Two-dimensional Boussinesq equations applied to channel flows: deducing and applying the equations
Autor(a) principal: | |
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Data de Publicação: | 2019 |
Outros Autores: | |
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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RBRH (Online) |
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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 |
_version_ |
1754734701891813376 |