求解刚性燃烧化学反应系统的Krylov子空间中的指数积分法  

An Exponential Integrator in Krylov Subspace to Solve Stiff Combustion Chemical Reaction System

作　　者：刘再刚 孔文俊[1,2] LIU Zai-Gang1,2 ,KONG Wen-Jun1,2(1. Key Laboratory of Light-Duty Gas-Turbine, Institute of Engineering Thermophysics Chinese Academy of Sciences, Beijing 100190, China; 2. University of Chinese Academy of Sciences, Beijing 100049, Chin)

机构地区：[1]中国科学院轻型动力重点实验室,中国科学院工程热物理研究所,北京100190 [2]中国科学院大学,北京100049

出　　处：《工程热物理学报》2018年第9期2062-2071,共10页Journal of Engineering Thermophysics

基　　金：国家自然科学基金资助项目(No.91441131); 国家重点基础研究发展规划项目(No.2014CB239603)

摘　　要：为了提高求解大时间步长的刚性燃烧化学反应方程组的效率,本文发展了一种使用Krylov子空间中的指数积分(EIKS)求解的方法。该方法基于多时间尺度法(MTS),使用指数积分格式求解线性化后的化学反应方程组,并使用Krylov子空间方法进行矩阵降维。本文使用MTS-EIKS方法模拟了H_2/CO/空气和CH4/空气的自着火过程,并引入自相关动态自适应化学(CoDAC)机理简化。结果表明,CoDAC-MTS-EIKS的联合简化加速方法可以准确、快速地模拟时间步长为10^(-6)s的自着火问题,在计算大步长刚性燃烧化学反应方程组方面有很好的应用前景。In order to improve the efficiency in solving stiff combustion chemical reaction equations with large time steps, an exponential integrator in Krylov subspace（EIKS） was developed. The method is based on the Multi-timescale（MTS） method. It employs exponential scheme to solve linearized stiff chemical reaction equations, and to reduce matrix dimension with Krylov subspace method. The MTS-EIKS was used to simulate the ignition delays of mixtures of H2/CO/air and CH4/air. Additionally, the Correlated dynamic adaptive chemistry（CoDAC） method was introduced.The results show that the combined reduction method CoDAC-MTS-EIKS method can predict the ignition delays accurately and efficiently with a time steps of 10^-6s, which demonstrates that the method has a good application prospect in solving stiff chemistry problems with large time steps.

关 键 词：刚性微分方程组 多时间尺度 KRYLOV子空间 指数积分 自相关动态自适应化学 

分 类 号：TK16[动力工程及工程热物理—热能工程]