Characteristic-based Level Set Method for Motion by Mean Curvature Analysis

Abstract

This paper presents a characteristic-based scheme for solving the level set equation in
arbitrary two-dimensional domain. The characteristic-based approach is used to derive a level set
equation in two dimensions for solving the evolving interface problems with zero level set along
their interfaces. An explicit finite volume method is employed to discretize the characteristic level
set equation. The scheme is used to study motion by mean curvature where the interface moves in
the normal direction with the velocity proportional to its curvature. Accuracy and robustness of the
proposed method are evaluated via test cases with prescribed velocity fields and its curvature on
structured triangular grids. The predicted results are compared with those in literatures.

Keywords: Characteristic Level Set Equation; Explicit Scheme; Finite Volume Method; Mean
Curvature Analysis.