A Hybrid Particle Level Set Method forImproved Interface Capturing

In this paper, we propose 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. Our method uses Lagrangian marker particles to rebuild the level set in regions which are under-resolved. This is often the case for flows undergoing stretching and tearing. The overall method maintains a smooth geometrical description of the interface and the implementation simplicity characteristic of the level set method. Our method compares favorably with volume of fluid methods in the conservation of mass and purely Lagrangian schemes for interface resolution. The method is presented in three spatial dimensions. ∗Research supported in part by an ONR YIP and PECASE award N00014-01-1-0620, and NSF DMS-0106694 †Research supported in part by DOE under the ASCI Academic Strategic Alliances Program (LLNL contract B341491) ‡Scientific Computing Computational Mathematics Program, Stanford University, Stanford, California 94305 §Computer Science Department, Stanford University, Stanford, California 94305 ¶Mechanical Engineering Department, Stanford University, Stanford, California 94305 ‖Research supported in part by DARPA under the Software Enabled Control Program (AFRL contract F33615-99-C-3014)