As a key branch of operator-driven modal decomposition methods, global linear stability analysis (GLSA) has remained a major research focus in fluid mechanics. In this study, we present a novel approach to perform the GLSA of fluid-induced vibration problems. The underlying idea is the combination of a validated immersed boundary solver for the non-linear coupled dynamics with Krylov-based techniques to obtain a robust and accurate global stability solver for incompressible viscous flows. The computation of the leading eigenvalues of the linearized system is carried out in a matrix-free framework by adopting the ARPACK software package. The proposed algorithm avoids the complex analytical linearization of the equations while retaining arbitrary order eigenvalues and eigenvectors of the whole flow field. The methodology has been tested on flow past a circular cylinder at Recr=46.7 for stability, receptivity, and sensitivity. The obtained results show a good quantitative agreement with those available in the literature. Then, the method was applied to investigate wake flows behind four canonical blunt body geometries for comparative analysis: the circular cylinder, square prism, D-section prism, and D-shaped square prism, with particular emphasis on cases having small aspect ratios and configurations at Re among first instabilities, revealing the D-section prism to be the most unstable. Finally, a passive flow control analysis is conducted by adding control cylinders, demonstrating the different effects of control cylinders on growth rate and frequency. For the D-section prism, the controlled flow differs significantly from the others, indicating enhanced controllability or susceptibility to external perturbations.
Li et al. (Thu,) studied this question.