Fluid-structure interaction analysis with interface control principle

TL;DR

This work tackles the high computational cost of unsteady FSI by introducing an interface control principle that minimizes the interface residual force between fluid and structure. A data-driven interface model combines SINDYc for the fluid force with a linear discrete model for the structure, enabling non-iterative coupling by driving the interface toward a coupled state and predetermined interface inputs for each subsystem. Demonstrations on vortex-induced vibration of a cylinder at Re = 150 show the residual force can be driven to near zero, yielding accurate limit-cycle behavior and good agreement with reference FSI in amplitude and frequency, even when starting from varied initial conditions. The approach promises reduced inter-system communication and computational overhead, with robustness observed under small contraction gains and within the lock-in regime, though accuracy hinges on the fluid ROM quality.

Abstract

An interface control principle is proposed for unsteady fluid-structure in- teraction (FSI) analyses. This principle introduces a method of explicitly controlling the interface motion in the temporal direction to minimize the residual force on the interface, which is defined as the discrepancy between the fluid and structural forces. The interface model is constructed using a data-driven approach that involves sparse identification of nonlinear dy- namics with control to evaluate the residual force. The interface model is subsequently subjected to control theory in order to minimize the residual force. Following the convergence of the residual force, the interface state is controlled to be that of the original unsteady FSI system. The fluid and structural simulations can be conducted independently without communication, as the interface state information is predetermined as inputs for each system. The proposed method is applied to the vortex-induced vibration (VIV) of a cylinder at a Reynolds number of 150 under several reduced velocity conditions corresponding to the lock-in regime with limit-cycle oscillations. The results demonstrate that the residual force is sufficiently minimized in time, and when the residual force is close to zero, the predicted fluid force and structural displacement of the VIV show good agreement with the reference FSI simulation.

Figures (10)

• Figure 1: Schematic of the interface control principle for the residual force minimization.
• Figure 2: Flow chart of the proposed method for minimizing the residual force and predicting the physical quantities.
• Figure 3: Schematic of VIV for two-dimensional cylinder.
• Figure 4: Comparisons of the maximum cylinder displacements for each $U^{*}$ between the present work and previous studies ahn2006stronglyborazjani2008curvilinear
• Figure 5: Time histories of $C_L$ (red solid lines) and $y^*$ (blue dashed lines) in the reference FSI simulations at (a) $U^{*}=4$, (b) $U^{*}=5$, (c) $U^{*}=6$, and (d) $U^{*}=7$. The training dataset is represented by the gray shading in each case.