A moving least squares based meshless local petrov-galerkin method for the simulation of contaminant transport in porous media

Abstract

Contamination of soil, surface and subsurface water resources through direct or indirect sources is a major problem in many parts of the world. To understand the contamination process in the porous media, we have to simulate the contaminant transport mechanism and predict its behaviour with respect to space and time. The contaminant transport process can be simulated by solving the well posed advection-dispersion partial differential equation by using numerical techniques with appropriate initial and boundary conditions. The transport equation is generally solved using grid based techniques like Finite Difference Method (FDM) and Finite Element Method (FEM). The Meshless methods are alternatively developed numerical methods to overcome the limitations of aforementioned grid based techniques. This paper presents a newly developed Meshless Local Petrov-Galerkin (MLPG) model based on the moving least squares (MLS) method for numerical simulation of contaminant transport equation in porous media. The Meshless MLPG-MLS model has been developed for one- and two- dimensional problems in MATLAB. These models are investigated and verified with available analytical and numerical solutions for its accuracy and efficiency. The models gave quiet promising results showing the efficacy and applicability of the method for the simulation of contaminant transport in porous media.