Abstract
This paper proposes a sediment-transport model based on coupled Saint-Venant and Exner equations. A finite volume method of Godunov type with predictor-corrector steps is used to solve a set of coupled equations. An efficient combination of approximate Riemann solvers is proposed to compute fluxes associated with sediment-laden flow. In addition, a new method is proposed for computing the water depth and velocity values along the shear wave. This method ensures smooth solutions, even for flows with high discontinuities, and on domains with highly distorted grids. The numerical model is tested for channel aggradation on a sloping bottom, dam-break cases at flume-scale and reach-scale with flat bottom configurations and varying downstream water depths. The proposed model is tested for predicting the position of hydraulic jump, wave front propagation, and for predicting magnitude of bed erosion. The comparison between results based on the proposed scheme and analytical, experimental, and published numerical results shows good agreement. Sensitivity analysis shows that the model is computationally efficient and virtually independent of mesh refinement.
Highlights
Numerical techniques for modeling morphodynamics are preferable over field and laboratory observations at large scales, due to reduced computational costs and time [1,2,3,4]
We extend and modify the source term treatment, the revised surface gradient method (RSGM), proposed by [37], for shallow water flows on non-erodible beds
This paper introduces a simple and robust model for bed evolution and its effects on water
Summary
Numerical techniques for modeling morphodynamics are preferable over field and laboratory observations at large scales, due to reduced computational costs and time [1,2,3,4]. Mathematical modeling of morphodynamics can be performed using depth-integrated shallow-water equations (continuity and momentum equations) representing the hydrodynamics, and an Exner equation (continuity of sediment) representing the morphological evolution. These equations can either be modeled using a coupled approach in which the hydrodynamic and morphodynamics flows are solved simultaneously, or using an uncoupled (quasi two-phase) approach, in which flow hydrodynamics are modeled first and the obtained velocity is used for modeling morphological evolution [5]. Coupled shallow-water and Exner equations have been widely used to model sediment transport in rivers, bed evolution in dam-break flows, siltation of reservoirs, and sediment flushing in sewers [4,9,10,11,12,13,14]. Used sediment-transport formulas include the Grass formula [15], Water 2016, 8, 212; doi:10.3390/w8050212 www.mdpi.com/journal/water
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