Numerical Simulation Of Pollutant Transport In Unsteady Open Channel Flow With Meshless Particle Method

The flood disaster is one of the most serious natural disasters in the world,and it often exists in those areas with densely population,more rivers and lakes,and abundant in rainfall.When the flood breaks out,it has the characteristics of high flow rate and large velocity,which may bring serious economic losses and casualties to the society,and even cause the concurrency of other disasters.In addition,the flood will carry a large amount of sediment and other pollutants,causing the environmental pollution problems in the affected area.Therefore,the study of the flow in the open channel and the transport of pollutants in the flow has great instructive significance for flood control and water quality optimization.In this paper,the mathematical model of open channel flow is derived and analyzed firstly.Based on the Navier-Stokes Equations which describes the viscous incompressible fluid,the one-dimensional(1D)Saint-Venant Equations and two-dimensional(2D)Shallow Water Equations are derived.As for the pollutant transport problems,the Convection-Diffusion Equation under turbulent conditions is introduced,and with some reasonable assumptions the ideal 1D and 2D Convection-Diffusion Equation are obtained.Secondly,in order to study the state of open channel flow and the transport of the pollutants in the fluid,a mathematical model coupling the Shallow Water Equations and the Convection-Diffusion Equation is constructed,and a typical meshless particle method(smoothed particle hydrodynamics,SPH)is used to solve the coupled model.Finally,in order to verify the effectiveness and advantage of using the SPH method to solve the coupled model,two 1D and two 2D dam-break numerical experiments are designed,and the numerical results show the accuracy and the simplicity of the SPH method in solving the Shallow Water Equations.Two experiments are also designed to simulate the transport of pollutants in the open channel flow,and the results show that the coupled model can be effectively solved by the SPH method.In addition,numerical experiments on Kinematic Wave Equation and Diffusive Wave Equation are carried out,in which the SPH solutions are compared with those of several mesh-based methods.The numerical results indicate that the SPH method has higher accuracy and better stability in solving the Kinematic Wave Equation,while the mesh-based methods and the SPH method have nearly the same performance on Diffusive Wave Equation problems.