Efficiency and accuracy of Lateralized HLL, HLLS and Augmented Roe's scheme with energy balance for river flows in irregular channels

This paper compares three different 1D numerical schemes used to simulate transient flows in rivers. All these schemes solve the shallow-water equations in cross-sections of arbitrary shape. Two are based on the HLL approach (namely Lateralized HLL and HLLS) and one on Roe’s approach (Augmented Roe’s solver with energy balance). The goal of the work presented hereafter is to highlight the capabilities and weaknesses of each scheme. Varied test cases are examined, including water at rest, steady flows, transient flows and a real river test case. Three conditions necessary to accurately simulate pure hydrodynamic flows are checked: (1) well-balanceness, (2) correct prediction of water level and (3) correct prediction of discharge across and within cells. The results revealed that the Lateralized HLL scheme is unable to provide accurate predictions for the discharge within the cells. However, if the focus is only on the water level, it gives good results and is also quite robust. The HLLS and the Augmented Roe’s scheme with energy balance give better solutions. Nevertheless, these schemes also show limitations: incorrect discharge at shocks, a problem shared by many other schemes, and difficulties to reach a perfect steady state when the topography is highly irregular