Linear stability analysis of fluid–structure interaction problems with an immersed boundary method

In this work, we present a novel approach to perform the linear stability analysis of fluid-structure interaction problems. The underlying idea is the combination of a validated immersed boundary solver for the nonlinear coupled dynamics with Krylovbased techniques to obtain a robust and accurate global stability solver for elastic structures interacting with incompressible viscous flows. The computation of the leading eigenvalues of the linearized system is carried out in a matrix-free framework by adopting a classical Krylov subspace method. The proposed algorithm avoids the complex analytical linearization of the equations while retaining all the relevant aspects of the fully-coupled fluid-structure system. The methodology has been tested for several cases involving two-dimensional incompressible flows around elastically mounted circular cylinders. The obtained results show a good quantitative agreement with those available in the literature. Finally, the method was applied to investigate the linear stability of the laminar flow past two elastically mounted cylinders in tandem configuration at Re = 100, revealing the existence of two complex dominant modes. For low values of the reduced velocity U*, only one mode is found to be unstable and related to the stationary wake mode. The loss of stability of the second mode at U* = 4 marks the beginning of the lock-in region. We also show that for U* = 5 the modes interact, giving rise to the beating phenomenon observable in the nonlinear time evolution of the system. For larger values of the reduced velocity, the linear dynamics is governed by one dominant mode characterized by wider oscillations of the rear cylinder, matching the results of the nonlinear simulations.(c) 2022 Elsevier Ltd. All rights reserved.