Using Radial Basis Function Collocation Method For Solving The Flow Problems Of Diving

The diving flow mathematical model is reflected by a nonlinear partialdifferential equation. Before the1960s, the analytical method is mainly used todeal with the analytical or semi-analytical solution of the equations, but theanalytic method is only applicable to solve the diving flow problems in thesimple boundary conditions. In order to study the water flow problems undermore complex conditions, the most effective way is to use numerical methods.In the past ten years, collocation method using radial basis functions aredeveloped to be a numerical solution of partial differential equations of themeshless method. The method in the partial differential equations for numericaldiscrete time does not need to rely on the grid, thus it can not only avoid themesh generation process, but also can reduce the adverse effect that caused by the mesh distortion in the traditional grid method (finite difference method andfinite element method). In this paper the first radial basis function collocationmethod is applied to solve the two-dimensional water flow problem, andapplying the method to do the groundwater flow numerical simulation isconducted to get a satisfied result.Paper can be divided into three chapters. The first chapter is about thebackground knowledge. The following parts are mainly introduced, includingthe groundwater numerical methods,the development, classification and themain advantages of meshless methods and the meshless collocation method. Thesecond chapter is about the approximation by radial basis function meshlesscollocation method. The concepts and types of radial basis function has beengiven. The basic theories and methods of the radial basis function interpolationare introduced, too.And in the final part of this chapter, the two methods of theradial basis function collocation typemeshless method (the symmetry methodand the asymmetric method)are discussed. The third chapter is to use the radial basis function collocation method to solve the flow problems of diving. First, themathematical model of the sport of diving flow has been determined. Becausethe water flow equation is nonlinear, three linear solutions are also given tosolve the diving flow equation.Second, the Radial Basis Function Collocationmeshless methods are used for the numerical simulation of the model, and thesolution steps of the numerical simulation of the diving flow are given as well.Finally, this method is used in the dewatering instance of the Yuanbaoshan openpit. The use of computer preparation of the corresponding MATLAB program ishelpful to realize the visualization of the algorithm. We can see from thesimulation results that the numerical model of the proceeds can reflect the actualsituation and can meet the operating requirements. The last chapter is aboutconclusion and prospect.