A One-Dimensional Numerical Simulation Of Riverbed Headcut Erosion Process Based On Finite Difference Method

The headcut is a riverbed shape formed by the sudden drop of riverbed elevation.The energy concentration on the wall of the plunge sill under the action of water flow leads to severe local scouring of the riverbed,which develops to the upstream riverbed and deposit on the downstream riverbed.Dam break,retrospective scouring and mountain rivers often occurs,causing violent erosion of the river bed,which causes severe scouring of riverbed and poses a serious threat to the stability of bank slope.Moreover,the flow pattern during water and sediment transport is complex and rapid flow alternates.Therefore,it is of great theoretical significance and practical value to simulate the scouring process of headcut.In this paper,the generalized physical figure of headcut scouring is taken as the research object,and a one-dimensional unsteady flow bed load transfer mathematical model of headcut scouring is established based on finite difference method.The causes of numerical oscillation in verification of flow model are analyzed,and the cross-critical flow is processed by the method of reducing convection acceleration to modify the flow model.Based on the measured data of tank test,the modified model is validated,the factors affecting the scouring rate of drop sill are analyzed,and the cross-critical flow problem under moving bed condition is simulated,which provides theoretical support for practical engineering problems such as surface line calculation of mountain flood,dam break and reservoir traceable scouring.The main contents and conclusions of this paper are as follows:(1)Establish one-dimensional unsteady flow bed load transport mathematical model suitable for fall scouring.One-dimensional Saint-Venant equations are used for the flow equation,and Pressimann four-point implicit difference scheme is used for the numerical discretion;the riverbed deformation equation is used for the sediment equation and the backward difference scheme is used for the numerical discretion.In addition,auxiliary equations such as the formula of sediment discharge rate,the formula of river bed shear stress and the formula of uniform dry sand density are added to solve the problem.The uncoupling method is used to solve the problem.First,the hydraulic elements of each section are solved by the flow equation,and then they are substituted for the sediment equation to calculate the riverbed deformation.Finally,the established water-sediment model is programmed and solved in Fortran language.(2)In the calculation of flow equation,because the Pressimann scheme often oscillates numerically when dealing with flow with discontinuous points,the method of deleting convection acceleration is adopted in this paper.The coefficient ? and ? are added to the convection term expansion as a function of Fr at the calculation point,and the flow equation is re-discretized.The modified model can adopt the type of " 1+1 " boundary condition in the whole calculation area.(3)Model validation is divided into three parts:firstly,the harmony of flow model is verified by flat bed hydrostatics and non-flat bed hydrostatics;secondly,the applicability of flow model is verified by fixed bed fall;finally,the calculation accuracy of flow and sediment model is verified by movable bed fall.The validation results show that the model meets the requirements of harmony,applicability and calculation accuracy.The relative error between measured and calculated water depth is basically maintained at 30%,the maximum relative error is 40%,and the minimum is 6.67%.The relative error of riverbed scouring and silting thickness is basically maintained at 20%,the maximum relative error is 24.3%,and the minimum is 6.9%.As the water depth at the drop sill is very small,the test measurement itself also has certain errors,but the simulation results basically meet the accuracy requirements and accord with the development law of the fall sill scouring.(4)The influencing factors of slump scouring are analyzed through the distribution of different flow,slump height difference,water surface under the slope of slump,elevation of riverbed bottom and Fr along the course.The simulation results show that the larger the flow rate and the deeper the drop height difference,the faster the riverbed scouring rate and the more severe the riverbed deformation;the slope gradient has little influence on the riverbed scouring rate,which can be basically ignored.At the initial stage,the turbulent intensity of water flow at the drop sill position is high and the rapid river section is short.With the increase of scouring time,the slope of riverbed at the drop sill becomes slower,the scouring rate becomes smaller,and the turbulent intensity of water flow decreases.The flow pattern shows a transition trend from rapid flow to slow flow.