Two-dimensional compact-finite-difference schemes for solving the bi-Laplacian operator with homogeneous wall-normal derivatives

[EN] In fluid mechanics, the bi-Laplacian operator with Neumann homogeneous boundary conditions emerges when transforming the Navier-Stokes equations to the vorticity-velocity formulation. In the case of problems with a periodic direction, the problem can be transformed into multiple, independent, t...

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Autores: Amo-Navarro, Jesús, Vinuesa, Ricardo, Conejero, J. Alberto|||0000-0003-3681-7533, Hoyas, Sergio|||0000-0002-8458-7288
Tipo de recurso: artículo
Fecha de publicación:2021
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/186635
Acceso en línea:https://riunet.upv.es/handle/10251/186635
Access Level:acceso abierto
Palabra clave:DNS
CFD
Turbulence
Bi-Laplacian
Fourth-order elliptic
INGENIERIA AEROESPACIAL
MATEMATICA APLICADA
07.- Asegurar el acceso a energías asequibles, fiables, sostenibles y modernas para todos
11.- Conseguir que las ciudades y los asentamientos humanos sean inclusivos, seguros, resilientes y sostenibles
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network_acronym_str ES
network_name_str España
repository_id_str
spelling Two-dimensional compact-finite-difference schemes for solving the bi-Laplacian operator with homogeneous wall-normal derivativesAmo-Navarro, JesúsVinuesa, RicardoConejero, J. Alberto|||0000-0003-3681-7533Hoyas, Sergio|||0000-0002-8458-7288DNSCFDTurbulenceBi-LaplacianFourth-order ellipticINGENIERIA AEROESPACIALMATEMATICA APLICADA07.- Asegurar el acceso a energías asequibles, fiables, sostenibles y modernas para todos11.- Conseguir que las ciudades y los asentamientos humanos sean inclusivos, seguros, resilientes y sostenibles[EN] In fluid mechanics, the bi-Laplacian operator with Neumann homogeneous boundary conditions emerges when transforming the Navier-Stokes equations to the vorticity-velocity formulation. In the case of problems with a periodic direction, the problem can be transformed into multiple, independent, two-dimensional fourth-order elliptic problems. An efficient method to solve these two-dimensional bi-Laplacian operators with Neumann homogeneus boundary conditions was designed and validated using 2D compact finite difference schemes. The solution is formulated as a linear combination of auxiliary solutions, as many as the number of points on the boundary, a method that was prohibitive some years ago due to the large memory requirements to store all these auxiliary functions. The validation has been made for different field configurations, grid sizes, and stencils of the numerical scheme, showing its potential to tackle high gradient fields as those that can be found in turbulent flows.This work was supported by RTI2018-102256-B-I00 of MINECO/FEDER and the ALBATROSS project (National Plan for Scientific and Technical Research and Innovation 2017-2020, No. PID2019-104978RB-I00).MDPI AGDepartamento de Matemática AplicadaDepartamento de Máquinas y Motores TérmicosEscuela Técnica Superior de Ingeniería Aeroespacial y Diseño IndustrialInstituto Universitario de Matemática Pura y AplicadaEscuela Técnica Superior de Ingeniería InformáticaAgencia Estatal de InvestigaciónRepositorio Institucional de la Universitat Politècnica de València Riunet20212021-10-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://riunet.upv.es/handle/10251/186635reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengAgencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2019-104978RB-I00 SISTEMA DE AYUDA A LA DECISION VALIDADO CLINICAMENTE BASADO EN MODELOS DE INTELIGENCIA ARTIFICIAL A NIVEL DE PIXEL PARA DECIDIR OPCIONES TERAPEUTICAS EN GLIOBLASTOMAAgencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 RTI2018-102256-B-I00 TRANSFERENCIA DE CALOR EN FLUJOS DE PARED: CANALES Y CAPAS LIMITESopen accesshttp://purl.org/coar/access_right/c_abf2Reconocimiento (by)http://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/1866352026-06-13T07:49:27Z
dc.title.none.fl_str_mv Two-dimensional compact-finite-difference schemes for solving the bi-Laplacian operator with homogeneous wall-normal derivatives
title Two-dimensional compact-finite-difference schemes for solving the bi-Laplacian operator with homogeneous wall-normal derivatives
spellingShingle Two-dimensional compact-finite-difference schemes for solving the bi-Laplacian operator with homogeneous wall-normal derivatives
