A Finite Element Formulation Satisfying the Discrete Geometric Conservation Law Based on Averaged Jacobians

Autores
Storti, Mario Alberto; Garelli, Luciano; Paz, Rodrigo Rafael
Año de publicación
2011
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this article a new methodology for developing DGCL (for Discrete Geometric Conservation Law) compliant formulations is presented. It is carried out in the context of the Finite Element Method (FEM) for general advective-diffusive systems on moving domains using an Arbitrary Lagrangian Eulerian (ALE) scheme. There is an extensive literature about the impact of DGCL compliance on the stability and precision of time integration methods. In those articles it has been proved that satisfying the DGCL is a necessary and sufficient condition for any ALE scheme to maintain on moving grids the nonlinear stability properties of its fixed-grid counterpart. However, only a few works propose a methodology for obtaining a compliant scheme. In this work, a DGCL compliant scheme based on an Averaged ALE Jacobians Formulation (AJF) is obtained. This new formulation is applied to the -family of time integration methods. In addition, an extension to the three-point Backward Difference Formula (BDF) is given. With the aim to validate the AJF formulation a set of numerical tests are performed. These tests include 2D and 3D diffusion problems with different mesh movements and the 2D compressible Navier-Stokes equations.
Fil: Storti, Mario Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Desarrollo Tecnológico Para la Industria Química (i); Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico. Centro de Investigación de Métodos Computacionales; Argentina. Universidad Nacional del Litoral; Argentina
Fil: Garelli, Luciano. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Desarrollo Tecnológico Para la Industria Química (i); Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico. Centro de Investigación de Métodos Computacionales; Argentina. Universidad Nacional del Litoral; Argentina
Fil: Paz, Rodrigo Rafael. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Desarrollo Tecnológico Para la Industria Química (i); Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico. Centro de Investigación de Métodos Computacionales; Argentina. Universidad Nacional del Litoral; Argentina
Materia
Finite Elements Method
Geometric Conservation Law
Arbitrary Lagrangian-Eulerian Method
Moving Meshes
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/13559
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/13559
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling A Finite Element Formulation Satisfying the Discrete Geometric Conservation Law Based on Averaged JacobiansStorti, Mario AlbertoGarelli, LucianoPaz, Rodrigo RafaelFinite Elements MethodGeometric Conservation LawArbitrary Lagrangian-Eulerian MethodMoving Mesheshttps://purl.org/becyt/ford/2.3https://purl.org/becyt/ford/2In this article a new methodology for developing DGCL (for Discrete Geometric Conservation Law) compliant formulations is presented. It is carried out in the context of the Finite Element Method (FEM) for general advective-diffusive systems on moving domains using an Arbitrary Lagrangian Eulerian (ALE) scheme. There is an extensive literature about the impact of DGCL compliance on the stability and precision of time integration methods. In those articles it has been proved that satisfying the DGCL is a necessary and sufficient condition for any ALE scheme to maintain on moving grids the nonlinear stability properties of its fixed-grid counterpart. However, only a few works propose a methodology for obtaining a compliant scheme. In this work, a DGCL compliant scheme based on an Averaged ALE Jacobians Formulation (AJF) is obtained. This new formulation is applied to the -family of time integration methods. In addition, an extension to the three-point Backward Difference Formula (BDF) is given. With the aim to validate the AJF formulation a set of numerical tests are performed. These tests include 2D and 3D diffusion problems with different mesh movements and the 2D compressible Navier-Stokes equations.Fil: Storti, Mario Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Desarrollo Tecnológico Para la Industria Química (i); Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico. Centro de Investigación de Métodos Computacionales; Argentina. Universidad Nacional del Litoral; ArgentinaFil: Garelli, Luciano. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Desarrollo Tecnológico Para la Industria Química (i); Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico. Centro de Investigación de Métodos Computacionales; Argentina. Universidad Nacional del Litoral; ArgentinaFil: Paz, Rodrigo Rafael. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Desarrollo Tecnológico Para la Industria Química (i); Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico. Centro de Investigación de Métodos Computacionales; Argentina. Universidad Nacional del Litoral; ArgentinaJohn Wiley & Sons Ltd2011-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/13559Storti, Mario Alberto; Garelli, Luciano; Paz, Rodrigo Rafael; A Finite Element Formulation Satisfying the Discrete Geometric Conservation Law Based on Averaged Jacobians; John Wiley & Sons Ltd; International Journal For Numerical Methods In Fluids; 6-20110271-2091enginfo:eu-repo/semantics/altIdentifier/doi/10.1002/fld.2669info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:04:59Zoai:ri.conicet.gov.ar:11336/13559instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 10:04:59.448CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A Finite Element Formulation Satisfying the Discrete Geometric Conservation Law Based on Averaged Jacobians
title A Finite Element Formulation Satisfying the Discrete Geometric Conservation Law Based on Averaged Jacobians
