@article{PB-VRVis-2019-009,
author = {Buttinger-Kreuzhuber, Andreas and Horvath, Zsolt and Noelle, Sebastian and Bl{\"o}schl, G{\"u}nter and Waser, J{\"u}rgen},
title = {A fast second-order shallow water scheme on two-dimensional
  structured grids over abrupt topography},
year = {2019},
journaltitle = {Advances in Water Resources},
doi = {10.1016/j.advwatres.2019.03.010},
url = {https://www.vrvis.at/publications/PB-VRVis-2019-009},
issn = {0309-1708},
pages = {89 - 108},
volume = {127},
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.},
keywords = {Shallow water, Saint-Venant, Slope source term, Well-balanced scheme, Second-order reconstruction},
}