Flood wave dynamics using Lagrangian block advection

Flood wave dynamics simulations are determined by a robust and accurate Lagrangian block advection (LBA) scheme that can track the dry-and-wet interface and capture the shocks without using any slope limiter to control the numerical oscillations. Two series of challenging numerical problems are considered using the LBA. First, computations are carried out for water waves in a parabolic bowl. The wetting-and-drying interface on the surface of the bowl is tracked by the LBA method with absolute computational stability. The accuracy of the LBA method is verified by the convergent of the numerical solution to an exact solution. Finally, the LBA method is applied to carry out a series of flood wave simulations, which have closely reproduced the data obtained from the laboratory experiments.