Assessment of different 1D numerical schemes for steady flows over a geometrical discontinuity

This paper focuses on the numerical modeling of steady flows and proposes a comparison of three 1D finite-volume schemes. These schemes are all adapted to arbitrary topographies. Two are based on the HLL scheme and one on Roe’s approach for the flux calculation. The main goal of the work presented here is to identify the best scheme, between those three, to be extended to sediment transport in rivers. This selected scheme should, in pure hydrodynamics, possess the following characteristics: (1) be well-balanced and (2) predict accurately the water level and discharge even with a coarse mesh. To compare those schemes, two types of numerical tests are used. First, the well-balanced property is verified by maintaining water at rest over an irregular topography. Then, a steady flow in a convergent / divergent channel is simulated. These tests highlighted the limits of HLL based schemes as they are unable to provide accurate results without a proper mesh refinement. The best identified scheme is thus the Augmented Roe’s scheme with energy balance. However this scheme showed its limitations in the treatment of shocks. A study of this particular issue is also presented in this paper