A local level-set method under involvement of topological aspects

Abstract

This paper proposes a general multi-dimensional front tracking concept for various physical problems involving specially discontinuous solution features. The tracking method is based on the level-set approach with a restricted dynamic definition range in the vicinity of the fronts on fixed grids of arbitrary cell structure. To combine the front tracking procedure with the continuous part of the field to be simulated, a double sided flux discretization called flux-separation and a set of inner boundary conditions over the discontinuities are used. The methods developed are not restricted to fluid dynamics, however all examples relate to this class of simulation problems. Special attention is drawn to the restrictions of the classical level-set method, i.e. accuracy issues and topological restrictions. In this concern, an improved time integration method for the front motion is introduced and the problem of interacting discontinuities is addressed. The methods are integrated in the object oriented Finite-Volume solution package MOUSE [1] for systems of conservation laws on arbitrary grids. © 2005 Springer-Verlag Berlin Heidelberg.