Numerical Simulation For Flow And Sediment Transport Based On Spectral Method

Sediment transport in meandering channels is the basic theory of the river dynamics of which researches on suspended load transportation in bend are very few.Suspended load is critical in determining fluvial processes of Lower Yellow River and the interaction of suspended load and water flow in meanders is the key on the microscopic level to understand the Yellow River morphology theory and therefore as a technical support for channel management.In this paper,a number of hydrodynamic models have been developed,in which high order numerical scheme is employed to investigate water flow and suspended sediment transport in meanders.The vertical profiles of physical variables are expressed in polynomials.A dynamic secondary flow model which fully considers the nonlinear interaction between main flow and secondary flow was developed in depth averaged 2D model.Curved open channel flow simulated by this dynamic secondary flow model was compared with two other 2D models,2D model without secondary flow effect and 2D model with a nonlinear secondary flow model.Good aggrement between the simulation of dynamic secondary flow model and measurement proofs that dynamic model is able to consider the nonlinear effect.Base on the spectral method,flow velocity components were expanded into orthogonal polynomials in vertical direction.Polynomial coefficient equations were obtained by Weighted Residuals Method and advection terms were tackled on vertical Gauss points by Eluerian Lagrangian mothod(ELM),then a simplified 3D model has been set up and verified in this paper.Simulated flow structures of a sharp bend open channel by this model are matched well with the experimental result when the polynomial degree is larger than 1.Mean error of predicted main flow location is equivalent with other 3D hydrodynamic models.Simulation shows reasonable flow structures by considering turbulence anisotropy between vertical and horizontal directions in a simple way.As this 3D model has no vertical grid,calculation efficiency is comparable to 2D models.3D hydrodynamic models that advection terms are tackled by ELM maintain stability with large time step while the linear interpolation would significantly bring about additional numerical resistance.By introducing spectral element method(SEM)to replace linear interpolation with polynomial interpolation in vertical direction,a new 3D ELM model was established.Numerical experiment of an open channel flow shows this 3D model takes advantage of both SEM and ELM and has the capability to break out Courant number constraint for time steps and eliminate the numerical resistance of classic ELM effectively,and therefore the accuracy is improved by an order of magnitude.Combining water flow equations,two equation turbulence closure model and susepended sediment transport equation,3D flow and sediment transport model without the Boussinesq approximation was developed to fully analyze the sediment effect on water flow.After the 3D model was validated by excellent simulations of experiments,the stratification and inertia effects caused by suspended sediment in meandering channels are analysed.As a coupled effects at different sediment concentration and size,suspended sediment mainly shows stratification effect and enhances the secondary flow strength at lower concentration;suspended sediment shows stratification and inertia effects and suppresses the secondary flow at higher concentration.Meanders has a non-equalibrium adjustment on sediment transport with the downstream straight section has coexstience of deposition and erosion in cross section.Thus the river performs lateral rolling.At the same time,the difference of the deposition and erosion rate leads the channel wider and shallower.