spellingShingle A Finite Element Formulation Satisfying the Discrete Geometric Conservation Law Based on Averaged Jacobians
Storti, Mario Alberto
Finite Elements Method
Geometric Conservation Law
Arbitrary Lagrangian-Eulerian Method
Moving Meshes
title_short A Finite Element Formulation Satisfying the Discrete Geometric Conservation Law Based on Averaged Jacobians
title_full A Finite Element Formulation Satisfying the Discrete Geometric Conservation Law Based on Averaged Jacobians
title_fullStr A Finite Element Formulation Satisfying the Discrete Geometric Conservation Law Based on Averaged Jacobians
title_full_unstemmed A Finite Element Formulation Satisfying the Discrete Geometric Conservation Law Based on Averaged Jacobians
title_sort A Finite Element Formulation Satisfying the Discrete Geometric Conservation Law Based on Averaged Jacobians
dc.creator.none.fl_str_mv Storti, Mario Alberto
Garelli, Luciano
Paz, Rodrigo Rafael
author Storti, Mario Alberto
author_facet Storti, Mario Alberto
Garelli, Luciano
Paz, Rodrigo Rafael
author_role author
author2 Garelli, Luciano
Paz, Rodrigo Rafael
author2_role author
author
dc.subject.none.fl_str_mv Finite Elements Method
Geometric Conservation Law
Arbitrary Lagrangian-Eulerian Method
Moving Meshes
topic Finite Elements Method
Geometric Conservation Law
Arbitrary Lagrangian-Eulerian Method
Moving Meshes
purl_subject.fl_str_mv https://purl.org/becyt/ford/2.3
https://purl.org/becyt/ford/2
dc.description.none.fl_txt_mv In this article a new methodology for developing DGCL (for Discrete Geometric Conservation Law) compliant formulations is presented. It is carried out in the context of the Finite Element Method (FEM) for general advective-diffusive systems on moving domains using an Arbitrary Lagrangian Eulerian (ALE) scheme. There is an extensive literature about the impact of DGCL compliance on the stability and precision of time integration methods. In those articles it has been proved that satisfying the DGCL is a necessary and sufficient condition for any ALE scheme to maintain on moving grids the nonlinear stability properties of its fixed-grid counterpart. However, only a few works propose a methodology for obtaining a compliant scheme. In this work, a DGCL compliant scheme based on an Averaged ALE Jacobians Formulation (AJF) is obtained. This new formulation is applied to the -family of time integration methods. In addition, an extension to the three-point Backward Difference Formula (BDF) is given. With the aim to validate the AJF formulation a set of numerical tests are performed. These tests include 2D and 3D diffusion problems with different mesh movements and the 2D compressible Navier-Stokes equations.
Fil: Storti, Mario Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Desarrollo Tecnológico Para la Industria Química (i); Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico. Centro de Investigación de Métodos Computacionales; Argentina. Universidad Nacional del Litoral; Argentina
Fil: Garelli, Luciano. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Desarrollo Tecnológico Para la Industria Química (i); Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico. Centro de Investigación de Métodos Computacionales; Argentina. Universidad Nacional del Litoral; Argentina
Fil: Paz, Rodrigo Rafael. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Desarrollo Tecnológico Para la Industria Química (i); Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico. Centro de Investigación de Métodos Computacionales; Argentina. Universidad Nacional del Litoral; Argentina
description In this article a new methodology for developing DGCL (for Discrete Geometric Conservation Law) compliant formulations is presented. It is carried out in the context of the Finite Element Method (FEM) for general advective-diffusive systems on moving domains using an Arbitrary Lagrangian Eulerian (ALE) scheme. There is an extensive literature about the impact of DGCL compliance on the stability and precision of time integration methods. In those articles it has been proved that satisfying the DGCL is a necessary and sufficient condition for any ALE scheme to maintain on moving grids the nonlinear stability properties of its fixed-grid counterpart. However, only a few works propose a methodology for obtaining a compliant scheme. In this work, a DGCL compliant scheme based on an Averaged ALE Jacobians Formulation (AJF) is obtained. This new formulation is applied to the -family of time integration methods. In addition, an extension to the three-point Backward Difference Formula (BDF) is given. With the aim to validate the AJF formulation a set of numerical tests are performed. These tests include 2D and 3D diffusion problems with different mesh movements and the 2D compressible Navier-Stokes equations.
publishDate 2011
dc.date.none.fl_str_mv 2011-06
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/13559
Storti, Mario Alberto; Garelli, Luciano; Paz, Rodrigo Rafael; A Finite Element Formulation Satisfying the Discrete Geometric Conservation Law Based on Averaged Jacobians; John Wiley & Sons Ltd; International Journal For Numerical Methods In Fluids; 6-2011
0271-2091
url http://hdl.handle.net/11336/13559
identifier_str_mv Storti, Mario Alberto; Garelli, Luciano; Paz, Rodrigo Rafael; A Finite Element Formulation Satisfying the Discrete Geometric Conservation Law Based on Averaged Jacobians; John Wiley & Sons Ltd; International Journal For Numerical Methods In Fluids; 6-2011
0271-2091
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1002/fld.2669
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv John Wiley & Sons Ltd
publisher.none.fl_str_mv John Wiley & Sons Ltd
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
_version_ 1842269884967288832
score 13.13397

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