Model studies of fluid-structure interaction problems

Abstract

In this work, we employ fluid-structure interaction (FSI) systems with immersed flexible structures with or without free surfaces to explore both Singular Value Decomposition (SVD)-based model reduction methods and mode superposition methods. For acoustoelastic FSI systems, we adopt a three-field mixed finite element formulation with displacement, pressure, and vorticity moment unknowns to effectively enforce the irrotationality constraint. We also propose in this paper a new Inf-Sup test based on the lowest non-zero singular value of the coupling matrix for the selection of reliable sets of finite element discretizations for displacement and pressure as well as vorticity moment. Our numerical examples demonstrate that mixed finite element formulations can be effectively used to predict resonance frequencies of fully coupled FSI systems within different ranges of respective physical motions, namely, acoustic, structural, and slosh motions, without the contamination of spurious (non-physical) modes with nonzero frequencies. Our numerical results also confirm that SVD-based model reduction methods can be effectively used to reconstruct from a few snapshots of transient solutions the dominant principal components with moderate level of signal to noise ratio, which may eventually open doors for simulation of long-term behaviors of both linear and nonlinear FSI systems.