A re-initialization free numerical approach based on space-time formulation for the level-set evolution simulation

Interface tracking is a challenging issue in numerical simulation of many practical mechanical problems. In this paper, a technique based on space-time formulation in the context of an integral-free meshfree method in an Eulerian approach is presented for interface tracking using the level-set method without needing for re-initialization. We use radial basis functions for function approximation in space-time domain. The method does not need to march in time to obtain interface development. It obtains instantly at all defined times by solving a sparse and symmetric linear system of equations. The method does not depend on tuning parameters for interface tracking which makes it a reliable and robust tool. A vectorized formulation of the proposed approach is illustrated in this paper. One benchmark problems is solved to show the accuracy of the presented technique.

Keywords:

Interface tracking , Level-set method , free-surface modeling , moving boundaries