Study On Modification Of Saint-Venant Equations For Rigid Vegetated Channel

Saint-Venant equations plays a fundamental role in the field of aerodynamic and hydraulic engineering calculation,and its research and application are still widely concerned.In the natural river course,the presence of vegetation will change the flow structure and increase the flow resistance,and the traditional drag coefficient and Saint-Venant equations are not applicable.In this paper,based on the theoretical analysis and modification of Manning coefficient and Manning formula of rigid vegetation,the one-dimensional Saint-Venant equations is modified and a numerical model is established.Combined with the vertical velocity distribution formula of rigid vegetation channel,the modified Saint-Venant equations is extended to two-dimensional numerical simulation.The reliability and accuracy of the modified model are discussed by comparing the results of one-dimensional and two-dimensional numerical simulation with the measured data.The main conclusions are as follows:(1)By introducing the modified Manning coefficient of rigid vegetation channel,the Saint-Venant equations can be effectively modified,and the one-dimensional mathematical model of rigid vegetation channel flow simulation can be established.The simulation results are in good agreement with the experimental results,the average error rate is less than 15%,and the correlation coefficient is greater than 0.78.(2)In the absence of vegetation,the vertical velocity distribution of river flow conforms to the form of power exponential function;However,with the increase of rigid vegetation,the fitting effect of vertical velocity distribution and power exponential function becomes worse and worse.Therefore,the two-dimensional simulation of river flow with rigid vegetation should be modified.(3)On the basis of the one-dimensional modified model,a two-dimensional mathematical model of river flow with rigid vegetation can be established according to the vertical velocity distribution law of rigid vegetation channel.The simulation results are in good agreement with the experimental results,the average error rate is less than 15%,and the correlation coefficient is greater than 0.73.(4)The modification of Manning coefficient and Manning formula is an effective way to solve the hydraulic calculation of complex vegetation channel,and the modified Manning coefficient of rigid vegetation channel has a strong application to the simulation of this type of river flow.In this paper,through the introduction of vegetation Manning coefficient,the modified Saint Vinant equations is established and well applied to the one-dimensional and two-dimensional hydrodynamic simulation of rigid vegetation channel.It has theoretical significance for the application of Saint Vinant equations in complex river channel and practical significance for numerical simulation of rigid vegetation channel flow.