Two-dimensional numerical models for overland flow simulations

Overland flow simulations are quite often carried out using simplified models based on the kinematic or diffusive approximation because the convective inertial terms included in the complete shallow water equations may be significantly lower than the values of the surface slope in those situations in which a strong topographic gradient occurs. At the present time, there is a tendency to develop more and more accurate models to manage the risk associated with potential extreme meteorological events at basin scale especially in the context of the prediction of the climate changes consequences. In order to obtain a reliable tool of analysis it is necessary to couple a meteorological model with an hydrodynamic model, both at high resolution, defining the components of a hydro-meteorological chain. From an hydraulic point of view, a high spatial resolution computation of the flood temporal evolution needs the use of an accurate numerical model able to simulate local hydraulic phenomenon such as backwater effects or hydraulic jumps. In this context, the 2D fully dynamic shallow water equations seems to be the required approach to deal with that situation because it allows to analyse in deep the flow behaviour in locally complex topography. The purpose of this paper is to analyse the performances of 2D numerical models based on the fully dynamic shallow water equations as well as on the kinematic and diffusive approximations. From a numerical point of view the systems have been solved by using both the MacCormack second order central scheme and HLL first order upwind scheme. The numerical results highlighted that the differences among the simulations are not very important when the simulations refer to commonly used ideal literature tests in which the topography is quite simplified while significant differences have been observed when the topography is more similar to the real situations.