Meshfree modelling of one-dimensional contaminant transport in unsaturated porous media

Abstract

This paper deals with the application of a meshless method called element-free Galerkin method (EFGM) for modelling the contaminant transport through the unsaturated porous media with transient flow condition. In EFGM, an approximate solution is constructed entirely in terms of a set of nodes and no elements or characterization of the interrelationship of the nodes is needed to construct the discrete equations. For analysis, the one-dimensional form of advection–dispersion equation with linear first-order degradation is considered. The unknown concentration values are approximated by using moving least square approximants. The weak form of the governing equation is formulated and the Lagrange multiplier method is used for enforcing the essential boundary conditions. The van Genuchten model is used for describing the hydraulic properties of the unsaturated soil. MATLAB code is developed to obtain the numerical solution. Numerical examples representing various phenomena that occur during the migration of contaminants are presented to illustrate the applicability of the proposed method and the results are compared with those obtained from the finite element method and the analytical solution.

Keywords:

• Contaminant transport
• Meshless method
• Element-free Galerkin method
• Continuous source
• Unsaturated soil