A New Koopman-Inspired Approach to Match Flow Field Excitation with Consequent Structure Responses for Nonlinear Fluid-Structure Interactions

This work presents a novel method to form constitutive fluid-to-structure, excitation-to-response correspondences for insights into nonlinear fluid-structure interactions (FSI). The method combines the Fourier analysis’s temporal orthogonality to match like-frequency modal components into fluid-structure pairs and utilizes the proper orthogonal decomposition (POD)’s phenomenological visualization to identify each pair’s underlying mechanisms. Exploiting the latest data-driven algorithm, the dynamic mode decomposition (DMD), it serves as a Koopman-inspired, POD-projected, and machine-learning-embedded method that can be seen as an advanced discrete Fourier/Z-transform. Successful implementation with a prism wake with homogenous and anisotropic turbulence attests to its capability to handle a broad spectrum of problems involving nonlinear and stochastic dynamics. A user guideline has been offered in this work, which is pedagogically demonstrated via a classical FSI system.