A combined compact finite difference scheme for predicting the evolution of a mean curvature driven interface

Abstract

This study is aimed to develop a high-order finite difference scheme to simulate the mean curvature equation for accurately predicting the time-evolving mean curvature driven interface. Within the semi-discretization framework, the optimal third-order accurate temporal scheme is applied for the approximation of the time derivative term. In a three-point grid stencil, a combined compact difference scheme has been developed for offering a fifth-order spatial accuracy for the first-order and second-order derivative terms shown in the level set equation for simulating mean curvature flow. In the simulation of the mean curvature equation, reinitialization procedure has been performed to improve the prediction of curve motion. The aim of this study is to give insights into the issue about “how a mean curvature driven curve is varied with time”. Two mechanisms leading to the change of curve slope are attributed partly to the damping Laplacian operator and partly to the embedded nonlinear differential operator. These mechanisms have been studied in detail with respect to the curvature of curve. The effect of performing reinitialization is also studied numerically.