Multilevel model for flood wave propagation in flood-affected areas

A hyperbolic model for the simulation of flood wave propagation on initially dry land is presented. The convective inertia terms are neglected in the momentum equations. This assumption allows the use of a finite element scheme with linear shape functions for the free surface elevations and constant unit discharges inside each element. An appropriate use of the explicit and implicit approximation of the spatial derivatives is able to avoid the introduction of internal boundaries in the case of vertical discontinuities of the terrain elevation. This is obtained without losing the desirable features of the system matrix or limiting the maximum Courant number. The efficiency and the reliability of the proposed method are investigated for a flood in the south of Sicily, Italy, where a detailed description of the ground morphology has been proved to be essential for obtaining a good match between measured and computed maximum water depths.