Research on high order Lagrangian interface tracking problems

Abstract

In this thesis, we proposed the method for tracking the interface with higher order accuracy, when given the normal velocity. Our proposed model combines the well-known Lagrangian surface tracking method with the high order interpolation method for discontinuity capturing. The proposed method not only tracks the surface with higher accuracy than the conventional method, but also depends little on the geometric parameters. Furthermore, the method accurately detects the local shapes of the surface, which is an essential part for a stable interface tracking method. The model developed on the two-dimensional interface can be extended naturally on the three-dimensional interface using the high order interpolation method on triangular meshes.