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

Abstract

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 (Δ t) 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 sol..