Modeling Rapid Flood Propagation over Natural Terrains using a Well-Balanced Scheme

The consequences of rapid and extreme flooding events, such as tsunamis, riverine flooding, and dam breaks show the necessity of developing efficient and accurate tools for studying these flow fields and devising appropriate mitigation plans for threatened sites. Two-dimensional simulations of these flows can provide information about the temporal evolution of water depth and velocities, but the accurate prediction of the arrival time of floods and the extent of inundated areas still poses a significant challenge for numerical models of rapid flows over rough and variable topographies. Careful numerical treatments are required to reproduce the sudden changes in velocities and water depths, evolving under strong nonlinear conditions that often lead to breaking waves or bores. In addition, new controlled experiments of flood propagation in complex geometries are also needed to provide data for testing the models and evaluating their performance in more realistic conditions. This work implements a robust, well-balanced numerical model to solve the nonlinear shallow water equations (NSWEs) in a nonorthogonal boundary fitted curvilinear coordinate system. It is shown that the model is capable of computing flows over highly variable topographies, preserving the positivity of the water depth, and providing accurate predictions for the wetting and drying processes. The model is validated against benchmark cases that consider the use of boundary fitted discretizations of the computational domain. In addition, a laboratory experiment is performed of a rapid flood over a complex topography, measuring the propagation of a dam break wave on a scaled physical model, registering time series of water depth in 19 cross sections along the flow direction. The data from this experiment are used to test the numerical model, and compare the performance of the current model with the numerical results of two other recognized NSWE models, showing that the current model is a reliable tool for efficiently and accurately predicting extreme inundation events and long-wave propagation over complex topographies.