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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. [ABSTRACT FROM AUTHOR]

An introduction to this issue is presented in which the editors discuss topics including fluid-structure interaction (FSI) modeling, Stokes interface problem, and finite element method.

We investigate the instability and subsequent dynamics of a closed rod with twist and bend in a viscous, incompressible fluid. A new version of the immersed boundary (IB) method is used in which the immersed boundary applies torque as well as force to the surrounding fluid and in which the equations of motion of the immersed boundary involve the local angular velocity as well as the local linear velocity of the fluid. An important feature of the IB method in this context is that self-crossing of the rod is automatically avoided because the rod moves in a continuous (interpolated) velocity field. A rod with a uniformly distributed twist that has been slightly perturbed away from its circular equilibrium configuration is used as an initial condition, with the fluid initially at rest. If the twist in the rod is sufficiently small, the rod simply returns to its circular equilibrium configuration, but for larger twists that equilibrium configuration becomes unstable, and the rod undergoes large excursions before relaxing to a stable coiled configuration. [ABSTRACT FROM AUTHOR]