In-Situ Residual Tracking in Reduced Order Modelling

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.