Two-dimensional Boussinesq equations applied to channel flows: deducing and applying the equations

Detalhes bibliográficos
Autor(a) principal: Fabiani,André Luiz Tonso
Data de Publicação: 2019
Outros Autores: Ota,José Junji
Tipo de documento: Artigo
Idioma: eng
Título da fonte: RBRH (Online)
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2318-03312019000100220
Resumo: ABSTRACT A basic hypothesis adopted for theoretical formulation of fluid flows is the hydrostatic pressure distribution. However, many researchers have pointed out that this simplification can lead to errors, in cases such as dam break flow. Discrepancy between computational solution and the experiment is attributed to the pressure distribution. These findings are not new, but it is not presented any formulation in the literature that considers the non-hydrostatic pressure distribution in 2D flow. This article deduces the Boussinesq Equations as an evolution of the Shallow Water Equations with the hypothesis of non-hydrostatic pressure distribution in the vertical direction. XYZ Orthogonal Cartesian System is used, considering the influence of channel bed slope and head losses of flow. It is presented the non-hydrostatical correction in the Boussinesq equation in two dimension using Fourier series. The solution uses Runge-Kutta Discontinuous Galerkin Method and the formulation is applied to a cylindrical dam-break.
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spelling Two-dimensional Boussinesq equations applied to channel flows: deducing and applying the equationsBoussinesq equationsChannel flowMathematical modelingNon-hydrostatic pressure distributionTwo-dimensional modelABSTRACT A basic hypothesis adopted for theoretical formulation of fluid flows is the hydrostatic pressure distribution. However, many researchers have pointed out that this simplification can lead to errors, in cases such as dam break flow. Discrepancy between computational solution and the experiment is attributed to the pressure distribution. These findings are not new, but it is not presented any formulation in the literature that considers the non-hydrostatic pressure distribution in 2D flow. This article deduces the Boussinesq Equations as an evolution of the Shallow Water Equations with the hypothesis of non-hydrostatic pressure distribution in the vertical direction. XYZ Orthogonal Cartesian System is used, considering the influence of channel bed slope and head losses of flow. It is presented the non-hydrostatical correction in the Boussinesq equation in two dimension using Fourier series. The solution uses Runge-Kutta Discontinuous Galerkin Method and the formulation is applied to a cylindrical dam-break.Associação Brasileira de Recursos Hídricos2019-01-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S2318-03312019000100220RBRH v.24 2019reponame:RBRH (Online)instname:Associação Brasileira de Recursos Hídricos (ABRH)instacron:ABRH10.1590/2318-0331.241920180159info:eu-repo/semantics/openAccessFabiani,André Luiz TonsoOta,José Junjieng2019-04-22T00:00:00Zoai:scielo:S2318-03312019000100220Revistahttps://www.scielo.br/j/rbrh/https://old.scielo.br/oai/scielo-oai.php||rbrh@abrh.org.br2318-03311414-381Xopendoar:2019-04-22T00:00RBRH (Online) - Associação Brasileira de Recursos Hídricos (ABRH)false
dc.title.none.fl_str_mv Two-dimensional Boussinesq equations applied to channel flows: deducing and applying the equations
title Two-dimensional Boussinesq equations applied to channel flows: deducing and applying the equations
spellingShingle Two-dimensional Boussinesq equations applied to channel flows: deducing and applying the equations
Fabiani,André Luiz Tonso
Boussinesq equations
Channel flow
Mathematical modeling
Non-hydrostatic pressure distribution
Two-dimensional model
title_short Two-dimensional Boussinesq equations applied to channel flows: deducing and applying the equations
title_full Two-dimensional Boussinesq equations applied to channel flows: deducing and applying the equations
title_fullStr Two-dimensional Boussinesq equations applied to channel flows: deducing and applying the equations
title_full_unstemmed Two-dimensional Boussinesq equations applied to channel flows: deducing and applying the equations
title_sort Two-dimensional Boussinesq equations applied to channel flows: deducing and applying the equations
author Fabiani,André Luiz Tonso
author_facet Fabiani,André Luiz Tonso
Ota,José Junji
author_role author
author2 Ota,José Junji
author2_role author
dc.contributor.author.fl_str_mv Fabiani,André Luiz Tonso
Ota,José Junji
dc.subject.por.fl_str_mv Boussinesq equations
Channel flow
Mathematical modeling
Non-hydrostatic pressure distribution
Two-dimensional model
topic Boussinesq equations
Channel flow
Mathematical modeling
Non-hydrostatic pressure distribution
Two-dimensional model
description ABSTRACT A basic hypothesis adopted for theoretical formulation of fluid flows is the hydrostatic pressure distribution. However, many researchers have pointed out that this simplification can lead to errors, in cases such as dam break flow. Discrepancy between computational solution and the experiment is attributed to the pressure distribution. These findings are not new, but it is not presented any formulation in the literature that considers the non-hydrostatic pressure distribution in 2D flow. This article deduces the Boussinesq Equations as an evolution of the Shallow Water Equations with the hypothesis of non-hydrostatic pressure distribution in the vertical direction. XYZ Orthogonal Cartesian System is used, considering the influence of channel bed slope and head losses of flow. It is presented the non-hydrostatical correction in the Boussinesq equation in two dimension using Fourier series. The solution uses Runge-Kutta Discontinuous Galerkin Method and the formulation is applied to a cylindrical dam-break.
publishDate 2019
dc.date.none.fl_str_mv 2019-01-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2318-03312019000100220
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2318-03312019000100220
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/2318-0331.241920180159
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
dc.publisher.none.fl_str_mv Associação Brasileira de Recursos Hídricos
publisher.none.fl_str_mv Associação Brasileira de Recursos Hídricos
dc.source.none.fl_str_mv RBRH v.24 2019
reponame:RBRH (Online)
instname:Associação Brasileira de Recursos Hídricos (ABRH)
instacron:ABRH
instname_str Associação Brasileira de Recursos Hídricos (ABRH)
instacron_str ABRH
institution ABRH
reponame_str RBRH (Online)
collection RBRH (Online)
repository.name.fl_str_mv RBRH (Online) - Associação Brasileira de Recursos Hídricos (ABRH)
repository.mail.fl_str_mv ||rbrh@abrh.org.br
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