Modeling of wetting–drying transitions in free surface flows over complex topographies

Numerical techniques development for the modeling and simulation of free surface flows has generated great interests over the last decades. In hydraulic engineering, the objectives include the predictions of dam break waves' propagation, fluvial floods and other catastrophic flooding phenomenon, the modeling of estuarine and coastal circulations, and the design and optimization of hydraulic structures. Most of the flooding events involve wetting and drying lands which are critical for the numerical modeling, especially when dealing with complex topographies. Extreme slopes and abrupt changes in irregular geometries, have often led to significant numerical errors and stability difficulties, and these are more critical for propagations over complex dry beds. This paper presents a simple and efficient numerical model for the wetting and drying effects over complex bathymetries. An overview of the key methods that have been suggested since the pioneering studies is first presented. A 2-D cell-centered finite-volume scheme is then proposed for solving the shallow-water equations using both structured and unstructured fixed meshes. Steady state C-property and global mass conservation properties are satisfied using appropriate numerical fluxes and wet/dry interfaces treatments. The resulting numerical model proved stable and robust and was validated through some benchmarks tests, including comparisons with exact solutions and experimental data, and a real case of wetting–drying simulation in a portion of the river “Rivière des Prairies” in a suburb of Laval, Quebec.