Two-dimensional Boussinesq equations applied to channel flows: deducing and applying the equations
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 experim...
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| Format: | Article |
| Language: | English |
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Associação Brasileira de Recursos Hídricos
2019-04-01
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| Series: | Revista Brasileira de Recursos Hídricos |
| Subjects: | |
| Online Access: | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S2318-03312019000100220&tlng=en |
| _version_ | 1798014381205749760 |
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| author | André Luiz Tonso Fabiani José Junji Ota |
| author_facet | André Luiz Tonso Fabiani José Junji Ota |
| author_sort | André Luiz Tonso Fabiani |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-04-11T15:17:40Z |
| format | Article |
| id | doaj.art-f46e9fb69f1848079118fb76aae31830 |
| institution | Directory Open Access Journal |
| issn | 2318-0331 |
| language | English |
| last_indexed | 2024-04-11T15:17:40Z |
| publishDate | 2019-04-01 |
| publisher | Associação Brasileira de Recursos Hídricos |
| record_format | Article |
| series | Revista Brasileira de Recursos Hídricos |
| spelling | doaj.art-f46e9fb69f1848079118fb76aae318302022-12-22T04:16:27ZengAssociação Brasileira de Recursos HídricosRevista Brasileira de Recursos Hídricos2318-03312019-04-012410.1590/2318-0331.241920180159Two-dimensional Boussinesq equations applied to channel flows: deducing and applying the equationsAndré Luiz Tonso Fabianihttps://orcid.org/0000-0001-6860-7595José Junji OtaABSTRACT 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.http://www.scielo.br/scielo.php?script=sci_arttext&pid=S2318-03312019000100220&tlng=enBoussinesq equationsChannel flowMathematical modelingNon-hydrostatic pressure distributionTwo-dimensional model |
| spellingShingle | André Luiz Tonso Fabiani José Junji Ota Two-dimensional Boussinesq equations applied to channel flows: deducing and applying the equations Revista Brasileira de Recursos Hídricos Boussinesq equations Channel flow Mathematical modeling Non-hydrostatic pressure distribution Two-dimensional model |
| title | 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_short | 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 |
| topic | Boussinesq equations Channel flow Mathematical modeling Non-hydrostatic pressure distribution Two-dimensional model |
| url | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S2318-03312019000100220&tlng=en |
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