Amo-Navarro, Jesús
DNS
CFD
Turbulence
Bi-Laplacian
Fourth-order elliptic
INGENIERIA AEROESPACIAL
MATEMATICA APLICADA
07.- Asegurar el acceso a energías asequibles, fiables, sostenibles y modernas para todos
11.- Conseguir que las ciudades y los asentamientos humanos sean inclusivos, seguros, resilientes y sostenibles
title_short Two-dimensional compact-finite-difference schemes for solving the bi-Laplacian operator with homogeneous wall-normal derivatives
title_full Two-dimensional compact-finite-difference schemes for solving the bi-Laplacian operator with homogeneous wall-normal derivatives
title_fullStr Two-dimensional compact-finite-difference schemes for solving the bi-Laplacian operator with homogeneous wall-normal derivatives
title_full_unstemmed Two-dimensional compact-finite-difference schemes for solving the bi-Laplacian operator with homogeneous wall-normal derivatives
title_sort Two-dimensional compact-finite-difference schemes for solving the bi-Laplacian operator with homogeneous wall-normal derivatives
dc.creator.none.fl_str_mv Amo-Navarro, Jesús
Vinuesa, Ricardo
Conejero, J. Alberto|||0000-0003-3681-7533
Hoyas, Sergio|||0000-0002-8458-7288
author Amo-Navarro, Jesús
author_facet Amo-Navarro, Jesús
Vinuesa, Ricardo
Conejero, J. Alberto|||0000-0003-3681-7533
Hoyas, Sergio|||0000-0002-8458-7288
author_role author
author2 Vinuesa, Ricardo
Conejero, J. Alberto|||0000-0003-3681-7533
Hoyas, Sergio|||0000-0002-8458-7288
author2_role author
author
author
dc.contributor.none.fl_str_mv Departamento de Matemática Aplicada
Departamento de Máquinas y Motores Térmicos
Escuela Técnica Superior de Ingeniería Aeroespacial y Diseño Industrial
Instituto Universitario de Matemática Pura y Aplicada
Escuela Técnica Superior de Ingeniería Informática
Agencia Estatal de Investigación
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv DNS
CFD
Turbulence
Bi-Laplacian
Fourth-order elliptic
INGENIERIA AEROESPACIAL
MATEMATICA APLICADA
07.- Asegurar el acceso a energías asequibles, fiables, sostenibles y modernas para todos
11.- Conseguir que las ciudades y los asentamientos humanos sean inclusivos, seguros, resilientes y sostenibles
topic DNS
CFD
Turbulence
Bi-Laplacian
Fourth-order elliptic
INGENIERIA AEROESPACIAL
MATEMATICA APLICADA
07.- Asegurar el acceso a energías asequibles, fiables, sostenibles y modernas para todos
11.- Conseguir que las ciudades y los asentamientos humanos sean inclusivos, seguros, resilientes y sostenibles
description [EN] In fluid mechanics, the bi-Laplacian operator with Neumann homogeneous boundary conditions emerges when transforming the Navier-Stokes equations to the vorticity-velocity formulation. In the case of problems with a periodic direction, the problem can be transformed into multiple, independent, two-dimensional fourth-order elliptic problems. An efficient method to solve these two-dimensional bi-Laplacian operators with Neumann homogeneus boundary conditions was designed and validated using 2D compact finite difference schemes. The solution is formulated as a linear combination of auxiliary solutions, as many as the number of points on the boundary, a method that was prohibitive some years ago due to the large memory requirements to store all these auxiliary functions. The validation has been made for different field configurations, grid sizes, and stencils of the numerical scheme, showing its potential to tackle high gradient fields as those that can be found in turbulent flows.
publishDate 2021
dc.date.none.fl_str_mv 2021
2021-10-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://riunet.upv.es/handle/10251/186635
url https://riunet.upv.es/handle/10251/186635
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://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2019-104978RB-I00 SISTEMA DE AYUDA A LA DECISION VALIDADO CLINICAMENTE BASADO EN MODELOS DE INTELIGENCIA ARTIFICIAL A NIVEL DE PIXEL PARA DECIDIR OPCIONES TERAPEUTICAS EN GLIOBLASTOMA
Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 RTI2018-102256-B-I00 TRANSFERENCIA DE CALOR EN FLUJOS DE PARED: CANALES Y CAPAS LIMITES
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento (by)
http://creativecommons.org/licenses/by/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
Reconocimiento (by)
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv MDPI AG
publisher.none.fl_str_mv MDPI AG
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,301629

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