Two-dimensional contaminant transport modeling using meshfree point collocation method (PCM)

Groundwater contamination is a severe problem in many parts of the world including India. The complex problem of groundwater flow and contaminant transport is studied generally by solving the governing equations of flow and transport using numerical models such as finite difference method (FDM) or finite element method (FEM). Meshfree (MFree) method is an alternative numerical approach to solve these governing equations in simple and accurate manner. MFree method does not require any grid and only makes the use of a set of scattered collocation points, regardless of the connectivity information between them. Kansa (1990) [9] developed a multi-quadratic (MQ) based MFree method for the solution of partial differential equations. Based on the Kansa’s method, the present study proposes a MFree point collocation method (PCM) with multi-quadric radial basis function (MQ-RBF) for the two-dimensional coupled groundwater flow and transport simulation in unconfined conditions. The accuracy of the developed model is verified with available analytical solutions in literature. The coupled model developed is further applied to a field problem to compute the groundwater head and concentration distribution and the results are compared with available finite element based simulation. The outcomes of the model results showed the applicability of the present approach.