Continuation Method for Calculation of Transonic Airfoil Flutter Boundaries

Reduced-order modelling of limit-cycle oscillation for aeroelastic systems

“…The aerodynamic equations are discretized in space to second-order accuracy with an upwind total variation diminishing (TVD) scheme previously applied to unsteady aerodynamic and aeroelastic problems (Pettit and Beran, 2000;Beran and Morton, 1997). Following discretization, the aerodynamic equations take the form '…”

“…These methods can provide accurate approximations of system behavior, but generally require very large computation times owing to the time-accurate nature of the calculations and the large integration times required to establish flow stability properties. Direct methods formulated from Hopf bifurcation theory have been developed to compute flutter and LCO onset speeds of aeroelastic systems without time integration [Beran and Morton (1997); Beran (1998); Morton and Beran (1999); Beran (1999)], but become computationally expensive when system order becomes large. Recent work has been carried out to apply POD to the Euler equations in an effort to capture aerodynamic nonlinearities in a reduced-order aeroelastic model.…”