Finite Point Method Apply To The Soil Water And Salt Movement Equations

The numerical simulation of the soil water and salt movement equations has been an important issue in the field of soil research.The essentially of the advection-dispersion equation which contain the coefficient of the advection and the hydrodynamic dispersion is the convection-dominant equation.The traditional methods of numerical simulation are Finite Difference Method and Finite Element Method for the advection-dispersion equation,but the numerical solution of Finite Difference Method is not ideal for the convection-dominant equation,Finite Element Method often increases the price of the numerical simulation for the division of grid.It has been paid attention by people for the meshless can reduce the price of the division of grid.The algorithm of this paper is made of the Onate's Finite Point Method and the upwind format,and Apply to the advection-dispersion equation.The work of the article is as follows:Firstly,this paper summarizes the soil water and salt movement models,and gives the derivation process of the advection-dispersion equation in detail.The meshless development at domestic and overseas is introduced in recent years,and carries on the simple classification and overview.The numerical simulation method of the soil water and salt movement equations are given in recent years.Secondly,the paper introduces the moving least squares method and deduces the forming process of shape function.The deduction process of the FPM is given by Onate,and the algorithm of this paper is based on the FPM.it is to study the influence of parameters on the numerical simulation results by an example in this paper.we could obtain the conclusion which the algorithm of this paper is suitable for the convection dominant equation.The influence of the support domain on the results of numerical simulation is studied by changing the size of the support domain.The algorithm of this paper has good simulation results in the area of the boundary and changing largely of the gradient by comparing with the FPM base the moving least squares.Finally,the algorithm of this paper is applied to one dimensional advection-dispersion equation and two dimensiona advection-dispersion equation.It is workable and efficient by comparing with FDM and FEM.Meanwhile,it is largely improvment in the area of the boundary and changing largely of the gradient by comparing with other algorithms.