Accuracy and efficiency in numerical river modelling : investigating the large effects of seemingly small numerical choices

To quantify the effects of numerical inaccuracies on the flow patterns and resistance (or backwater) in a river, several building blocks of the governing flow equations were analysed. It is demonstrated that the artificial backwater contribution from the momentum advection approximation can be of the same order of magnitude as the bottom friction contribution, depending on the advection scheme. The discretized equations for the z-layer model are analyzed and the cause of the inaccuracies is clearly shown to come from the emergence of thin near-bed layers. Based on this analysis, a new method is presented that significantly reduces the errors and the grid dependency of the results. The method consists of a near-bed layer-remapping and a modified near-bed discretization of the k-E turbulence model. The applicability of the approach is demonstrated for uniform channel flow, using a schematized 2D vertical (2DV) model and for the flow over a bottom sill using the Delft3D modeling system. Finally a new modelling strategy is presented for improving the efficiency of computationally intensive flow problems in environmental freesurface flows. The method allows the incorporation of high-resolution data on subgrid scale to obtain a more accurate and efficient hydrodynamic model. The efficiency and applicability of the method is demonstrated using a schematic test for the vortex shedding around a circular cylinder and a real-world case study on the Elbe River in Germany.