Divergence-Free Bases and Multiresolution Methods for Reduced-Order Flow Modeling
Jeonghwan Ko, Andrew J. Kurdila, Othon K. Rediniotis · AIAA Journal · 2000
While reduced order modeling methods have flourished in the study of structural system dynamics, similar methodologies for the representation of flow are few in comparison. This paper presents a novel methodology based on biorthogonal wavelet constructions and multiresolution analysis for order reduction of velocity fields obtained via digital particle image velocimetry or computational fluid dynamics. The derivation, algorithmic implementation, and experimental verification of fast projective filtering methods based on divergence-free wavelets are discussed. Experimental evidence presented in this paper demonstrates the feasibility of achieving several hundred fold compression for typical velocity fields obtained via experiments using particle image velocimetry. The results in this paper also illustrate the feasibility and amenability of wavelet methods for diverse problems of interest to the aerospace community including (i) experimental data denoising, (ii) local cross-correlation c...