Abstract
Proper orthogonal decomposition (POD) based reduced-order modelling is demonstrated to be a weighted residual technique similar to Galerkin's method. Estimates of weighted residuals of neglected modes are used to determine relative importance of neglected modes to the model. The cumulative effects of neglected modes can be used to estimate error in the reduced order model. Thus, once the snapshots have been obtained under prescribed training conditions, the need to perform full-order simulations for comparison is eliminates. This has the potential to allow the analyst to initiate further training when the reduced modes are no longer sufficient to accurately represent the predominant phenomenon of interest. The response of a fluid moving at Mach 1.2 above a panel to a forced localized oscillation of the panel at and away from the training operating conditions is used to demonstrate the evaluation method.
Highlights
Computational determination of flutter boundaries in the transonic regime is an especially demanding problem owing to essential nonlinearities in the aerodynamics
To properly capture the effects of aerodynamic nonlinearities on flutter onset, time-integration methods based on the transonic small-disturbance [6], Euler [15], and Navier-Stokes [7,8,21] equations have been developed to simulate the behavior of aeroelastic systems
Reduced-order modeling (ROM) with proper orthogonal decomposition (POD) is being applied to unsteady flows for the purpose of developing control models of these systems [16,18]
Summary
Computational determination of flutter boundaries in the transonic regime is an especially demanding problem owing to essential nonlinearities in the aerodynamics. To properly capture the effects of aerodynamic nonlinearities on flutter onset, time-integration methods based on the transonic small-disturbance [6], Euler [15], and Navier-Stokes [7,8,21] equations have been developed to simulate the behavior of aeroelastic systems. Direct methods based on Hopf bifurcation theory have been developed to compute critical flutter onset speeds of the discrete aeroelastic equations without time integration [3,14]. The former class of techniques generally require large computation times due to the time-accurate nature of the calculations and the large integration times required to establish flow stability properties. In-situ monitoring promises to allow the analyst to adjust the ROM during simulation in an appropriate fashion to optimize for simulation speed and accuracy
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