The rapid developments of computational mechanics and computer technology during the last two decades have brought immensely powerful computational tools at the disposal of scientists and engineers. With the recent advent of teraflop and parallel computers, simulation-based engineering processes are gaining more acceptance and are rapidly becoming viable design alternatives. Furthermore, the traditional classification of various disciplines of mechanics has been blurred, and interaction problems involving two or more disciplines are often encountered in ever more challenging engineering practices. One of such interactive disciplines is fluid-solid interaction (FSI), which is the triangle discipline among fluid mechanics, solid mechanics, and dynamics. Although significant progress has been made on developing finite element methods (FEM) and computational fluid dynamics (CFD) for single-field problems, namely, solids or fluids, and to some extent, general procedures for combining FEM with CFD in the study of FSI systems, effective solution strategies of instability analysis for extremely large nonlinear dynamical systems derived from semi-discretized FSI systems have not been well established. Starting from a brief overview of various FSI analysis tools, this paper illustrates a few efficient algorithms using the existing time-stepping FEM and CFD codes for general purpose instability analysis of large FSI systems.

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