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The one-dimensional gravity wave model (GWM) is the result of ignoring the convection term in the Saint-Venant Equations (SVEs), and has the characteristics of fast numerical calculation and low stability requirements. To study its performances and limitations in 1D dam-break flood, this paper verifies the model using a dam-break experiment. The experiment was carried out in a large-scale flume with depth ratios (initial downstream water depth divided by upstream water depth) divided into 0 and 0.1~0.4. The data were collected by image processing technology, and the hydraulic parameters, such as water depth, flow discharge, and wave velocity, were selected for comparison. The experimental results show that the 1D GWM performs an area with constant hydraulic parameters, which is quite different from the experimental results in the dry downstream case. For a depth ratio of 0.1, the second weak discontinuity point, which is connected to the steady zone in the 1D GWM, moves upstream, which is contrary to the experimental situation. For depth ratios of 0.2~0.4, the moving velocity of the second weak discontinuity point is faster than the experimental value, while the velocity of the shock wave is slower. However, as the water depth ratio increases, the hydraulic parameters calculated by 1D GWM in the steady zone gradually approach the experimental value.

Saint-Venant Equations (SVE) are often simplified for the sake of practicality, faster computational times, or physical representation. The Gravity Wave Model (GWM), or Local Inertial Equations, is a simplification of the SVE whereby the convective terms are neglected. The aim of this work is to present an analytical solution for the dam-break problem based on the GWM set of equations without source terms using the method of characteristics (MOC) and compare it with the analytical solution of SVE. The formulas for the depth and velocity are derived and explained along with the wave propagation characteristics. Conclusions are drawn about the propagation and analytical solution. [ABSTRACT FROM AUTHOR]

In this paper a finite volume method with an unstructured node based grid is developed in order to integrate the local inertial equations for flood modelling: the Gravity Wave Model (GWM). The GWM is based on the Shallow Water Equation (SWE) but neglects the convective term for improving the model computational speed. The numerical integration of the GWM equations is made using a first order in time and space well-balanced Roe Riemann Solver derived for the GWM set of equations. Several well-known SWE and urban flood model benchmark tests are used to verify the applicability of the GWM model. In addition analytical and numerical solutions of the SWE are also compared to the GWM. The results show a good agreement between the GWM and the SWE in all tested cases. [ABSTRACT FROM AUTHOR]

The one-dimensional gravity wave model (GWM) is the result of ignoring the convection term in the Saint-Venant Equations (SVEs), and has the characteristics of fast numerical calculation and low stability requirements. To study its performances and limitations in 1D dam-break flood, this paper verifies the model using a dam-break experiment. The experiment was carried out in a large-scale flume with depth ratios (initial downstream water depth divided by upstream water depth) divided into 0 and 0.1~0.4. The data were collected by image processing technology, and the hydraulic parameters, such as water depth, flow discharge, and wave velocity, were selected for comparison. The experimental results show that the 1D GWM performs an area with constant hydraulic parameters, which is quite different from the experimental results in the dry downstream case. For a depth ratio of 0.1, the second weak discontinuity point, which is connected to the steady zone in the 1D GWM, moves upstream, which is contrary to the experimental situation. For depth ratios of 0.2~0.4, the moving velocity of the second weak discontinuity point is faster than the experimental value, while the velocity of the shock wave is slower. However, as the water depth ratio increases, the hydraulic parameters calculated by 1D GWM in the steady zone gradually approach the experimental value. [ABSTRACT FROM AUTHOR]