Nouveau développement de la méthode Level Set sur la base d'une équation modifiée de suivi d'interface

The level set method was introduced by Osher & Sethian (1988) as a general technique to capture moving interfaces. It has been used to study crystal growth, to simulate water and fire for computer graphics applications, to study two-phase flows and in many other fields. The wellknown problem of the level set method is the following: if the flow velocity is not constant, the level set scalar may become strongly distorted. Thus, the numerical integration may suffer from loss of accuracy. In level set methods, this problem is remedied by the reinitialization procedure, i.e. by reconstruction of the level set function in a way to satisfy the eikonal equation. We propose an alternative approach. We modify directly the level set equation by embedding a source term. The exact expression of this term is such that the eikonal equation is automatically satisfied. Furthermore on the interface, this term is equal to zero. In the meantime, the advantage of our approach is this: the exact expression of the source term allows for the possibility of derivation of its local approximate forms, of first-and-higher order accuracy. Compared to the extension velocity method, this may open the simplifications in realization of level set methods. Compared to the standard approach with the reinitialization procedure, this may give the economies in the number of level set re-initializations, and also, due to reduced number of reinitializations, one may expect an improvement in resolution of zero-set level. Hence, the objective of the present dissertation is to describe and to assess this approach in different test cases.Pas de résum