Abstract
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.
Highlights
The study of non-steady flow in channels is very important, considering the possible effects of floods or transient waves on population downstream
This work presents the deduction of these simplified forms, called 2D Boussinesq Equations, an evolution from the Shallow Water Equations, and the non-hydrostatic pressure distribution is focused upon
The results presented were obtained by limiting the maximum variation at 10% - at each point and at each time step - of the original variation by the conventional Shallow Water Equations at the same instant
Summary
The study of non-steady flow in channels is very important, considering the possible effects of floods or transient waves on population downstream. This work presents the deduction of these simplified forms, called 2D Boussinesq Equations, an evolution from the Shallow Water Equations, and the non-hydrostatic pressure distribution is focused upon.
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