The Application Of Radial Basis Functions Collocation Method To The Numerical Simulation In The Unsaturated Soil Water-Salt Transport Problems

The mathematical models reflecting the soil water-salt transport law are mostly nonlinear partial differential equations. Before 1960s, the analytic method is primarily used to research the analytical solution or half analytical solution of the equations, however, it only applies to the soil water movement problems under the simple definite conditions. In order to study the soil water and salt transport issues under the complex conditions, the numerical method is the most effective way at present. Radial basis functions (RBF) collocation method, researched in recent ten years, is a new meshless method to solve the numerical solution of differential equation. This method discrete the partial differential equations without grid, thereby not only avoiding the complex process of the grid generation, but also eliminating the numerical concussion phenomenon which happens when traditional grid methods (such as finite element method, the finite difference method, etc.) are used to solve the convection dominant problem. This paper mainly aims at the meshless numerical simulation methods of soil water movement and solute transport problems in film drip irrigation. By preliminary studies, we get some results as follows:(1) Under the conditions of infiltration and evaporation, the numerical models of 1D soil water movement are constructed by incorporating with the difference method, the collocation method and a new radial basis function interpolation. Further, the existence and uniqueness of the solution to the proposed method are established. According to the analysis of the calculated result, the numerical simulation is exact.(2) The meshless numerical models of 1D soil solute transport are constructed by RBF collocation method and the Hermite collocation method, and the numerical simulation is performed. Further, the existence and uniqueness of the solution to the proposed method are established. It can be seen that the simulated results correspond with solute transport law and can be used to practical work.(3) The mathematical model and the numerical model of 3D unsaturated soil water-salt transport are established. It can be seen that the models correspond with the practical situation and can perfectly meet for the demand of practical work.