Comparison of Fast Shallow-Water Schemes on Real-World Floods

Abstract

Two-dimensional shallow-water schemes on Cartesian grids are amendable for graphics processing units and thus a convenient choice for fast flood simulations. A comparison of recent schemes and validation of important use cases is essential for developers and practitioners working with flood simulation tools. In this paper, we discuss three state-of-the-art shallow-water schemes: a first-order upwind scheme, a second-order upwind scheme, and a second-order central-upwind scheme. We analyze the advantages and disadvantages of each scheme on historical Danube river floods at three regions in Austria. We study the Lobau region as a floodplain with several small channels, the Wachau region with the meandering Danube in a steep valley, and the Marchfeld region located at the river confluence of March and Danube. The validation case studies show that the second-order schemes provide better estimates of the water levels than the first-order scheme. Still, the first order scheme is useful because it offers fast simulations and reasonable results at higher resolutions. The best trade-off between accuracy and computational effort for simulating river floods is provided by the second-order upwind scheme.