Flow problems with free and moving boundaries are encountered in many engineering applications. Flow in dams, pollutant transport in unconfined aquifers, viscous flow on the ocean free surface, molten metal flows, casting, sloshing in tanks, oil recovery, and open channel flows are examples in this category. In modeling steady and unsteady flow with viscous fluid interfaces, the location of the interface is also a part of the overall solution and needs to be determined. Accurate representation of the interface is one of the major challenges in simulation of this class of fluid dynamics problems, particularly when the flow has nonlinear characteristics. The finite element method (FEM), based on an approximation of field variables over a finite element mesh, has turned out to be one of the major numerical techniques for handling these types of problems. The FE numerical model in this book is formulated using an interface-capturing technique. The adopted interface-capturing technique is based on an algorithm derived from the level set method (LSM), and the Eulerian framework constitutes the main basis of the formulations.

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