Using the Particle Level Set Method and a Second Order Accurate Pressure Boundary Condition for Free Surface Flows

In this paper, we present an enhanced resolution capturing method for topologically complex two and three dimensional incompressible free surface flows. The method is based upon the level set method of Osher and Sethian to represent the interface combined with two recent advances in the treatment of the interface, a second order accurate discretization of the Dirichlet pressure boundary condition at the free surface (2002, J. Comput. Phys.176, 205) and the use of massless marker particles to enhance the resolution of the interface through the use of the particle level set method (2002, J. Comput. Phys., 183, 83). Use of these methods allow for the accurate movement of the interface while at the same time preserving the mass of the liquid, even on coarse computational grids. Also, these methods complement the level set method in its ability to handle changes in interface topology in a robust manner. Surface tension effects can be easily included in our method. The method is presented in three spatial dimensions, with numerical examples in both two and three spatial dimensions.