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Second-order splitting schemes for a class of reactive systems

机译：一类反应系统的二阶分裂方案

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摘要

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 + H-2 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. (C) 2008 Elsevier Inc. All rights reserved.
机译：我们考虑一类反应-传输系统的数值时间积分，该系统由一组主要变量的常微分方程描述。在控制方程中，涉及的术语可能需要了解次级变量，这些变量是初级变量的函数。具体来说，我们考虑以下情况：给定主要变量，对次要变量的评估在计算上非常昂贵。为了解决这类反应-传输方程，我们开发并演示了几种计算有效的拆分方案，其中控制方程中包含化学反应项的部分与包含传输项的部分是分开的。通过使用线性化或预测器校正器方法，可以实现对运输子步骤的高效计算解决方案。拆分方案适用于具有Davis-Skodjie反应模型的连续搅拌釜式反应器（CSTR）中的反应流，具有详细化学动力学的CSTR中CO + H-2氧化以及具有以下特征的反应扩散系统Belousov-Zhabotinsky反应的Oregonator模型的扩展。如测试问题所示，提出的拆分方案为运输子步骤提供了有效的解决方案，并在时间上达到了二阶精度。 （C）2008 Elsevier Inc.保留所有权利。

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