Measuring the effectiveness of extrapolation techniques associated with the multigrid method applied to the Navier-Stokes equations
Autor(a) principal: | |
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Data de Publicação: | 2022 |
Outros Autores: | , , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Acta scientiarum. Technology (Online) |
Texto Completo: | http://www.periodicos.uem.br/ojs/index.php/ActaSciTechnol/article/view/57398 |
Resumo: | In this work, we applied different extrapolation techniques in association with the multigrid method to discover which one is the most effective in reducing the iteration error and the processing time (CPU time), as well as in improving the convergence factors. The mathematical model studied refers to the two-dimensional laminar flow of an isothermal time-dependent incompressible fluid modeled by the Navier-Stokes equations, with , solved iteratively with the projection method and the Finite Volume Method. The extrapolation methods used were: Aitken, Empiric, Mitin, scalar Epsilon, scalar Rho, topological Epsilon, and topological Rho. A two-step application was performed: first, extrapolators methods were applied individually after the use of the multigrid method. Then, the best-performing extrapolation techniques were used in the second step, where they were applied between the cycles of the multigrid method. The methods that presented the best convergence properties in the first stage were topological and scalar Epsilon. In the second stage, both methods maintained their performance, however, the topological Epsilon method presented more significant convergence rates than the scalar Epsilon. The other parameters analyzed were: the storage memory peak, the dimensionless norm of the residual based on the initial estimate, and the error norms of iteration. Thus, it was possible to state which extrapolation technique performed best and to compare it with the multigrid method with no extrapolation, which in this study was the topological Epsilon method. |
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Measuring the effectiveness of extrapolation techniques associated with the multigrid method applied to the Navier-Stokes equations Measuring the effectiveness of extrapolation techniques associated with the multigrid method applied to the Navier-Stokes equations Finite volume method; projection method; convergence acceleration; topological Epsilon.Finite volume method; projection method; convergence acceleration; topological Epsilon.In this work, we applied different extrapolation techniques in association with the multigrid method to discover which one is the most effective in reducing the iteration error and the processing time (CPU time), as well as in improving the convergence factors. The mathematical model studied refers to the two-dimensional laminar flow of an isothermal time-dependent incompressible fluid modeled by the Navier-Stokes equations, with , solved iteratively with the projection method and the Finite Volume Method. The extrapolation methods used were: Aitken, Empiric, Mitin, scalar Epsilon, scalar Rho, topological Epsilon, and topological Rho. A two-step application was performed: first, extrapolators methods were applied individually after the use of the multigrid method. Then, the best-performing extrapolation techniques were used in the second step, where they were applied between the cycles of the multigrid method. The methods that presented the best convergence properties in the first stage were topological and scalar Epsilon. In the second stage, both methods maintained their performance, however, the topological Epsilon method presented more significant convergence rates than the scalar Epsilon. The other parameters analyzed were: the storage memory peak, the dimensionless norm of the residual based on the initial estimate, and the error norms of iteration. Thus, it was possible to state which extrapolation technique performed best and to compare it with the multigrid method with no extrapolation, which in this study was the topological Epsilon method.In this work, we applied different extrapolation techniques in association with the multigrid method to discover which one is the most effective in reducing the iteration error and the processing time (CPU time), as well as in improving the convergence factors. The mathematical model studied refers to the two-dimensional laminar flow of an isothermal time-dependent incompressible fluid modeled by the Navier-Stokes equations, with , solved iteratively with the projection method and the Finite Volume Method. The extrapolation methods used were: Aitken, Empiric, Mitin, scalar Epsilon, scalar Rho, topological Epsilon, and topological Rho. A two-step application was performed: first, extrapolators methods were applied individually after the use of the multigrid method. Then, the best-performing extrapolation techniques were used in the second step, where they were applied between the cycles of the multigrid method. The methods that presented the best convergence properties in the first stage were topological and scalar Epsilon. In the second stage, both methods maintained their performance, however, the topological Epsilon method presented more significant convergence rates than the scalar Epsilon. The other parameters analyzed were: the storage memory peak, the dimensionless norm of the residual based on the initial estimate, and the error norms of iteration. Thus, it was possible to state which extrapolation technique performed best and to compare it with the multigrid method with no extrapolation, which in this study was the topological Epsilon method.Universidade Estadual De Maringá2022-03-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttp://www.periodicos.uem.br/ojs/index.php/ActaSciTechnol/article/view/5739810.4025/actascitechnol.v44i1.57398Acta Scientiarum. Technology; Vol 44 (2022): Publicação contínua; e57398Acta Scientiarum. Technology; v. 44 (2022): Publicação contínua; e573981806-25631807-8664reponame:Acta scientiarum. Technology (Online)instname:Universidade Estadual de Maringá (UEM)instacron:UEMenghttp://www.periodicos.uem.br/ojs/index.php/ActaSciTechnol/article/view/57398/751375153847Copyright (c) 2022 Acta Scientiarum. Technologyhttp://creativecommons.org/licenses/by/4.0info:eu-repo/semantics/openAccessRutyna, Bruno BenatoPinto, Marcio Augusto VillelaNeundorf, Reverton Luis AntunesAnunciação, Marcio Alexandro MacielMartins, Marcio André2022-04-01T17:55:15Zoai:periodicos.uem.br/ojs:article/57398Revistahttps://www.periodicos.uem.br/ojs/index.php/ActaSciTechnol/indexPUBhttps://www.periodicos.uem.br/ojs/index.php/ActaSciTechnol/oai||actatech@uem.br1807-86641806-2563opendoar:2022-04-01T17:55:15Acta scientiarum. Technology (Online) - Universidade Estadual de Maringá (UEM)false |
