This paper is an overview of the finite element methods developed by the Team for Advanced Flow Simulation and Modeling (T*AFSM) [http://www.mems.rice.edu/TAFSM/] for computation flow problems with moving boundaries and interfaces. This class of problems include those with free surfaces, two-fluid interfaces, fluid-object and fluid-structure interactions, and moving mechanical components. The methods developed can be classified into two main categories. The interface tracking methods are based on the Deforming-Spatial-Deforming-Spatial-Domain/Stabilized Space-Time (DSD/SST) formulation, where the mesh moves to track the interface, with special attention paid to reducing the frequency of remeshing. The interface-capturing methods, typically used for free-surface and two-fluid flows, are based on the stabilized formulation, over non-moving meshes, of both the flow equations and the advection equation governing the time-evolution of an interface function marking the location of the interface. In this category, when it becomes necessary to increase the accuracy in representing the interface beyond the accuracy provided by the existing mesh resolution around the interface,he Enhanced-Discretization Interface-Capturing: Technique (EDICT) can be used to to accomplish that Real. In development of these two classes of methods, we had to keep in mind the requirement that tilt methods need to be applicable to 3D problems with complex geometries and that the associated large-scale computations need to be carried out on parallel computing platforms. Therefore our parallel implementations of these methods are based on unstructured grids and on both the distributed and shared memory parallel computing approaches. In addition to these two main classes of methods, a number of other ideas and methods have been developed to increase the scope and accuracy of these two classes of methods. The review of all these methods in our presentation here is supplemented by a number numerical examples from parallel computation of complex, 3D flow problems.
