Operator splitting for stiff chemical reaction systems

Abstract

AbstractChemical reaction systems often result in high‐dimensional, stiff differential equations. Solving these differential equations is computational demanding. The computational effort can be reduced by the usage of an operator splitting scheme. The most frequently used splitting schemes are the Lie‐Trotter splitting [1] and the Strang splitting [2]. However, the usage of a splitting scheme results in an additional splitting error. The Lie‐Trotter splitting is a first order scheme, and the Strang splitting is a second order scheme. If the timescale of the fastest chemical reaction is smaller than the splitting time step, the Strang splitting suffers from order reduction. Therefore, the Lie‐Trotter splitting and the Strang splitting are first order schemes for reasonable step sizes. The Richardson extrapolation of the Lie‐Trotter splitting is a second order scheme. We show that the Richardson extrapolation does not suffer from order reduction for a splitting between a fast chemical source term and a slow transport term.