Theoretical analysis and physical interpretation of temporal truncation errors in operator split algorithms

The temporal truncation error (TTE) associated with a noniterative operator split (OS) method for application to a system of m coupled transport partial differential equations (pdes) is analysed. The system incorporates arbitrary n-dimensional linear transport and arbitrary nonequilibrium coupling kinetics. An expression for the exact form of the O(Δt) TTE is derived for transport-reaction (TR) splitting as well as reaction-transport (RT) splitting. The analysis allows us to predict the characteristics of the TTE a priori from the structure of the governing equations. The TTE can be interpreted in the form of a pde. Some common examples of multicomponent reactive transport problems are solved to physically demonstrate the influence of the OS TTE and confirm the theoretical TTE expressions. The general expressions for the TR and RT TTE are equal and opposite implying that the O(Δt) TTE can always be removed with standard alternating OS schemes. This result differs from previous research which has shown that alternating OS schemes are not useful for other types of reactive transport pdes.