POD-ROMs for Incompressible Flows Including Snapshots of the Temporal Derivative of the Full Order Solution

SIAM journals are fully compliant with Plan S under the “repository route”, also known as “green open access”. SIAM journal authors are permitted to deposit the Author’s Accepted Manuscript (AAM) in an institutional or subject repository at the time of final publication with a CC BY license or anoth...

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Autores: García-Archilla, Bosco, John, Volker, Novo, Julia
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2023
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/152951
Acceso en línea:https://hdl.handle.net/11441/152951
https://doi.org/10.1137/22M1503853
Access Level:acceso abierto
Palabra clave:Incompressible Navier–Stokes equations
Proper orthogonal decomposition
Reduced order models
Snapshots of the temporal derivative
Grad-div stabilization
Robust pointwise in time estimates
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spelling POD-ROMs for Incompressible Flows Including Snapshots of the Temporal Derivative of the Full Order SolutionGarcía-Archilla, BoscoJohn, VolkerNovo, JuliaIncompressible Navier–Stokes equationsProper orthogonal decompositionReduced order modelsSnapshots of the temporal derivativeGrad-div stabilizationRobust pointwise in time estimatesSIAM journals are fully compliant with Plan S under the “repository route”, also known as “green open access”. SIAM journal authors are permitted to deposit the Author’s Accepted Manuscript (AAM) in an institutional or subject repository at the time of final publication with a CC BY license or another creative commons license as permitted under Plan S licensing requirements (Last Accessed: March 2022).In this paper we study the influence of including snapshots that approach the velocitytime derivative in the numerical approximation of the incompressible Navier--Stokes equations bymeans of proper orthogonal decomposition (POD) methods. Our set of snapshots includes thevelocity approximation at the initial time from a full order mixed finite element method (FOM)together with approximations to the time derivative at different times. The approximation at theinitial velocity can be replaced by the mean value of the velocities at the different times so thatwhen implementing the method to the fluctuations, as done mostly in practice, only approximationsto the time derivatives are included in the set of snapshots. For the POD method we study thedifferences between projecting onto L2 and H1. In both cases pointwise in time error bounds canbe proved. Including grad-div stabilization in both the FOM and the POD methods, error boundswith constants independent of inverse powers of the viscosity can be obtained.Ministerio de Ciencia, Innovación y Universidades PGC2018-096265-B-I00 PID2019-104141GB-I00.Ministerio de Economía PID2019-104141GB-I00 VA169P20Society for Industrial and Applied Mathematics (SIAM)Matemática Aplicada IITIC130: Investigación en Sistemas Dinámicos en IngenieríaMinisterio de Ciencia, Innovación y Universidades (MICINN). EspañaMinisterio de Economía. España2023info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/152951https://doi.org/10.1137/22M1503853reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésSIAM Journal on Numerical Analysis, 61 (3), 1340-1368.PGC2018-096265-B-I00PID2019-104141GB-I00VA169P20https://epubs.siam.org/doi/full/10.1137/22M1503853info:eu-repo/semantics/openAccessoai:idus.us.es:11441/1529512026-06-17T12:51:07Z
dc.title.none.fl_str_mv POD-ROMs for Incompressible Flows Including Snapshots of the Temporal Derivative of the Full Order Solution
title POD-ROMs for Incompressible Flows Including Snapshots of the Temporal Derivative of the Full Order Solution
spellingShingle POD-ROMs for Incompressible Flows Including Snapshots of the Temporal Derivative of the Full Order Solution
García-Archilla, Bosco
Incompressible Navier–Stokes equations
Proper orthogonal decomposition
Reduced order models
Snapshots of the temporal derivative
Grad-div stabilization
Robust pointwise in time estimates
title_short POD-ROMs for Incompressible Flows Including Snapshots of the Temporal Derivative of the Full Order Solution
title_full POD-ROMs for Incompressible Flows Including Snapshots of the Temporal Derivative of the Full Order Solution
title_fullStr POD-ROMs for Incompressible Flows Including Snapshots of the Temporal Derivative of the Full Order Solution
title_full_unstemmed POD-ROMs for Incompressible Flows Including Snapshots of the Temporal Derivative of the Full Order Solution
title_sort POD-ROMs for Incompressible Flows Including Snapshots of the Temporal Derivative of the Full Order Solution
dc.creator.none.fl_str_mv García-Archilla, Bosco
John, Volker
Novo, Julia
author García-Archilla, Bosco
author_facet García-Archilla, Bosco
John, Volker
Novo, Julia
author_role author
author2 John, Volker
Novo, Julia
author2_role author
author
dc.contributor.none.fl_str_mv Matemática Aplicada II
TIC130: Investigación en Sistemas Dinámicos en Ingeniería
Ministerio de Ciencia, Innovación y Universidades (MICINN). España
Ministerio de Economía. España
dc.subject.none.fl_str_mv Incompressible Navier–Stokes equations
Proper orthogonal decomposition
Reduced order models
Snapshots of the temporal derivative
Grad-div stabilization
Robust pointwise in time estimates
topic Incompressible Navier–Stokes equations
Proper orthogonal decomposition
Reduced order models
Snapshots of the temporal derivative
Grad-div stabilization
Robust pointwise in time estimates
description SIAM journals are fully compliant with Plan S under the “repository route”, also known as “green open access”. SIAM journal authors are permitted to deposit the Author’s Accepted Manuscript (AAM) in an institutional or subject repository at the time of final publication with a CC BY license or another creative commons license as permitted under Plan S licensing requirements (Last Accessed: March 2022).
publishDate 2023
dc.date.none.fl_str_mv 2023
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/152951
https://doi.org/10.1137/22M1503853
url https://hdl.handle.net/11441/152951
https://doi.org/10.1137/22M1503853
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv SIAM Journal on Numerical Analysis, 61 (3), 1340-1368.
PGC2018-096265-B-I00
PID2019-104141GB-I00
VA169P20
https://epubs.siam.org/doi/full/10.1137/22M1503853
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Society for Industrial and Applied Mathematics (SIAM)
publisher.none.fl_str_mv Society for Industrial and Applied Mathematics (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
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score 15,811543

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