Improvement of an unstructured grid Finite Volume scheme for flood simulation

In this work a numerical model, designed to study the propagation of inundation waves over floodplains due to breach formations in river banks, is presented. The two-dimensional model is developed performing a space-time integration of the Shallow Water Equations with source terms due to bed slope and friction slope. The spatial domain is discretized using unstructured triangular grids, based on a Delaunay algorithm for 2D mesh generation. The numerical scheme is a Finite Volume Godunov-type method, based on classical approximate solutions of the Riemann problem. The second order space-time accuracy is achieved by the MUSCL and a SSPRK techniques, respectively. The model introduces successful recent novelties: a) in treating bed slope source terms (a Divergence Form for the Bed slope source term, Valiani and Begnudelli, 2006); b) in facing the wetting and drying sequence of partially submerged cells (Volume/Free surface Relationships, Begnudelli and Sanders, 2006). Such a numerical model is tested over significant test cases suggested in literature, and then applied to an hypothetical inundation of a floodplain area near Ferrara (Italy), due to a possible breach in the Po river bank. The numerical model is stable, accurate and - due to its flexibility - easily applicable to real world events. Consequently, it appears to be a proper tool for environmental planning and disaster prevention design