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

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.