Study On Finite Point Method For Solving Soil Water-salt Transport Equation

Meshless method define the shape function at the node in the local domain,which can increase or decrease nodes in the calculation area and overcome the weakness that finite element method depends on the grid in numerical calculation.The finite point method presented in this paper constructs shape function by moving least squares and discretizes governing equation using collocation method.This algorithm belongs to meshless method,owning obvious superiority to finite element method.Convection diffusion model is a classical and popular model among soil water-salt transport model.Going into this model,we find that if utilizing finite element method or finite difference method to simulate these models,the numerical results are prone to shock in case of convection dominance.However,the proposed method by applying stability terms to the governing equations before the discrete governing equations,and making its support domain gradually tend to windward in the area of large gradient change can effectively avoid numerical shock.The main research work of this paper is as follows:Firstly,a basic principle and implementation detail of finite point method is given,including structuring shape function by moving least squares method,the selection of the weight function and support domain size,the process of adding stability term,adaptive upwind scheme and the discrete principle of the control equation etc.Secondly,an algorithm has been established for one-dimensional and two-dimensional soil salt transport equation using the finite point method.For nonlinear equation of soil water movement equation,presentation format and implicit format processing method are introduced in the process of constructing finite point algorithm;an algorithm has been established for one-dimensional and two-dimensional soil salt transport equation.Finally,the numerical simulation of one-dimensional and two-dimensional soil water movement equation and soil salt transport equation is offered.Besides,we fully discuss the Meanwhile,convergence order and computing time is analyzed in this section.Compared with the finite element method,characteristic finite element method and finite difference method with numerical examples results indicate that the proposed method is effective and easy to implement.