Numerical simulation of interface time evolution by oriented lagrangian particles and level-set method

A new computational approach for tracking evolving interfaces is proposed. The procedure is based on the coupling of lagrangian massless particles and the standard Level-Set methodology, and the use of evolution equations for fundamental vector and tensor quantities related to the geometrical properties of the interface Γ. In particular, the normal vector n and the second fundamental tensor ▽ n are linked to the particles and advected with them; in this way, the particles can be located upon Γ and enable a step-by-step calculation of the Level-Set function φ through a direct solution of the eikonal equation. No transport equation and reinitialization procedure for φ have to be taken into account and the usual numerical diffusion affecting the Level-Set approach is removed. The method is easy to code and carries out an accurate reconstruction of the front, limited only by the spatial resolution of the mesh. © 2009 by ASME.