Numerical simulation of immiscible fluids with FEM level set techniques

Abstract

Multiphase flows, including free surface and two-phase flows, are commonly encountered in many industrial applications. Effects of wave phenomena are for example important when designing boats, drop formation is essential for ink jet printers, and bubbles may come into play in chemical reactors and heat exchangers. Numerical simulation of these phenomena is a complex and challenging task. The desire to have both high accuracy and computational speed often stands in direct contradiction to each other. The aim of this thesis was to describe a suitable methodology with potential to be both very accurate and also efficient. High resolution benchmarks were also developed in order to validate and quantify the performance of a code (TP2D) developed according to the presented approach. The developed methodology combined a non-conforming finite element discretization with the level set method for tracking the interfaces. A semi-implicit approach to implementing surface tension forces was also derived, which allowed for significantly larger time steps in comparison with the traditional explicit approach. The benchmarks were used to compare the developed code with two commercial CFD codes (Comsol Multiphysics and Ansys Fluent). The commercial codes did not show strong convergence towards the reference solution, in contrast to TP2D which was both faster and significantly more accurate. TP2D even computed a more accurate solution on the very coarsest grid compared to the best results of the commercial codes.