Modeling of fluid-structure interaction

The interaction of a flexible structure with a flowing fluid in which it is submersed or by which it is surrounded gives rise to a rich variety of phy sical phenomena with applications in many fields of engineering, for exampl e, the stability and response of aircraft wings, the flow of blood through arteries, the response of bridges and tall buildings to winds, the vibratio n of turbine and compressor blades, and the oscillation of heat exchangers. To understand these phenomena we need to model both the structure and the fluid. However, in keeping with the overall theme of this volume, the empha sis here is on the fluid models. Also, the applications are largely drawn f rom aerospace engineering although the methods and fundamental physical phe nomena have much wider applications. In the present article, we emphasize r ecent developments and future challenges. To provide a context for these, t he article begins with a description of the various physical models for a f luid undergoing time-dependent motion, then moves to a discussion of the di stinction between linear and nonlinear models, time-linearized models and t heir solution in either the time or frequency domains, and various methods for treating nonlinear models, including time marching, harmonic balance, a nd systems identification. We conclude with an extended treatment of the mo dal character of time-dependent flows and the construction of reduced-order models based on an expansion in terms of fluid modes. The emphasis is on t he enhanced physical understanding and dramatic reductions in computational cost made possible by reduced-order models, time linearization, and method ologies drawn from dynamical system theory.