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. In particular, the normal vector and the second fundamental tensor are linked to the particles and advected with them; in this way, the particles can be located upon the interface and enable a step-by-step calculation of the Level-Set function through a direct solution of the eikonal equation. No transport equation and reinitialization procedure for 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.