Analysis of split operator methods for nonlinear and multispecies groundwater chemical transport models

Coupled solute transport and reaction models are computationally demanding when multispecies, multidimensional simulations are considered. Split operator methods provide approximate solutions to the reactive solute transport problem that are both relatively efficient to compute and to construct. The transport and reaction operators are split into two separate computational steps. Split operator methods are introduced in the context of single species sorption to the soil, with an emphasis on the splitting errors that are induced. For standard two-step methods, the splitting error is proportional to nt, the temporal step size of the numerical scheme. The alternating split operator scheme, in which the order of the operations is switched at succeeding time steps, apparently does not remove the splitting error for nonlinear reactions, whereas it is removed for linear cases. The truncation error is extended to the case of two reacting species.