Second-order splitting schemes for a class of reactive systems

We consider the numerical time integration of a class of reaction–transport systems that are described by a set of ordinary differential equations for primary variables. In the governing equations, the terms involved may require the knowledge of secondary variables, which are functions of the primary variables. Specifically, we consider the case where, given the primary variables, the evaluation of the secondary variables is computationally expensive. To solve this class of reaction–transport equations, we develop and demonstrate several computationally efficient splitting schemes, wherein the portions of the governing equations containing chemical reaction terms are separated from those parts containing the transport terms. A computationally efficient solution to the transport sub-step is achieved through the use of linearization or predictor–corrector methods. The splitting schemes are applied to the reactive flow in a continuously stirred tank reactor (CSTR) with the Davis–Skodjie reaction model, to the CO+H2CO+H2 oxidation in a CSTR with detailed chemical kinetics, and to a reaction–diffusion system with an extension of the Oregonator model of the Belousov–Zhabotinsky reaction. As demonstrated in the test problems, the proposed splitting schemes, which yield efficient solutions to the transport sub-step, achieve second-order accuracy in time.