Incompressible Flows
spellingShingle Numerical Analysis of a Projection-Based Stabilized POD-ROM for Incompressible Flows
Rubino, Samuele
Navier--Stokes equations
projection stabilization
proper orthogonal decomposition
reduced order models
incompressible flows
numerical analysis
title_short Numerical Analysis of a Projection-Based Stabilized POD-ROM for Incompressible Flows
title_full Numerical Analysis of a Projection-Based Stabilized POD-ROM for Incompressible Flows
title_fullStr Numerical Analysis of a Projection-Based Stabilized POD-ROM for Incompressible Flows
title_full_unstemmed Numerical Analysis of a Projection-Based Stabilized POD-ROM for Incompressible Flows
title_sort Numerical Analysis of a Projection-Based Stabilized POD-ROM for Incompressible Flows
dc.creator.none.fl_str_mv Rubino, Samuele
author Rubino, Samuele
author_facet Rubino, Samuele
author_role author
dc.contributor.none.fl_str_mv Ecuaciones Diferenciales y Análisis Numérico
FQM120: Modelado Matemático y Simulación de Sistemas Medioambientales
dc.subject.none.fl_str_mv Navier--Stokes equations
projection stabilization
proper orthogonal decomposition
reduced order models
incompressible flows
numerical analysis
topic Navier--Stokes equations
projection stabilization
proper orthogonal decomposition
reduced order models
incompressible flows
numerical analysis
description In this paper, we propose a new stabilized projection-based proper orthogonal de-composition reduced order model (POD-ROM) for the numerical simulation of incompressible flows.The new method draws inspiration from successful numerical stabilization techniques used in thecontext of finite element (FE) methods, such as local projection stabilization (LPS). In particular,the new LPS-ROM is a velocity-pressure ROM that uses pressure modes as well to compute thereduced order pressure needed for instance in the computation of relevant quantities, such as dragand lift forces on bodies in the flow. The new LPS-ROM circumvents the standard discrete inf-supcondition for the POD velocity-pressure spaces, whose fulfillment can be rather expensive in realisticapplications in computational fluid dynamics (CFD). Also, the velocity modes do not have to beeither strongly or weakly divergence-free, which allows the use of snapshots generated, for instance,with penalty or projection-based stabilized methods. The numerical analysis of the fully Navier--Stokes discretization for the new LPS-ROM is presented by mainly deriving the corresponding errorestimates. Numerical studies are performed to discuss the accuracy and performance of the newLPS-ROM on a two-dimensional laminar unsteady flow past a circular obstacle.
publishDate 2020
dc.date.none.fl_str_mv 2020
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/138505
https://doi.org/10.1137/19M1276686
url https://hdl.handle.net/11441/138505
https://doi.org/10.1137/19M1276686
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv SIAM journal on numerical analysis, 58 (4), 2019-2058.
http://doi.org/10.1137/19M1276686
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
text/html
dc.publisher.none.fl_str_mv SIAM
publisher.none.fl_str_mv SIAM
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869422672612425728
score 15,301603

Similares en LA Referencia