Numerical Simulations of Water Wave Propagation and Flooding

Abstract

In this paper we present main points in the process of application of numerical schemes for hyperbolic balance laws to water wave propagation and flooding. The appropriate mathematical models are the one-dimensional open channel flow equations and the two-dimensional shallow water equations. Therefore good simulation results can only be obtained with well-balanced numerical schemes such as the ones developed by Bermudez and Vazquez, Hubbard and Garcia-Navarro, LeVeque, etc. as well as the ones developed by the authors of this paper. We also propose a modification of the well-balanced Q-scheme for the two-dimensional shallow water equations that solves the wetting and drying problem. Finally, we present numerical results for three simulation tasks: the CADAM dam break experiment, the water wave propagation in the Toce river, and the catastrophic dam break on the Malpasset river.