Contaminants dispersed at the land surface migrate through the unsaturated and saturated porous media before reaching the groundwater. In order to ease and develop the practical way of contaminant transport simulation for complex geometry and boundary conditions, numerical formulations have been used extensively. In recent years, a group of new methods called meshfree methods have been developed; whose main aim is to eliminate structure of the mesh and construct approximate solutions for the discrete equation entirely in terms of a set of nodes. A limited amount of research is undertaken...