Multi-Phase Flow Computation with Semi-Lagrangian Level Set Method on Adaptive Cartesian Grids

The level set method, introduced by Osher and Sethian in 1988, is a powerful numerical approach for computing multi-phase flow problems. In 1994, Sussman, et al employed the level set approach to solve 2D incompressible two-phase flow problems. This approach was improved again by Sussman, et al in 1998. These methods are accurate but designed for structured uniform meshes only. In this paper, a quadtree-based fast Semi-Lagrangian level set method is coupled with a characteristics upwind finite volume incompressible flow solver to tackle multi-phase flow problems. By using unstructured adaptive Cartesian grids with automatic refinement near the interface, the solution accuracy and efficiency is dramatically improved. Several representative multi-phase flow problems are tackled to evaluate the effectiveness of the method. The computational results using the adaptive grids are compared with the results using uniform grids to demonstrate the ability of the method.