Operator-splitting procedures for reactive transport and comparison of mass balance errors

Abstract

Operator-splitting (OS) techniques are very attractive for numerical modelling of reactive transport, but they induce some errors. Considering reactive mass transport with reversible and irreversible reactions governed by a first-order rate law, we develop analytical solutions of the mass balance for the following operator-splitting schemes: standard sequential non-iterative (SNI), Strang-splitting SNI, standard sequential iterative (SI), extrapolating SI, and symmetric SI approaches. From these analytical solutions, the operator-splitting methods are compared with respect to mass balance errors and convergence rates independently of the techniques used for solving each operator. Dimensionless times, N OS, are defined. They control mass balance errors and convergence rates. The following order in terms of decreasing efficiency is proposed: symmetric SI, Strang-splitting SNI, standard SNI, extrapolating SI and standard SI schemes. The symmetric SI scheme does not induce any operator-splitting errors, the Strang-splitting SNI appears to be O( N OS 2) accurate, and the other schemes are first-order accurate.