Performances and limitations of the diffusive approximation of the 2-d shallow water equations for flood simulation in urban and rural areas

The Shallow Water Equations (SWE) are a time-dependent system of non-linear partial differential equations of hyperbolic type. Flood propagation in rivers and in the neighbouring areas is a typical example for which the use of the SWE is required. The numerical integration of the SWE needs complicated schemes that still require a significant computational effort. This fact has maintained interest in techniques that can approximate simulations from full two-dimensional (2-D) shallow water models with less computation heaviness. In particular, an approximation of the full SWE consists in neglecting the inertial terms, leading to a degradation of the original hyperbolic model to a parabolic one. This approximation is traditionally justified by the fact that flooding over plain areas is characterized by a slow evolution. Although there are important papers on model benchmarking and comparative analysis of flood propagation models, detailed analyses of effective ability and limitations of simplified models in reproducing floods processes are still rare, especially for urban environments. Therefore, this paper aims at providing a contribution to the model benchmarking and to the influence induced by the application of simplified models on the numerical simulations of flood events, overcoming some limitations that characterize part of the studies in the literature. In particular, on the one hand, more complicated experimental tests will be considered and, on the other hand, the same numerical grid for every model considered herein will be used in order to remove its effect from the numerical results. The simulations discussed here seem to suggest that the use of diffusive-type models is questionable, especially in urban districts, due to the poor predictions of the events that might be simulated around the buildings. Conversely, the application of the shallow water model gave excellent results in all the situations considered in this paper and, therefore, its use is recommended to obtained reliable estimations of flood hazard.