On the influence of the nonlinear term in the numerical approximation of Incompressible Flows by means of proper orthogonal decomposition methods

This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Detalles Bibliográficos
Autores: García-Archilla, Bosco, Novo, Julia, Rubino, Samuele
Tipo de recurso: artículo
Estado:Versión publicada
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:11441/143596
Acceso en línea:https://hdl.handle.net/11441/143596
https://doi.org/10.1016/j.cma.2022.115866
Access Level:acceso abierto
Palabra clave:Navier–Stokes equations
Proper orthogonal decomposition
Nonlinear term discretization
Grad–div stabilization
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spelling On the influence of the nonlinear term in the numerical approximation of Incompressible Flows by means of proper orthogonal decomposition methodsGarcía-Archilla, BoscoNovo, JuliaRubino, SamueleNavier–Stokes equationsProper orthogonal decompositionNonlinear term discretizationGrad–div stabilizationThis is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).We consider proper orthogonal decomposition (POD) methods to approximate the incompressible Navier–Stokes equations. We study the case in which one discretization for the nonlinear term is used in the snapshots (that are computed with a full order method (FOM)) and a different discretization of the nonlinear term is applied in the POD method. We prove that an additional error term appears in this case, compared with the case in which the same discretization of the nonlinear term is applied for both the FOM and the POD methods. However, the added term has the same size as the error coming from the FOM so that the rate of convergence of the POD method is barely affected. We analyze the case in which we add grad–div stabilization to both the FOM and the POD methods because it allows to get error bounds with constants independent of inverse powers of the viscosity. We also study the case in which no stabilization is added. Some numerical experiments support the theoretical analysis.ElsevierMatemática Aplicada IIEcuaciones Diferenciales y Análisis NuméricoTIC130: Investigación en Sistemas Dinámicos en Ingeniería2023info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/143596https://doi.org/10.1016/j.cma.2022.115866reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésComputer Methods in Applied Mechanics and Engineering, 405, 115866.https://www.sciencedirect.com/science/article/pii/S0045782522008222info:eu-repo/semantics/openAccessoai:idus.us.es:11441/1435962026-06-17T12:51:07Z
dc.title.none.fl_str_mv On the influence of the nonlinear term in the numerical approximation of Incompressible Flows by means of proper orthogonal decomposition methods
title On the influence of the nonlinear term in the numerical approximation of Incompressible Flows by means of proper orthogonal decomposition methods
spellingShingle On the influence of the nonlinear term in the numerical approximation of Incompressible Flows by means of proper orthogonal decomposition methods
García-Archilla, Bosco
Navier–Stokes equations
Proper orthogonal decomposition
Nonlinear term discretization
Grad–div stabilization
title_short On the influence of the nonlinear term in the numerical approximation of Incompressible Flows by means of proper orthogonal decomposition methods
title_full On the influence of the nonlinear term in the numerical approximation of Incompressible Flows by means of proper orthogonal decomposition methods
title_fullStr On the influence of the nonlinear term in the numerical approximation of Incompressible Flows by means of proper orthogonal decomposition methods
title_full_unstemmed On the influence of the nonlinear term in the numerical approximation of Incompressible Flows by means of proper orthogonal decomposition methods
title_sort On the influence of the nonlinear term in the numerical approximation of Incompressible Flows by means of proper orthogonal decomposition methods
dc.creator.none.fl_str_mv García-Archilla, Bosco
Novo, Julia
Rubino, Samuele
author García-Archilla, Bosco
author_facet García-Archilla, Bosco
Novo, Julia
Rubino, Samuele
author_role author
author2 Novo, Julia
Rubino, Samuele
author2_role author
author
dc.contributor.none.fl_str_mv Matemática Aplicada II
Ecuaciones Diferenciales y Análisis Numérico
TIC130: Investigación en Sistemas Dinámicos en Ingeniería
dc.subject.none.fl_str_mv Navier–Stokes equations
Proper orthogonal decomposition
Nonlinear term discretization
Grad–div stabilization
topic Navier–Stokes equations
Proper orthogonal decomposition
Nonlinear term discretization
Grad–div stabilization
description This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
publishDate 2023
dc.date.none.fl_str_mv 2023
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/11441/143596
https://doi.org/10.1016/j.cma.2022.115866
url https://hdl.handle.net/11441/143596
https://doi.org/10.1016/j.cma.2022.115866
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Computer Methods in Applied Mechanics and Engineering, 405, 115866.
https://www.sciencedirect.com/science/article/pii/S0045782522008222
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 Elsevier
publisher.none.fl_str_mv Elsevier
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
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score 15,300724

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