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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]