Pragmatic Apparatus – Spectral Characterization by the Koopman Linearly-Time-Invariant Analysis: Constitutive Fluid-Structure Correspondence

Cited by Lee Sonogan

Reduced-order models for coupled dynamical systems: Data-driven methods and  the Koopman operator: Chaos: An Interdisciplinary Journal of Nonlinear  Science: Vol 31, No 5

Abstract by Cruz Y. Li, Zengshun Chen, Tim K.T. Tse, Asiri Umenga Weerasuriya, Xuelin Zhang, Yunfei Fu, Xisheng Lin

This work delineates a new architecture of the Koopman operatory theory called the Koopman Linearly-Time-Invariant (Koopman-LTI) analysis. The Koopman-LTI is formulated to explain fluid-structure interactions by providing a constitutive relationship between fluid excitation and structural pressure response. Results from a demonstrative rendering on a prototypical fluid-structure system, the subcritical prism wake, showed that the Koopman-LTI globally linearizes and approximates the original flow into a linear superposition of temporally orthogonal Ritz descriptors. The approximation proved close to exact and perennially stable. The subsequent analysis of 18 Koopman-LTI systems also alluded to the a posteriori existence of a configuration-wise universal Koopman system. Spectral characterization of the system suggested the complex morphology of the prism wake during the shear layer transition II consists of only six dominant and constitutively interactive excitation-response mechanisms. Merely two excitations at St=0.1242 and 0.0497 primarily dictate the behaviours of the upstream and crosswind walls, and four other collectively distinct mechanisms at St=0.0683, 0.1739, 0.1925, and 0.2422 overshadow the downstream wall. The success with a free-shear configuration and inhomogeneous and anisotropic turbulence attests to the applicability of the Koopman-LTI to a range of fluid-structure systems. The Koopman-LTI also stands as a new system identification method of vast practical significance because, through it, one can pinpoint the exact fluid origin of a specific pressure pattern of structural response, or vice versa. It also illuminates one visionary possibility to reduce the intricacies of fluid-structure interaction into constitutive correspondences that are identifiable by inspection — making the complicated matter ever so straightforward.

Publication: Cornell University (Peer-Reviewed Journal)

Pub Date: 6 Dec, 2021 Doi: https://arxiv.org/abs/2112.02985

Keywords: Fluid Dynamics, Pragmatic Linear, Time-Invariant, Constitutive Correspondence

https://arxiv.org/abs/2112.02985 (Plenty more sections and references in this research article)

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