FLOOD MODELLING IN URBAN AREAS: LIMITATIONS OF THE DIFFUSIVE APPROXIMATION OF THE 2-D SHALLOW WATER EQUATIONS

It is generally accepted that the flood propagation in rivers and in the neighbouring areas can be described by the shallow water equations (SWE). While the efficacy of the SWE approach has been discussed several times, its numerical integration needs complicated schemes that still require a significant computational effort. This fact maintained interest in techniques that can approximate the solutions provided by the twodimensional shallow water models with fewer computations. Recent examples include porosity-based methods for representing sub-grid scale features in coarse resolution models, models that consider inertia and diffusion but ignore advection, diffusive models. 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. In the literature, there are several studies related to the application of 2-D numerical models based on the diffusive wave equations (i.e. Prestininzi, 2008; Dottori and Todini, 2013), mainly referred to inundations due to slow-varying floods. Other studies have looked at benchmarking two-dimensional shallow water models (Horritt et al., 2007) focusing also on urban settings. Néelz and Pender (2010) benchmarked the majority of industry codes used for flood risk modelling in the UK in a number of numerical cases. Similarly, Neal et al. (2012) benchmarked three two-dimensional explicit hydraulic models, which can be broadly defined as simulating diffusive, inertial or shallow water waves using test cases for which results from industry models are also available. It is important to observe that the most complicated laboratory test used in the aforementioned studies, from a hydrodynamic point of view, is a dam break wave interacting with an isolated building. Indeed, more complicated experimental tests, available in the literature, have not been considered in the previous studies such as the urban flood experiment developed within the IMPACT project. In this paper, the attention will be focused on an experimental test in urban areas in order to evaluate the limitations of the diffusive model against a shallow water model considering the same computational grid. This latter aspect seems to be essential in models benchmarking sincedifferent meshes might lead to significant differences especially in terms of flood hydrographs, but also in terms of local water surfaces predictions (Kim et al. 2014).