ABSTRACT
This chapter aims to introduce the basic background of shallow water flow models and robust numerical methods as well as to represent different examples of applications. After briefly explaining the main characteristics of shallow water flow problems and pointing out the specific numerical requirements to appropriately simulate those processes, one of the preferred methods in terms of a cell-centered Godunov-type finite-volume scheme in space and explicit time discretization is represented. Here, the HLLC Riemann solver is used to approximate the fluxes over the cell interfaces, and total variation diminishing (TVD) techniques in terms of slope limiter functions are applied to achieve second-order accuracy in space without generating spurious oscillations. The ability of the implemented methods to appropriately simulate different complex flow processes and the propagation of wet-dry fronts are proven with different benchmarks, in terms of a one-dimensional dam break, and a two-dimensional rainfall-runoff simulation. Finally, two real-case studies are represented. The first one includes the consideration of infiltration processes to consider runoff-generation processes in addition to the shallow water flow model. Flash floods in a wadi system in the Eastern Desert of Egypt are simulated under consideration of different scenarios regarding infiltration and mitigation measures. The second real-case study is a rainfall-runoff simulation in an alpine catchment in Austria, and besides an automated parameter calibration, an upscaling approach to reduce the computing time is represented. The latter one is crucial for the development of real-time simulations.
