Practical Aspects of the Implementation of Proper Orthogonal Decomposition

This paper discusses two practical aspects of the implementation of reduced-order models based on proper orthogonal decomposition (POD). The POD method calculates basis functions used in a reduced-order representation of two-phase flow in fluidized beds by calculating the eigenvectors of an autocorrelation matrix composed of snapshots of the flow. The aspects discussed are: (i) the time sampling of snapshots that minimize error in the POD reconstruction of the flowfield, and (ii) the form of the autocorrelation matrix that minimizes error in the POD reconstruction of the flowfield. Two regions in the flow are identified, a transient region and a quasi-steady region. Two methods are then proposed for time sampling the flow to retain additional snapshots in the transient region. Both methods are shown to produce less error than the case where snapshots are sampled a constant frequency. A time sampling rate based on a logarithmic distribution with 200 snapshots is shown to produce error on the same order as an evenly spaced snapshot database with 800 snapshots. The composition of the autocorrelation matrix is also considered. An approach treating field variables entirely separately is shown to produce less error than a coupled approach when the field variables are reconstructed.

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