Contaminant Transport in Partially Saturated Porous Media

Abstract

We discuss the numerical modelling of unsaturated flow in porous media with contaminant transport, dispersion and adsorption. The mathematical model for unsaturated flow is based on Richard's nonlinear and degenerate equation. The model of contaminant transport is based on Darcy's law and mass balance equation. We present the operator splitting method for this problem. In nature all of the physical processes are realized simultaneously and the time scale for adsorption differs from diffusion and convection significantly. In our numerical approximation we consider three sub-problems - first one is the problem of unsaturated flow, second one the problem of transport and dispersion and third one the adsorption problem. Our numerical solution is based on implicit time discretization and space discretization. To achieve more correct numerical approximation we treat each of the sub-problems with another time scale and the data computed from one sub-problem, is the input data for the next sub-problem in each time interval. The convergence to the weak solution of the original problem is also discussed. Finally we show a couple of practical applications of the method and numerical experiments for direct problems.