Direct aeroelastic bifurcation analysis of a symmetric wing based on Euler equations

The application of a sparse matrix solver for the direct calculation of Hopf bifurcation points for the flexible AGARD 445.6 wing in a transonic flow modeled using computational fluid dynamics is considered. The iteration scheme for solving the Hopf equations is based on a modified Newton's method. Direct solution of the linear system for the updates has previously been restrictive for application of the method, and the sparse solver overcomes this limitation. Previous work has demonstrated the scheme for aerofoil calculations. The current paper gives the first three-dimensional results with the method, showing that an entire flutter boundary for the AGARD 445.6 wing can be traced out in a time comparable to that required for a small number of time-marching calculations, yielding two orders of magnitude improvement when compared to the time-marching approach.