High order face-offsetting method for interface tracking problem using WENO schemes

In this article, a new high order interface tracking method is developed that combines Face Offsetting Method (FOM) with Weighted Essentially Non-Oscillatory (WENO) scheme. Since FOM is Lagrangian-based method, it requires less computation time and results in smaller volume loss compared with methods based on the Eulerian approach. However, it is a first order method even in smooth regions because it uses only neighboring face normals to determine offsetting directions. Moreover, the method is greatly influenced by parameters that determine the local shape at each node, which in turn determines the correct propagating direction. We introduce a high order FOM which not only tracks the surface with higher accuracy than the conventional method but also depends less on the parameters and accurately determines the local shapes of the surface. Various numerical results are presented for verifying these advantages.