Simulation of Flow and Transport Process—Scope of Meshless Methods

Groundwater flow and contaminant transport are complex phenomena which require partial differential equations to be solved numerically throughout the problem domain. Finite Difference method (FDM) and Finite Element method (FEM) based models are traditionally employed for these simulations. These methods suffer from certain instabilities due to the presence of mesh/grid. Stabilization techniques such as adaptive meshing/re-meshing, operator splitting and upwinding are used to counter these issues. Recently, meshless methods are being applied to a variety of groundwater flow and transport problems. In this study, a meshless method named Radial Point Collocation Method (RPCM) is demonstrated with two case studies. This method doesn’t use operator splitting for simulating decay reactions. Due to the use of local support domain, these methods are known to have better stability compared to FDM and FEM. The support domain size can be easily increased in order to enhance the model stability which is difficult to achieve in mesh/grid-based methods. A coupled reactive transport model involving single species first-order decay in an unconfined aquifer is developed for the first case study. For case study 2, a three-species decay chain-based reactive transport model is developed for an aquifer having irregular boundary. The model simulation results are compared with FDM- and FEMbased numerical models developed using well-established MODFLOW-MT3DMS and COMSOL models, respectively. The results indicate good agreement between the meshless and mesh/grid-based methods which shows the effectiveness of meshless methods.