Abstract:Lattice Boltzmann method is applied extensively in the field of fluid motion for concise programming, parallel computing, and dealing with complex geometrical boundary easily and so on. As the main force of soil water erosion process, accurate simulation of the process of overland flow has important significance for analyzing the mechanism of slope erosion and building the physical process of soil erosion model. However, there is less research on the application of the lattice Boltzmann method to overland flow at present. In this paper, lattice Boltzmann method with D1Q5 velocity model is applied in motion equation of overland flow, in which, only time is considered in the process of multiple scales, and undetermined coefficient method is adopted to determine the equilibrium distribution function by means of multi-scale analysis. And then using analytical solution as a standard, lattice Boltzmann method and Preissmann four-point implicit scheme method are compared through ideal numerical example. The results indicate that the calculation precision of lattice Boltzmann method using D1Q5 velocity model is higher than that of Preissmann four-point implicit scheme method in simulating the variations of water depth and discharge per unit width at the bottom of slope, especially in the stage of recession flow, and in describing the distribution of water depth and discharge per unit width along the slope length before equilibrium time. But after equilibrium time, the calculation precision of lattice Boltzmann method using D1Q5 velocity model is lower in calculating the distribution of water depth and discharge per unit width along the slope length because at the point of x=1 m, a large relative error occurs. The relaxation time is recommended to be taken in ［1, 1.2］ s when lattice Boltzmann method is applied to solve the motion equation of overland flow.
