Efficiency and accuracy of LHLL, HLLS and Augmented Roe’s scheme with energy balance on arbitrary topography

This paper compares three different 1D numerical schemes used to simulate transient flows in rivers. All solve the shallow-water equations in cross-sections of arbi- trary shape. Two are based on the HLL scheme and one on Roe’s approach. The goal of the work presented hereafter is to identify the best scheme to be extended to sediment transport in rivers. This scheme should satisfy the following conditions which are necessary to have an accurate model for sediment transport: it should, in pure hydrodynamics, (1) be well-balanced and (2) give a correct prediction of both water level and discharge even with a coarse mesh. Tests of water at rest and steady flows in a convergent/divergent channel are used to compare those schemes. The results revealed that HLL based schemes are unable to provide accurate results without a proper mesh refinement. The best identified scheme is, finally, the Augmented Roe’s scheme with energy balance, even though it has shown some limitations in the treatment of shocks