A fast second-order shallow water scheme on two-dimensional structured grids over abrupt topography

Abstract

This paper presents a finite volume scheme on structured grids to simulate shallow flows over complex terrain. The situation of shallow downhill flow over a step is particularly challenging for most shallow water schemes. We study this situation in detail and devise a novel second-order reconstruction strategy, which gives superior results over former hydrostatic reconstruction (HR) schemes. The reconstruction step is based on a recent first-order hydrostatic reconstruction HR method, which improves shallow flows over steps. The proposed second-order scheme is well-balanced, positivity-preserving, and handles dry cells. When compared with the original HR, we lower the computational burden by using a simplified quadrature for the bed slope source term. We test the scheme on various benchmark setups to assess accuracy and robustness, where the method produces comparable results to other HR-based schemes in most cases and superior results in the case of shallow downhill flow over steps. The novel second-order scheme is capable of simulating large-scale real-world flood scenarios fast and accurately.