A cure for instabilities due to advection-dominance in POD solution to advection-diffusion-reaction equations

In this paper, we propose to improve the stabilized POD-ROM introduced in [48] to deal with the numerical simulation of advection-dominated advection-diffusion-reaction equations. In particular, we propose a three-stage stabilizing strategy that will be very useful when considering very low diffusio...

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Autores: Azaïez, Mejdi, Chacón Rebollo, Tomás, Rubino, Samuele
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2021
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/138465
Acceso en línea:https://hdl.handle.net/11441/138465
https://doi.org/10.1016/j.jcp.2020.109916
Access Level:acceso abierto
Palabra clave:Finite element method
Filtered advection stabilization
A-posteriori stabilization
Proper orthogonal decomposition
Reduced order models
Convection-dominated flows
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spelling A cure for instabilities due to advection-dominance in POD solution to advection-diffusion-reaction equationsAzaïez, MejdiChacón Rebollo, TomásRubino, SamueleFinite element methodFiltered advection stabilizationA-posteriori stabilizationProper orthogonal decompositionReduced order modelsConvection-dominated flowsIn this paper, we propose to improve the stabilized POD-ROM introduced in [48] to deal with the numerical simulation of advection-dominated advection-diffusion-reaction equations. In particular, we propose a three-stage stabilizing strategy that will be very useful when considering very low diffusion coefficients, i.e. in the strongly advection-dominated regime. This approach mainly consists in three ingredients: (1) the addition of a “streamline diffusion” stabilization term to the governing projected equations, (2) the modification of the correlation matrix defining the POD modes associated to the advection stabilization term, and (3) an a-posteriori stabilization scheme. Numerical studies are performed to discuss the accuracy and performance of the new method in handling strongly advection-dominated cases.ElsevierEcuaciones Diferenciales y Análisis NuméricoFQM120: Modelado Matemático y Simulación de Sistemas Medioambientales2021info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/138465https://doi.org/10.1016/j.jcp.2020.109916reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésJournal of Computational Physics, 425, 109916.https://doi.org/10.1016/j.jcp.2020.109916info:eu-repo/semantics/openAccessoai:idus.us.es:11441/1384652026-06-17T12:51:07Z
dc.title.none.fl_str_mv A cure for instabilities due to advection-dominance in POD solution to advection-diffusion-reaction equations
title A cure for instabilities due to advection-dominance in POD solution to advection-diffusion-reaction equations
spellingShingle A cure for instabilities due to advection-dominance in POD solution to advection-diffusion-reaction equations
Azaïez, Mejdi
Finite element method
Filtered advection stabilization
A-posteriori stabilization
Proper orthogonal decomposition
Reduced order models
Convection-dominated flows
title_short A cure for instabilities due to advection-dominance in POD solution to advection-diffusion-reaction equations
title_full A cure for instabilities due to advection-dominance in POD solution to advection-diffusion-reaction equations
title_fullStr A cure for instabilities due to advection-dominance in POD solution to advection-diffusion-reaction equations
title_full_unstemmed A cure for instabilities due to advection-dominance in POD solution to advection-diffusion-reaction equations
title_sort A cure for instabilities due to advection-dominance in POD solution to advection-diffusion-reaction equations
dc.creator.none.fl_str_mv Azaïez, Mejdi
Chacón Rebollo, Tomás
Rubino, Samuele
author Azaïez, Mejdi
author_facet Azaïez, Mejdi
Chacón Rebollo, Tomás
Rubino, Samuele
author_role author
author2 Chacón Rebollo, Tomás
Rubino, Samuele
author2_role author
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 Finite element method
Filtered advection stabilization
A-posteriori stabilization
Proper orthogonal decomposition
Reduced order models
Convection-dominated flows
topic Finite element method
Filtered advection stabilization
A-posteriori stabilization
Proper orthogonal decomposition
Reduced order models
Convection-dominated flows
description In this paper, we propose to improve the stabilized POD-ROM introduced in [48] to deal with the numerical simulation of advection-dominated advection-diffusion-reaction equations. In particular, we propose a three-stage stabilizing strategy that will be very useful when considering very low diffusion coefficients, i.e. in the strongly advection-dominated regime. This approach mainly consists in three ingredients: (1) the addition of a “streamline diffusion” stabilization term to the governing projected equations, (2) the modification of the correlation matrix defining the POD modes associated to the advection stabilization term, and (3) an a-posteriori stabilization scheme. Numerical studies are performed to discuss the accuracy and performance of the new method in handling strongly advection-dominated cases.
publishDate 2021
dc.date.none.fl_str_mv 2021
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/11441/138465
https://doi.org/10.1016/j.jcp.2020.109916
url https://hdl.handle.net/11441/138465
https://doi.org/10.1016/j.jcp.2020.109916
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Journal of Computational Physics, 425, 109916.
https://doi.org/10.1016/j.jcp.2020.109916
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
repository.mail.fl_str_mv
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score 15.300724

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