A forward tracking scheme for solving radionuclide advective problems in unsaturated porous media

In this paper we consider the numerical approximation of the problem of radionuclide contaminant transport in unsaturated porous media. The problem is modelled by a system of equations that describes the two-phase water?air flow and the radionuclide transport. We solve numerically the water?air flow equations combining mixed finite elements with a non-oscillatory central finite difference scheme. For the numerical approximation of the advective transport of the radionuclide, we introduce the Forward Integral-Tube Tracking (FIT) scheme, which is locally mass conservative and virtually free of numerical diffusion. Moreover, large time steps can be used without loss of accuracy in the numerical solution. We perform numerical experiments to compare the Locally Conservative Eulerian-Lagrangian Method (LCELM) and the FIT scheme; our results show that the FIT scheme produces more accurate results.