Vertically-averaged and moment equations for flow and sediment transport

Abstract

Simulation of river flow processes including sediment transport is usually conducted using the shallow water flow equations, which are based on a hydrostatic pressure distribution. To increase the accuracy of predictions in a variety of scenarios involving horizontal length scales of the order of vertical length scales, an improved representation of the vertical flow structure is necessary. The mathematical approximation to field variables like the velocity and fluid pressure must be enhanced during the depth-integrating process. Therefore, this paper presents a 1D non-hydrostatic flow and sediment transport model developed by using the method of the weighted residuals into the RANS equations. Using continuity, momentum, and moment equations, the fluid pressure distribution is modelled using a quadratic predictor with perturbation parameters to deviate the vertical momentum balance from the hydrostatic law. The flow equations are a generalized non-hydrostatic flow solver, where the fluid density variation due to suspension of sediments and the bed deformation due to erosion-sedimentation processes are accounted for. A hybrid semi-implicit finite volume-finite difference numerical scheme is developed to solve the system of conservation laws. Two different approaches are used to model the sediment transport processes: (i) Unified computation of the total-load transport and (ii) separate computation of suspended and bed loads. The accuracy of the non-hydrostatic model is demonstrated by comparison with experimental data, highlighting better results accounting for separate determinations of the suspended and bed loads in highly erosive flows.