An overview of Eulerian–Lagrangian schemes applied to radionuclide transport in unsaturated porous media

Abstract This paper presents an overview of the recent progress achieved in the development of Eulerian–Lagrangian schemes for approximating the transport of radionuclides in unsaturated porous media. Our focus is on a particular class of schemes that are well suited for advection-dominated transport problems. We first considered a computationally efficient procedure, the Modified Method of Characteristics (MMOC), to approximate the hyperbolic part of the governing transport equation; the numerical results obtained indicate that the MMOC scheme leads to inaccurate, non-conservative numerical solutions. In order to overcome this lack of mass conservation the Locally Conservative Eulerian–Lagrangian Method (LCELM) was implemented; the new set of results showed that numerical diffusion may have a strong impact on numerical solutions computed over long periods of time, typical of investigations of transport of radionuclides in the subsurface. Aiming at a better numerical approximation of the transport problem at hand we have developed a new procedure, the Forward Integral-Tube Tracking (FIT) scheme, which inherits the local conservation property of the LCELM scheme and is virtually free of numerical diffusion. Numerical results comparing the MMOC, the LCELM, and the FIT schemes are presented. They clearly illustrate the recent evolution in this area, of particular importance to the evaluation of the impact on the environment of leaking nuclear waste containers.