Space-time Radial Basis Collocation Method For Groundwater Pollution Simulation

Over the past decades,the increasingly serious groundwater pollution problem has attracted great attention of the state and governments at all levels.In order to understand the general situation of pollution comprehensively and accurately before treatment,researchers often use finite element method and finite difference method to solve the problem of groundwater pollution transport,but these methods are all based on the grid or unit,which brings many limitations to solving the problem.In order to overcome the dependence of the method on the grid,the meshless method emerges at the historic moment and has been widely used in the field of engineering calculation.Based on the groundwater contaminant transport model,this paper constructs a numerical algorithm to solve the model,and compiles the corresponding program by MATLAB,and obtains a good simulation result,which verifies the feasibility of the space-time radial basis function collocation method to solve the groundwater contaminant transport problem.The main contents of this article are as follows:(1)Taking the problem of two-dimensional groundwater contaminant transport as an example,the basic principle of radial basis function collocation method for time difference is expounded.On this basis,the time items are discretized according to the weight ?,and it uses discrete form to solve three-dimensional groundwater contaminant transport problem.(2)It uses the space-time radial basis function collocation method to solve the problem of groundwater contaminant transport.From the theoretical derivation,it can be seen that when the space-time radial basis function collocation method is used to solve the problem of groundwater contaminant transport,the time variable and the space variable are treated equally to avoid the complex process of making time items different,the space-time radial basis function collocation method is insensitive to dimension,and it is easy to extend from low-dimensional problems to high-dimensional problems.(3)Through MATLAB,it compiles programs to solve one-dimensional and two-dimensional groundwater pollution transport problems.When generating coefficient matrix of linear equations,these programs adopt matrix programming in MATLAB,which makes the processing of the program more convenient,the expression of the program more concise,and also speeds up the running speed of the program.The simulation results demonstrate the feasibility of solving groundwater contaminant transport problem by the space-time radial basis collocation method.The effects of node distribution,number andparameters on the accuracy of the space-time radial basis collocation method are analyzed through experiments.