Numerical modelling of groundwater radionuclide transport with finite difference-based method of lines

In this study, the advection–dispersion equation with decay is numerically solved by the finite difference-based method of lines (FD-MOL) to simulate groundwater radionuclide transport. Finite difference orders of 1,2,…,8 are used for spatial approximation, while the linearly implicit Euler scheme is employed adaptively for temporal discretization. Four different problems are investigated, and results show that FD-MOL provides accurate and stable numerical solutions. Coarse temporal grids can be utilized implicitly, for instance, a maximum step of 1000 years with 400 spatial nodes yields RMS errors of 7.508 × 10⁻⁶, 7.395 × 10⁻⁵ and 7.705 × 10⁻⁶ in 92234U,90230Th and 88226Ra normalized concentrations, respectively, for the decay chain problem.