Three-Dimensional Flow Stability Analysis Based on the Matrix-Forming Approach Made Affordable
Autor(a) principal: | |
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Data de Publicação: | 2017 |
Outros Autores: | |
Tipo de documento: | Artigo de conferência |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1007/978-3-319-65870-4_46 http://hdl.handle.net/11449/170385 |
Resumo: | Theoretical developments for hydrodynamic instability analysis are often based on eigenvalue problems, the size of which depends on the dimensionality of the reference state (or base flow) and the number of coupled equations governing the fluid motion. The straightforward numerical approach consisting on spatial discretization of the linear operators, and numerical solution of the resulting matrix eigenvalue problem, can be applied today without restrictions to one-dimensional base flows. The most efficient implementations for one-dimensional problems feature spectral collocation discretizations which produce dense matrices. However, this combination of theoretical approach and numerics becomes computationally prohibitive when two-dimensional and three-dimensional flows are considered. This paper proposes a new methodology based on an optimized combination of high-order finite differences and sparse algebra, that leads to a substantial reduction of the computational cost. As a result, three-dimensional eigenvalue problems can be solved in a local workstation, while other related theoretical methods based on the WKB expansion, like global-oscillator instability or the Parabolized Stability Equations, can be extended to three-dimensional base flows and solved using a personal computer. |
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Three-Dimensional Flow Stability Analysis Based on the Matrix-Forming Approach Made AffordableTheoretical developments for hydrodynamic instability analysis are often based on eigenvalue problems, the size of which depends on the dimensionality of the reference state (or base flow) and the number of coupled equations governing the fluid motion. The straightforward numerical approach consisting on spatial discretization of the linear operators, and numerical solution of the resulting matrix eigenvalue problem, can be applied today without restrictions to one-dimensional base flows. The most efficient implementations for one-dimensional problems feature spectral collocation discretizations which produce dense matrices. However, this combination of theoretical approach and numerics becomes computationally prohibitive when two-dimensional and three-dimensional flows are considered. This paper proposes a new methodology based on an optimized combination of high-order finite differences and sparse algebra, that leads to a substantial reduction of the computational cost. As a result, three-dimensional eigenvalue problems can be solved in a local workstation, while other related theoretical methods based on the WKB expansion, like global-oscillator instability or the Parabolized Stability Equations, can be extended to three-dimensional base flows and solved using a personal computer.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Department of Mechanical Engineering Universidade Federal FluminensePontifical Catholic University of Rio de JaneiroSão Paulo State University (UNESP) Campus of São João da Boa VistaSão Paulo State University (UNESP) Campus of São João da Boa VistaFAPESP: 2014/24782-0FAPESP: 2017/01586-0Universidade Federal Fluminense (UFF)Pontifical Catholic University of Rio de JaneiroUniversidade Estadual Paulista (Unesp)Rodríguez, DanielGennaro, Elmer M. [UNESP]2018-12-11T16:50:35Z2018-12-11T16:50:35Z2017-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/conferenceObject639-650http://dx.doi.org/10.1007/978-3-319-65870-4_46Lecture Notes in Computational Science and Engineering, v. 119, p. 639-650.1439-7358http://hdl.handle.net/11449/17038510.1007/978-3-319-65870-4_462-s2.0-85034265605Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengLecture Notes in Computational Science and Engineering0,357info:eu-repo/semantics/openAccess2021-10-23T15:48:52Zoai:repositorio.unesp.br:11449/170385Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462021-10-23T15:48:52Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Three-Dimensional Flow Stability Analysis Based on the Matrix-Forming Approach Made Affordable |
title |
Three-Dimensional Flow Stability Analysis Based on the Matrix-Forming Approach Made Affordable |
spellingShingle |
Three-Dimensional Flow Stability Analysis Based on the Matrix-Forming Approach Made Affordable Rodríguez, Daniel |
title_short |
Three-Dimensional Flow Stability Analysis Based on the Matrix-Forming Approach Made Affordable |
title_full |
Three-Dimensional Flow Stability Analysis Based on the Matrix-Forming Approach Made Affordable |
title_fullStr |
Three-Dimensional Flow Stability Analysis Based on the Matrix-Forming Approach Made Affordable |
title_full_unstemmed |
Three-Dimensional Flow Stability Analysis Based on the Matrix-Forming Approach Made Affordable |
title_sort |
Three-Dimensional Flow Stability Analysis Based on the Matrix-Forming Approach Made Affordable |
author |
Rodríguez, Daniel |
author_facet |
Rodríguez, Daniel Gennaro, Elmer M. [UNESP] |
author_role |
author |
author2 |
Gennaro, Elmer M. [UNESP] |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Universidade Federal Fluminense (UFF) Pontifical Catholic University of Rio de Janeiro Universidade Estadual Paulista (Unesp) |
dc.contributor.author.fl_str_mv |
Rodríguez, Daniel Gennaro, Elmer M. [UNESP] |
description |
Theoretical developments for hydrodynamic instability analysis are often based on eigenvalue problems, the size of which depends on the dimensionality of the reference state (or base flow) and the number of coupled equations governing the fluid motion. The straightforward numerical approach consisting on spatial discretization of the linear operators, and numerical solution of the resulting matrix eigenvalue problem, can be applied today without restrictions to one-dimensional base flows. The most efficient implementations for one-dimensional problems feature spectral collocation discretizations which produce dense matrices. However, this combination of theoretical approach and numerics becomes computationally prohibitive when two-dimensional and three-dimensional flows are considered. This paper proposes a new methodology based on an optimized combination of high-order finite differences and sparse algebra, that leads to a substantial reduction of the computational cost. As a result, three-dimensional eigenvalue problems can be solved in a local workstation, while other related theoretical methods based on the WKB expansion, like global-oscillator instability or the Parabolized Stability Equations, can be extended to three-dimensional base flows and solved using a personal computer. |
publishDate |
2017 |
dc.date.none.fl_str_mv |
2017-01-01 2018-12-11T16:50:35Z 2018-12-11T16:50:35Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/conferenceObject |
format |
conferenceObject |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://dx.doi.org/10.1007/978-3-319-65870-4_46 Lecture Notes in Computational Science and Engineering, v. 119, p. 639-650. 1439-7358 http://hdl.handle.net/11449/170385 10.1007/978-3-319-65870-4_46 2-s2.0-85034265605 |
url |
http://dx.doi.org/10.1007/978-3-319-65870-4_46 http://hdl.handle.net/11449/170385 |
identifier_str_mv |
Lecture Notes in Computational Science and Engineering, v. 119, p. 639-650. 1439-7358 10.1007/978-3-319-65870-4_46 2-s2.0-85034265605 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Lecture Notes in Computational Science and Engineering 0,357 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
639-650 |
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 |
|
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1799965323672158208 |