Adaptive stabilized finite element analysis of multi-phase flows using level set approach

Multiphase flows containing mixtures of liquids, gases, and solids abound in both nature and many technological processes. The present work is focused on developing a stabilized finite element method to solve the multi-phase compressible/incompressible flow problems in three dimensions using a level set approach. The Streamline-Upwind/Petrov-Galerkin method was used to discretize the governing flow and level set equations. The method developed enables accurate computation of flows with large density and viscosity differences and allows the fronts to self-intersect, merge, break, and change topology. An adaptive-mesh strategy was designed to study various problems with reduced computational cost. Additionally, the "Ghost Fluid Method" was generalized for the finite element framework to solve multi-fluid systems with vast physical property differences. Furthermore, a fourth order accurate, explicit time integrator has been implemented to advance in time. These strategies are novel in the field of computational fluid dynamics and are expected to have a major impact on the efficient finite element analysis of multiphase flows.; Various numerical studies were performed, namely, effect of viscosity and surface tension on single and multiple bubble dynamics, non-linear dynamics of free surface flows, single and two-phase shock tubes, converging spherical shock and Rayleigh-Taylor interfacial instabilities. Using the developed framework, an effort is made to develop a three-dimensional algorithm for the hydrodynamic simulation of single bubble sonoluminescence. As a preliminary step towards the simulation of single bubble sonoluminescence, the hydrodynamics of the collapse and rebound of a 10 micron air bubble in water is studied with direct numerical simulations, It was shown that due to the inertial effect of the liquid compressing the gas, a bubble implosion takes place. The air bubble reaches a minimum radius during the implosion and then bounces back due to the high internal gas pressure. The motion of the air/water interface during the initial stages of the collapse was found to be consistent with the Rayleigh-Plesset model. However, the three dimensional simulations show that during the final stage of energetic implosions, the bubble may become asymmetric.