A Fast Level Set Method with Particle Correction on Adaptive Cartesian Grid

The level set method, devised by Osher and Sethian in 1988, is a powerful approach for tracking moving interfaces and widely used in physics, fluid mechanics, chemistry, combustion, material science, image processing etc. During the past two decades, the level set method has been under significant development. Techniques of solving the level set equation, including high-order essentially non-oscillatory (ENO) schemes, the discontinuous Galerkin (DG) method, weight ENO (WENO) schemes and hybrid particle level set method, have been developed on both structure uniform mesh and unstructured mesh. In this paper, following the work by Strain, a second-order semi-Lagrangian level set method is developed and coupled with a new efficient particle correction algorithm on 2D adaptive Cartesian mesh. This solver is general and capable of solving 2D interface moving problems under different velocity fields, including passive transport fields, first-order and second-order geometric velocity. Through the particle correction algorithm, the semi-Lagrangian level set method can achieve much better mass conservation. Numerical results are presented and compared with other simulations to demonstrate the ability of the level set solver developed in this paper.