Effectiveness of meshless methods for advection dominant groundwater contaminant transport problems

Abstract

Meshless methods are efficient tools in prediction of fate of groundwater contamination. In these methods, the choice of amount of discretization in space and time affects the accuracy of solution and computational time. Peclet number is a controlling parameter of such numerical transport simulation models and is the measure of space discretization adequacy for a given velocity and dispersion coefficient. Greater value of Peclet number indicates highly advective flow with negligible diffusion. In this study, the effect of Peclet number on accuracy of meshless methods is analysed. Three meshless methods of three different categories of formulation are considered, namely, Radial Point Collocation Method (RPCM), a meshless strong form method, weak form Meshless Petrov Galerkin Method (MLPG) and hybrid RPCM-MLPG Meshless Weak Strong (MWS) form method. These are applied for modelling Groundwater Contaminant Transport (GCT) phenomenon. The three models are demonstrated using hypothetical case studies and the results are verified with analytical solutions. After a successful validation, the models are subjected to changes in Peclet number and the errors with respect to analytical solutions are studied. It is found that MLPG-GCT model is the most stable and MWS-GCT model is more accurate within less computational time for reasonably high Peclet numbers.