Comparison between local and global Mesh-free methods for Ground-Water modeling

Ground water pollution is a serious environmental problem that may damage human health, destroy the ecosystem and cause water shortage. In all situations, we need tool to predict the pollutant distribution in ground water. The only tool that we can use is mathematical modeling. Recently, very intensive efforts have been devoted to develop meshless or element free methods that eliminate the need of element connectivity. The motivation is to cut down modeling costs in industrial applications by avoiding the labor intensive step of mesh generation. In this paper we develop and compare two types of a meshfree method for modeling groundwater contaminant transport: globally supported multiquadric radial basis function (MQRBF) and locally supported compactly supported radial basis functions (CSRBF). The algorithm uses collocation method with radial basis functions. RBF is a truly meshfree method and can be used to solve complex geometry and high dimensional problems very easily compared to other classical numerical method. Numerical results are presented for 1-D, 2-D and 3-D groundwater contaminant transport models. The results show that the method is very simple and accurate.