Robust RRE technique for increasing the order of accuracy of SPH numerical solutions
Autor(a) principal: | |
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Data de Publicação: | 2022 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1016/j.matcom.2022.03.016 http://hdl.handle.net/11449/239895 |
Resumo: | This study presents the use of a post-processing technique called repeated Richardson extrapolation (RRE) to improve the accuracy of numerical solutions of local and global variables obtained using the smoothed particle hydrodynamics (SPH) method. The investigation focuses on both the steady and unsteady one-dimensional heat conduction problems with Dirichlet boundary conditions, but this technique is applicable to multidimensional and other mathematical models. By using all the variables of the real type and quadruple precision (extended precision or Real*16) we were able to, for example, reduce the discretization error from 1.67E−08 to 3.46E−33 with four extrapolations, limited only by the round-off error and, consequently, determining benchmark solutions for the variable of interest ψ(1/2) using the SPH method. The increase in CPU time and memory usage owing to post-processing was almost null. RRE has proven to be robust in determining up to a sixteenth order of accuracy in meshless discretization for the spatial domain. |
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Repositório Institucional da UNESP |
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Robust RRE technique for increasing the order of accuracy of SPH numerical solutionsDiscretization errorHeat diffusionSixteenth order of accuracySPH benchmark solutionsSPH with RRE highly accurate schemeVerificationThis study presents the use of a post-processing technique called repeated Richardson extrapolation (RRE) to improve the accuracy of numerical solutions of local and global variables obtained using the smoothed particle hydrodynamics (SPH) method. The investigation focuses on both the steady and unsteady one-dimensional heat conduction problems with Dirichlet boundary conditions, but this technique is applicable to multidimensional and other mathematical models. By using all the variables of the real type and quadruple precision (extended precision or Real*16) we were able to, for example, reduce the discretization error from 1.67E−08 to 3.46E−33 with four extrapolations, limited only by the round-off error and, consequently, determining benchmark solutions for the variable of interest ψ(1/2) using the SPH method. The increase in CPU time and memory usage owing to post-processing was almost null. RRE has proven to be robust in determining up to a sixteenth order of accuracy in meshless discretization for the spatial domain.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Graduate Program in Numerical Methods in Engineering (PPGMNE) Federal University of Paraná (UFPR), P.O. Box 19011Laboratory of Numerical Experimentation (LENA) Department of Mechanical Engineering (DEMEC) Federal University of Paraná (UFPR), P.O. Box 19040São Paulo State University (UNESP) Department of Mathematics and Computer Science (DMC)Graduate Program in Mechanical Engineering (PGMEC) Federal University of Paraná (UFPR), P.O. Box 19040São Paulo State University (UNESP) Department of Mathematics and Computer Science (DMC)Universidade Federal do Paraná (UFPR)Universidade Estadual Paulista (UNESP)Silva, L. P. daMarchi, C. H.Meneguette, M. [UNESP]Foltran, A. C.2023-03-01T19:52:13Z2023-03-01T19:52:13Z2022-09-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article231-252http://dx.doi.org/10.1016/j.matcom.2022.03.016Mathematics and Computers in Simulation, v. 199, p. 231-252.0378-4754http://hdl.handle.net/11449/23989510.1016/j.matcom.2022.03.0162-s2.0-85128335156Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengMathematics and Computers in Simulationinfo:eu-repo/semantics/openAccess2023-03-01T19:52:13Zoai:repositorio.unesp.br:11449/239895Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T19:17:18.064052Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Robust RRE technique for increasing the order of accuracy of SPH numerical solutions |
title |
Robust RRE technique for increasing the order of accuracy of SPH numerical solutions |
spellingShingle |
Robust RRE technique for increasing the order of accuracy of SPH numerical solutions Silva, L. P. da Discretization error Heat diffusion Sixteenth order of accuracy SPH benchmark solutions SPH with RRE highly accurate scheme Verification |
title_short |
Robust RRE technique for increasing the order of accuracy of SPH numerical solutions |
title_full |
Robust RRE technique for increasing the order of accuracy of SPH numerical solutions |
title_fullStr |
Robust RRE technique for increasing the order of accuracy of SPH numerical solutions |
title_full_unstemmed |
Robust RRE technique for increasing the order of accuracy of SPH numerical solutions |
title_sort |
Robust RRE technique for increasing the order of accuracy of SPH numerical solutions |
author |
Silva, L. P. da |
author_facet |
Silva, L. P. da Marchi, C. H. Meneguette, M. [UNESP] Foltran, A. C. |
author_role |
author |
author2 |
Marchi, C. H. Meneguette, M. [UNESP] Foltran, A. C. |
author2_role |
author author author |
dc.contributor.none.fl_str_mv |
Universidade Federal do Paraná (UFPR) Universidade Estadual Paulista (UNESP) |
dc.contributor.author.fl_str_mv |
Silva, L. P. da Marchi, C. H. Meneguette, M. [UNESP] Foltran, A. C. |
dc.subject.por.fl_str_mv |
Discretization error Heat diffusion Sixteenth order of accuracy SPH benchmark solutions SPH with RRE highly accurate scheme Verification |
topic |
Discretization error Heat diffusion Sixteenth order of accuracy SPH benchmark solutions SPH with RRE highly accurate scheme Verification |
description |
This study presents the use of a post-processing technique called repeated Richardson extrapolation (RRE) to improve the accuracy of numerical solutions of local and global variables obtained using the smoothed particle hydrodynamics (SPH) method. The investigation focuses on both the steady and unsteady one-dimensional heat conduction problems with Dirichlet boundary conditions, but this technique is applicable to multidimensional and other mathematical models. By using all the variables of the real type and quadruple precision (extended precision or Real*16) we were able to, for example, reduce the discretization error from 1.67E−08 to 3.46E−33 with four extrapolations, limited only by the round-off error and, consequently, determining benchmark solutions for the variable of interest ψ(1/2) using the SPH method. The increase in CPU time and memory usage owing to post-processing was almost null. RRE has proven to be robust in determining up to a sixteenth order of accuracy in meshless discretization for the spatial domain. |
publishDate |
2022 |
dc.date.none.fl_str_mv |
2022-09-01 2023-03-01T19:52:13Z 2023-03-01T19:52:13Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://dx.doi.org/10.1016/j.matcom.2022.03.016 Mathematics and Computers in Simulation, v. 199, p. 231-252. 0378-4754 http://hdl.handle.net/11449/239895 10.1016/j.matcom.2022.03.016 2-s2.0-85128335156 |
url |
http://dx.doi.org/10.1016/j.matcom.2022.03.016 http://hdl.handle.net/11449/239895 |
identifier_str_mv |
Mathematics and Computers in Simulation, v. 199, p. 231-252. 0378-4754 10.1016/j.matcom.2022.03.016 2-s2.0-85128335156 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Mathematics and Computers in Simulation |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
231-252 |
dc.source.none.fl_str_mv |
Scopus reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1808129047158325248 |