Reduced-Order Model Development Using Proper Orthogonal Decomposition and Volterra Theory

Abstract

A new approach for generating reduced-order models of fluid systems was developed using proper orthogonal decomposition in combination with Volterra theory. The method involves identifying fluid basis functions with proper orthogonal decomposition and applying systems realization theory to generate a low-dimensional model for the scalar coefficients. The method was tested on a two-dimensional inviscid flow over a bump with forcing. Eight fluid basis functions were identified, and the eigensystem realization algorithm was used to identify an eight-state, reduced-order model. Time histories of both the reduced-order coefficients and the expanded flowfield data accurately tracked the full-order results in both amplitude and phase (average error less than 5%). The reduced-order model demonstrated four-orders-of-magnitude reduction in compute time relative to the full system, which represents a computational improvement on the same order as the reduction in degrees of freedom.