Lyapunov Inverse Iteration for Stability Analysis using Computational Fluid Dynamics

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.