Miscible pollutant transport model for unsaturated soils and characteristic finite element method

A framework for numerical modelling of miscible pollutant transport in saturated unsaturated soils is presented. The mathematical model of the transport process integrates the following governing phenomena: convection, molecular diffusion, mechanical dispersion, sorption, immobile water effect and degradation, including both physical and chemical nonequilibrium processes. A finite element method based on the characteristic Galerkin discretization is developed. A corresponding implicit algorithm is devised to numerically solve the initial and boundary value problem for the model governing equations. The implicit algorithm is based on the operator splitting procedure and formulated by means of a combination of both the precise and the traditional numerical integration procedures in the Lagrange coordinates. The numerical results and the stability analysis of the algorithm validate good performance of the present model and efficiency, accuracy and stability of the present numerical method.