Résumé
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 devise 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 the flood and the extent of the inundated areas still pose 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 evaluate their performance in more realistic conditions. In this work we implement a robust well-balanced numerical model to solve the nonlinear shallow water equations (NSWE) in a non-orthogonal boundary-fitted curvilinear coordinate system. We show that the model is capable of computing flows over highly variable topographies, preserving the positivity of the water depth, and providing accurate predictions for 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, we perform a laboratory experiment 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. We use the data from this experiment to test our numerical model, and compare our model performance with the numerical results of two other recognized NSWE models, showing that ours is a reliable tool for predicting efficiently and accurately extreme inundation eventsand long-wave propagation over complex topographies.