Rudolph Manfred
Chemische Fakultät, Am Steiger 3, Friedrich-Schiller-Universität, D-07743 Jena, Germany.
J Comput Chem. 2005 Apr 30;26(6):633-41. doi: 10.1002/jcc.20201.
This article demonstrates that exponential convergence of the flux error can be achieved for any kinetic-diffusion system comprising an arbitrary number of (pseudo) first-order chemical reactions if the underlying PDEs are discretized as outlined for the box 2 or box 4 method in the preceding part of this article. By investigating the eigenvalues and eigenvectors of the first-order kinetic coupling matrix in general form the present article demonstrates that the simulation of any multispecies first-order kinetic diffusion system can be as accurately done as the simulation of a single representative one-species system. The Fourier coefficients governing the error level of the flux are much smaller in the limiting case of kinetic control as those reported in the preceding article for the limiting case of diffusion control. The higher rate of exponential convergence predicted on the basis of the mathematical model has been fully verified by the numerical results.
本文表明，如果按照本文前一部分中框2或框4方法所概述的那样对基础偏微分方程进行离散化，那么对于任何包含任意数量（伪）一级化学反应的动力学 - 扩散系统，通量误差都可以实现指数收敛。通过研究一般形式的一级动力学耦合矩阵的特征值和特征向量，本文表明，任何多物种一级动力学扩散系统的模拟都可以像单个代表性单物种系统的模拟一样准确。在动力学控制的极限情况下，控制通量误差水平的傅里叶系数比上一篇文章中报道的扩散控制极限情况下的傅里叶系数小得多。基于数学模型预测的更高指数收敛速率已得到数值结果的充分验证。