dc.title.none.fl_str_mv |
Measuring the effectiveness of extrapolation techniques associated with the multigrid method applied to the Navier-Stokes equations Measuring the effectiveness of extrapolation techniques associated with the multigrid method applied to the Navier-Stokes equations |
title |
Measuring the effectiveness of extrapolation techniques associated with the multigrid method applied to the Navier-Stokes equations |
spellingShingle |
Measuring the effectiveness of extrapolation techniques associated with the multigrid method applied to the Navier-Stokes equations Rutyna, Bruno Benato Finite volume method; projection method; convergence acceleration; topological Epsilon. Finite volume method; projection method; convergence acceleration; topological Epsilon. |
title_short |
Measuring the effectiveness of extrapolation techniques associated with the multigrid method applied to the Navier-Stokes equations |
title_full |
Measuring the effectiveness of extrapolation techniques associated with the multigrid method applied to the Navier-Stokes equations |
title_fullStr |
Measuring the effectiveness of extrapolation techniques associated with the multigrid method applied to the Navier-Stokes equations |
title_full_unstemmed |
Measuring the effectiveness of extrapolation techniques associated with the multigrid method applied to the Navier-Stokes equations |
title_sort |
Measuring the effectiveness of extrapolation techniques associated with the multigrid method applied to the Navier-Stokes equations |
author |
Rutyna, Bruno Benato |
author_facet |
Rutyna, Bruno Benato Pinto, Marcio Augusto Villela Neundorf, Reverton Luis Antunes Anunciação, Marcio Alexandro Maciel Martins, Marcio André |
author_role |
author |
author2 |
Pinto, Marcio Augusto Villela Neundorf, Reverton Luis Antunes Anunciação, Marcio Alexandro Maciel Martins, Marcio André |
author2_role |
author author author author |
dc.contributor.author.fl_str_mv |
Rutyna, Bruno Benato Pinto, Marcio Augusto Villela Neundorf, Reverton Luis Antunes Anunciação, Marcio Alexandro Maciel Martins, Marcio André |
dc.subject.por.fl_str_mv |
Finite volume method; projection method; convergence acceleration; topological Epsilon. Finite volume method; projection method; convergence acceleration; topological Epsilon. |
topic |
Finite volume method; projection method; convergence acceleration; topological Epsilon. Finite volume method; projection method; convergence acceleration; topological Epsilon. |
description |
In this work, we applied different extrapolation techniques in association with the multigrid method to discover which one is the most effective in reducing the iteration error and the processing time (CPU time), as well as in improving the convergence factors. The mathematical model studied refers to the two-dimensional laminar flow of an isothermal time-dependent incompressible fluid modeled by the Navier-Stokes equations, with , solved iteratively with the projection method and the Finite Volume Method. The extrapolation methods used were: Aitken, Empiric, Mitin, scalar Epsilon, scalar Rho, topological Epsilon, and topological Rho. A two-step application was performed: first, extrapolators methods were applied individually after the use of the multigrid method. Then, the best-performing extrapolation techniques were used in the second step, where they were applied between the cycles of the multigrid method. The methods that presented the best convergence properties in the first stage were topological and scalar Epsilon. In the second stage, both methods maintained their performance, however, the topological Epsilon method presented more significant convergence rates than the scalar Epsilon. The other parameters analyzed were: the storage memory peak, the dimensionless norm of the residual based on the initial estimate, and the error norms of iteration. Thus, it was possible to state which extrapolation technique performed best and to compare it with the multigrid method with no extrapolation, which in this study was the topological Epsilon method. |
publishDate |
2022 |
dc.date.none.fl_str_mv |
2022-03-11 |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://www.periodicos.uem.br/ojs/index.php/ActaSciTechnol/article/view/57398 10.4025/actascitechnol.v44i1.57398 |
url |
http://www.periodicos.uem.br/ojs/index.php/ActaSciTechnol/article/view/57398 |
identifier_str_mv |
10.4025/actascitechnol.v44i1.57398 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
http://www.periodicos.uem.br/ojs/index.php/ActaSciTechnol/article/view/57398/751375153847 |
dc.rights.driver.fl_str_mv |
Copyright (c) 2022 Acta Scientiarum. Technology http://creativecommons.org/licenses/by/4.0 info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
Copyright (c) 2022 Acta Scientiarum. Technology 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 |
Universidade Estadual De Maringá |
publisher.none.fl_str_mv |
Universidade Estadual De Maringá |
dc.source.none.fl_str_mv |
Acta Scientiarum. Technology; Vol 44 (2022): Publicação contínua; e57398 Acta Scientiarum. Technology; v. 44 (2022): Publicação contínua; e57398 1806-2563 1807-8664 reponame:Acta scientiarum. Technology (Online) instname:Universidade Estadual de Maringá (UEM) instacron:UEM |
instname_str |
Universidade Estadual de Maringá (UEM) |
instacron_str |
UEM |
institution |
UEM |
reponame_str |
Acta scientiarum. Technology (Online) |
collection |
Acta scientiarum. Technology (Online) |
repository.name.fl_str_mv |
Acta scientiarum. Technology (Online) - Universidade Estadual de Maringá (UEM) |
repository.mail.fl_str_mv |
||actatech@uem.br |
_version_ |
1799315337579069440 |