Arnoldi方法简述及其在流动稳定性中的应用  

Arnoldi Method and Its Application in Flow Stability Problem

作　　者：李武庸 涂国华[2,3] 陈曦 LI Wu-yong;TU Guo-hua;CHEN Xi(School of Aerodynamics,Mathematics and Statistics,Yunnan University,Kunming 650500,China;State Key Laboratory of Aerdynamics,China Aerodynamics Research and Development Center,Mianyang 621000,China;Computational Aerodynamics Institute,China Aerodynamics Research and Development Center,Mianyang 621000,China)

机构地区：[1]云南大学数学与统计学院,云南昆明650500 [2]中国空气动力研究与发展中心空气动力学国家重点实验室,四川绵阳621000 [3]中国空气动力研究与发展中心计算空气动力研究所,四川绵阳621000

出　　处：《气体物理》2022年第5期16-28,共13页Physics of Gases

基　　金：国家重点研发计划(2016YFA0401200);国家数值风洞工程(2018-ZT1A03)。

摘　　要：流动稳定性问题常常归结于巨型非对称矩阵特征值问题。多数求解巨型非对称矩阵特征问题的算法均是经基本的Arnoldi算法演化而来。首先简述基本的Arnoldi算法;其次简述基于Arnoldi算法的几类变体,如显式重启Arnoldi算法,隐式重启Arnoldi算法与多重隐式重启Arnoldi算法;最后基于Arnoldi算法及其变体结合谱位移技术求解计算流动稳定性问题,并通过数值实验比较可知结合谱位移技术的多重隐式重启Arnoldi算法的求解效率最高。The problem of flow stability is often attributed to the eigenvalue problem of giant asymmetric matrix.Most algorithms for solving the eigenvalue problems of giant asymmetric matrices are evolved from the basic Arnoldi algorithm.Firstly,the basic Arnoldi algorithm was briefly described.Secondly,several variants based on Arnoldi algorithm were briefly described,such as explicitly restarted Arnoldi algorithm,implicitly restarted Arnoldi algorithm and multiple implicitly restarted Arnoldi algorithm.Finally,the Arnoldi algorithm and its variants,combined with spectral displacement technology to solve the problem of flow stability.Through numerical experiments,it is found that the multiple implicitly restarted Arnoldi algorithm combined with spectral displacement technology has the highest efficiency.

关 键 词：Arnoldi算法 特征值 HESSENBERG矩阵 流动稳定性 

分 类 号：O302[理学—力学] O355