Lyapunov Inverse Iteration for Stability Analysis using Computational Fluid Dynamics
Lyapunov Inverse Iteration for Stability Analysis using Computational Fluid Dynamics
复制标题
使用计算流体动力学进行稳定性分析的李雅普诺夫逆迭代
DOI：
10.2514/6.2012-1563
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
A. Spence
中科院分区：
文献类型：
--
作者：
S. Timme;K. Badcock;Minghao Wu;A. Spence
本文提出了一种新的非精确Lyapunov逆迭代方法，用于在计算流体动力学建模中分析带有Hopf分岔的气动弹性和流体稳定性问题。其思想是取雅可比矩阵及其对独立参数的导数，在平衡点处求值，以得到除了独立参数的临界值之外的临界特征对的估计。对于频率估计的先验知识，不需要在标准逆迭代中作为移位所要求的知识。给出了两自由度翼型和柔性翼遭遇颤振和低雷诺数流下圆柱后非定常旋涡脱落的试验案例。
The recently developed inexact Lyapunov inverse iteration method is presented for the analysis of aeroelastic and fluid stability problems with Hopf bifurcations when using computational fluid dynamics in the modelling. The idea is to take the Jacobian matrix and its derivative with respect to an independent parameter, both evaluated at an equilibrium point, to obtain estimates of the critical eigenpair in addition to the critical value of the independent parameter. Prior knowledge of a frequency estimate, required as shift in standard inverse iteration, is not needed. The test cases presented include a two–degrees– of–freedom aerofoil and a flexible wing encountering flutter, and unsteady vortex shedding behind a circular cylinder in low Reynolds number flow.