Solving Solute Transport Equation With Radial Basis Function Collocation Method

The article mainly study how to properly solve groundwater contaminant transport modeling with Radial basis function collocation method. The article divide into four chapters. It is introduced respectively Mesh-less method、basic principle of the radial basis function interpolation、the methoh to slove solute transport equations and practical verification. When sloving solute transport equations with traditional method causes consuming time, high cost and unreasonable results. So, in the third chapter of the article will discusse three ways to solve solute transport problems. The three methods mainly discusse how to cope with time-term of the solute transport equations. The processing method of the first method is easy. It treat time-term with difference, then slove the approximate value at each node with Radial basis function collocation method. The second method is an improved algorithm to the first method. It difference discrete the time-term according to weight θ, then apply Radial basis function collocation method for discrete form. The third method is the new idea of the article. We call it Radial basis function collocation method of time and space coincidental. This method divide solution region into many subregions, then apply Radial basis function collocation method at each subregion. It is consider time as a variable and apply PLU decomposition procedure for result matrix, then solve the problems. Also,in order to make the result more accurate, we give the approximate function some improvement. It is different from former two methods in the way to cope with time-term. This method consider time as a variable and it can overcome the recurrence difficulty caused by difference in time. when we solve the one-dimensional heterogeneous diffusion problem, it is similar to the method that solve two-dimensional stable problem. It is easy to implement in the numerical calculation. At the last of the article, we take three methods into practical examples. After verification by actual exemple, the result of Radial basis function collocation method of time and space coincidental is more ideal.