Use of the particle level set method for enhanced resolution of free surface flows

A new numerical method for improving the mass conservation properties of the level set method when the interface is passively advected in a flow field is proposed. The method, a hybrid “Particle Level Set Method”, uses Lagrangian marker particles to rebuild a level set representation of the interface in regions which are under-resolved. This is often the case for flows undergoing stretching and tearing. A level set only approach towards maintaining small-scale interface features is subject to excessive amounts of numerical regularization. This numerical regularization artificially alters or destroy these features. By combining a simple Lagrangian method, massless marker particles, with the level set method, the ability to smoothly represent both large and small scale geometrical features is obtained while maintaining the implementation simplicity characteristic of the level set method. A variety of interface tracking tests, including a newly proposed three dimensional deformation flow test case, are performed to demonstrate that the method compares favorably with volume of fluid methods in the conservation of mass and purely Lagrangian schemes for interface resolution.; The robustness of the method in representing complex, three dimensional free surface fluid flows is illustrated through its use in producing physically based animations of the pouring of a glass of water; the splash generated by the impact of a ball thrown into a tank of water; and the breaking of a wave on a submerged beach. The behavior of the water is calculated by a three dimensional Navier-Stokes free surface fluid simulation. A novel application of a level set based velocity extrapolation technique is used to provide a smooth, physically based velocity field away from the liquid at the interface. This velocity field satisfies the physical boundary conditions at the interface and provides a plausible velocity field for use by Lagrangian particles outside the liquid as required by the “Particle Level Set Method”. Selected frames from each of the animations are provided.