Two-dimensional Boussinesq equations applied to channel flows: deducing and applying the equations
TLDR
In this article, a non-hydrostatical correction in the Boussinesq equation in two dimension using Fourier series is presented, considering the influence of channel bed slope and head losses of flow.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.read more
Citations
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Book ChapterDOI
Boundary Layer Theory
TL;DR: The boundary layer equations for plane, incompressible, and steady flow are described in this paper, where the boundary layer equation for plane incompressibility is defined in terms of boundary layers.
Journal ArticleDOI
New formulation of the two-dimensional steep-slope shallow water equations. Part I: Theory and analysis
TL;DR: In this paper , a new formulation of the 2D depth-averaged shallow water equations on steep bottom slopes is presented, in which water depth is defined along the vertical direction and flow velocity is assumed parallel to the bottom surface.
Estudo da equação de Boussinesq em duas dimensões horizontais
TL;DR: In this paper, the Boussinesq equations were applied to two-dimensional rupture flows of a cylindrical dam with two downstream flow conditions and to a supercritical flow in a contraction.
References
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Book ChapterDOI
Boundary Layer Theory
TL;DR: The boundary layer equations for plane, incompressible, and steady flow are described in this paper, where the boundary layer equation for plane incompressibility is defined in terms of boundary layers.
Review Article Runge-Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Bernardo Cockburn,Chi-Wang Shu +1 more
TL;DR: The theoretical and algorithmic aspects of the Runge–Kutta discontinuous Galerkin methods are reviewed and several applications including nonlinear conservation laws, the compressible and incompressible Navier–Stokes equations, and Hamilton–Jacobi-like equations are shown.
Book
Introduction to continuum mechanics
TL;DR: This new edition offers expanded coverage of the subject matter both in terms of details and contents, providing greater flexibility for either a one or two-semester course in either continuum mechanics or elasticity, and contains expanded and improved problem sets providing both intellectual challenges and engineering applications.
Book
Runge-Kutta discontinuous Galerkin methods for convection-dominated problems
Bernardo Cockburn,Chi-Wang Shu +1 more
TL;DR: The Runge-Kutta discontinuous Galerkin (RKDG) method as discussed by the authors is one of the state-of-the-art methods for non-linear convection-dominated problems.
Book
Shock-Capturing Methods for Free-Surface Shallow Flows
TL;DR: In this article, the Shallow Water Equations are expressed as linearised shallow water equations, and the Riemann solver is used to solve the problem of Dam-Break Modelling.
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