An Immersed Boundary technique for the linear stability analysis of fluid-structure interactions

To date, the global stability analysis of three-dimensional elastic structures interacting with incompressible flows remains a prohibitive task due to the high computational costs. Here we present a Jacobian-free strategy to perform global stability analyses of interacting fluid-structure systems, which is incorporated into a validated FSI solver based on a Moving-Least-Squares Immersed Boundary. The linear stability analysis is carried out using the fluid-structure interaction solver as a black box to be interfaced with a matrix-free eigenvalue solver. The process consists of three different stages: 1) Determination of the equilibrium solution through the use of BoostConv, a stabilization procedure which numerically suppresses the instabilities and forces the simulation to converge towards the steady state; 2) Retrieval of the linear dynamics around the base state by numerically approximating the Jacobian-vector product; 3) Computation of the leading eigenvalues by supplying the matrix-vector product to an iterative eigenvalue solver. The procedure will be described in details and results on simple configurations will be compared with those obtained with mesh-deforming techniques. The efficiency and limitations of the proposed methodology will be discussed.