A self-adaptive oriented particles Level-Set method for tracking interfaces

A new method for tracking evolving interfaces by lagrangian particles in conjunction with a Level-Set approach is introduced. This numerical technique is based on the use of time evolution equations for fundamental vector and tensor quantities defined on the front and represents a new and convenient way to couple the advantages of the Eulerian description given by a Level-Set function ϕϕ to the use of Lagrangian massless particles. The term oriented points out that the information advected by the particles not only concern the spatial location, but also the local (outward) normal vector n to the interface ΓΓ and the second fundamental tensor (the shape operator) ∇n∇n. The particles are exactly located upon ΓΓ and provide all the requested information for tracking the interface on their own. In addition, a self-adaptive mechanism suitably modifies, at each time step, the markers distribution in the numerical domain: each particle behaves both as a potential seeder   of new markers on ΓΓ (so as to guarantee an accurate reconstruction of the interface) and a de-seeder   (to avoid any useless gathering of markers and to limit the computational effort). The algorithm is conceived to avoid any transport equation for ϕϕ and to confine the Level-Set function to the role of a mere post-processing tool; thus, all the numerical diffusion problems usually affecting the Level-Set methodology are removed. The method has been tested both on 2D and 3D configurations; it carries out a fast reconstruction of the interface and its accuracy is only limited by the spatial resolution of the mesh.