Final Document on the Third Year, First Activity : 'Numerical Techniques for Preventing Computational Instability Problems to Simulate Floods Due to Low-Intensity Rainfall'

The purpose of the collaboration between LAMPIT (Department of Soil Defence, University of Calabria) and CMCC is to develop an hydrometeorological chain in order to obtain a reliable tool in the context of flood evolution prediction able to provide quantitative information of practical importance within the civil protection activities. The LAMPIT contribution to the project concerns the mathematical description of both the generation and propagation of flood events at basin scale. The work here presented has been carried out in close cooperation with CIRA researchers (Dr. Pasquale Schiano and Dr. Paola Mercogliano). The evaluation in time and magnitude of the overland flow phenomena caused by rainfall is very important in a variety of environmental and hydraulics situations. The mathematical representation of the flow processes is based on the fully dynamic shallow water equations. The solution of these equations, excluding some simplified cases, can be obtained by numerical integration only. Many schemes based on fully dynamic and simplified shallow water equations have been proposed in literature. Some of these schemes are implemented in the LAMPIT laboratory and applied to simulate simple cases of overland flow as already presented. Afterwards the implemented codes have been applied to simulate overland flow over real topography. In this contest some numerical anomalies appear due to the presence of small water depth over high slope and irregular topography. In this work a careful analysis of these problems has been made and some numerical techniques have been implemented in order to prevent them. The work has been organized as follows: -Numerical schemes and techniques -Applications -Numerical techniques for preventing computational instability problems