
In the study of biological systems, the coupling of fluid and solid/structure plays an important role. Traditionally, staggered iterations are used to link available finite element codes with computational fluid dynamics codes. Although this procedure is convenient, complex dynamical system behaviors often get lost in the process. In order to derive corresponding system model reduction procedures, and more importantly, effectively and efficiently capture the system dynamical behaviors, we must solve fluid–solid interaction (FSI) systems simultaneously as a whole. Current development of immersed boundary/continuum methods has demonstrated the feasibility and potential in handling complex FSI systems with significant solid/structure motions. Since its inception, the immersed boundary method has been extended to a variety of problems. The initial application of this method is for very flexible structures for which time step restriction is not so severe. In current versions of immersed boundary methods, complex nonlinear structures can be represented by both elastic fiber and beam (rod) networks. In addition, sophisticated nonlinear solid models have also be introduced in immersed finite element formulations. The preliminary results of the implicit compressible immersed continuum method have shown that reasonable time steps can be used for stiff FSI systems. Moreover, it is possible to apply immersed boundary/continuum methods to compressible fluid flow problems. This chapter provides an overview of recent development of these immersed finite element methods.
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