A Streamline-Upwind/Petrov-Galerkin (SUPG) Finite Element (FE) Level Set method is presented, which may be used for solving problems involving incompressible two-phase flow with moving inter-phase boundaries. The method is three-dimensional, and can be used on both structured and unstructured grids. Two formulations are given. The first considers the coupled motion of both phases, and is implemented in the framework of the commercial Computational Fluid Dynamics (CFD) code CFX-4. The second can be applied for gas-liquid flows when effects of the gaseous phase on the motion of the liquid phase are negligible; consequently, the gaseous phase is removed from consideration. This Level Set formulation is implemented in the commercial CFD code FIDAP. The resulting Level Set formulations are tested on sample problems involving two-phase flows with density ratio of the order of 103 and viscosity ratio as high as 105. The numerical results are compared against experimental data.

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