Fast Approximated POD for a Flat Plate Benchmark with a Time Varying Angle of Attack

Abstract

An approximate POD algorithm provides an empirical Galerkin approximation with guaranteed a priori lower bound on the required resolution. The snapshot ensemble is partitioned into several sub-ensembles. Cross correlations between these sub-ensembles are approximated in terms of a far smaller correlation matrix. Computational speedup is nearly linear in the number of partitions, up to a saturation that can be estimated a priori. The algorithm is particularly suitable for analyzing long transient trajectories of high dimensional simulations, but can be applied also for spatial partitioning and parallel processing of very high spatial dimension data. The algorithm is demonstrated using transient data from two simulations. First, a two dimensional simulation of the flow over a flat plate, as it transitions from AOA = 30° to a horizontal position and back. Second, a three dimensional simulation of a flat plate with aspect ratio two as it transitions from a horizontal position to AOA = 30°.

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