Characteristic Level Set Method for Solving Motion in Normal Direction Problems

Abstract

A level set method based on the characteristic finite volume formulation is presented. The method solves the evolving interface problems with zero level set along their interfaces. The idea of the characteristic-based technique is implemented to derive a level set equation in two dimensions. An explicit finite volume formulation is employed to discretize the equations applicable for arbitrary grids. The paper focuses on numerical simulation of the motion of an interface under an internally generated velocity field for constant motion in the normal direction. Several test cases are presented to evaluate the performance of the proposed method. Results are compared with the exact solutions or those in the literatures.