| A stabilized finite element formulation is presented for solving multiphase fluid flows. The time-discontinuous Galerkin space-time method is employed with least squares stabilization operators for both advective-diffusive control and equal-order interpolation. Local instantaneous balance equations for mass, momentum and energy are developed for fluid flows containing singular surfaces. Macroscopic balance equations are developed by averaging the microscopic local instantaneous formulation. The equations are expressed in terms of physical entropy variables for both liquids and gases. A general expression for interfacial momentum is developed which does not rely upon flow dependent parameters. A predictor-multicorrector solution strategy is implemented to solve the complete system. Tracking of phases is accomplished through the solution of volume fraction conservation equations. The performance of the method is demonstrated by the solution of several numerical examples. A review of other methods for two-phase flow simulations is also provided. |
