A fast second-order shallow water scheme on two-dimensional structured grids over abrupt topography. (May 2019)

• Record Type: Journal Article
• Authors: Buttinger-Kreuzhuber, Andreas; Horváth, Zsolt; Noelle, Sebastian; Blöschl, Günter; Waser, Jürgen
• Is Part Of: Advances in water resources. Volume 127(2019)
• Page Start: 89
• Page End: 108
• Publication Date: 2019-05
• Subjects: Shallow water -- Saint-Venant -- Slope source term -- Well-balanced scheme -- Second-order reconstruction; Hydrology -- Periodicals; Hydrodynamics -- Periodicals; Hydraulic engineering -- Periodicals; 551.48
• DOI: 10.1016/j.advwatres.2019.03.010
• Languages: English
• ISSNs: 0309-1708

Abstract

Highlights: An efficient two-dimensional finite volume scheme for the SWEs. The scheme is well-balanced, robust and second-order acccurate. A novel reconstruction yields superior results for shallow downhill flow over steps. Improved speed estimates at the wet-dry front by reconstructing velocity slopes. 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.