Application Of Finite Subdomain Radial Basis Collocation Method In Groundwater Simulation

Radial basis function collocation method is a meshless method.Compared with the traditional finite element and finite difference methods,it has many advantages,such as direct method,simple principle,fast convergence speed,no numerical integration,flexible node arrangement and so on.While maintaining the advantages of the radial basis function collocation method,the finite subdomain radial basis function collocation method can better reflect the local characteristics of the problem and reduce the full rank of the collocation matrix.The main contents and conclusions of this paper are as follows:(1)The radial basis function collocation method is used to solve the groundwater confined stable flow problem with piecewise constant permeability coefficient tensor,which is a common problem in practical numerical simulation of groundwater flow.In this method,nodes are arranged at the abrupt change of the permeability coefficient,and the permeability coefficient of such nodes is approximately replaced by the average value of the permeability coefficient of adjacent nodes,and the partial derivative of the permeability coefficient is approximately replaced by the central difference quotient constructed by the permeability coefficient of adjacent nodes.The solution method of the radial basis function collocation method established by this method effectively avoids the failure of the radial basis function collocation method because no nodes are arranged at the sudden change of permeability coefficient.The results of MATLAB programming show that the precision of the proposed method is sufficient to meet the needs of practical problems.(2)The problem in(1)is further solved by the finite subdomain radial basis function collocation method.According to the feature that the permeability tensor is a shard constant,the solving domain is decomposed into several subdomains,and in each subdomain,an approximate function expressed by radial basis function is established by using the center node of radial basis function.In each subdomain and at the configuration nodes where the boundary of the subdomain and the outer boundary overlap,the partial differential equations and the definite solution conditions are used to establish the coordinate point equations where the undetermined coefficients of the approximate solution function are satisfied.The equations are solved simultaneously and the approximate solution over the whole domain is obtained.In this method,the corresponding shape parameters can be applied according to the local characteristics of the subdomain,so as to better reflect the local characteristics.MATLAB programming calculation results of practical examples show that the method is compared with(1)the method of error,especially on the demarcation line between adjacent subdomains significantly reduced,reached a very high accuracy.(3)When the inite subdomain radial basis function collocation method is used,according to the local characteristic that the closer the function to be solved is to the well,the greater the hydraulic slope is,the solving domain is divided into several subdomains,and the subdomains are finer the closer the function is to the well.The programming results of a practical example show that this method can reduce the error and reflect the characteristics of the unsolved function when the hydraulic slope is large.