材料界面运动的Level Set算法

Level Set Method for Tracking the Motion of Material Interfaces

多材料结构中材料界面的变形运动在几何上可以抽象为闭曲线或闭曲面随时间的演化。本文导出了材料界面演化过程的隐函数描述,得到了材料界面运动所满足的Halmilton-Jacobi.方程,并且采用数值粘性最小,捕捉函数奇异性的能力最强的Godunov格式来求解。从而将材料界面演化变形的LevelSet算法归纳为初始化,速度扩展、材科界面变形计算与重新新初始化并循环迭代计算四部分。为了消除界面变形所产生的振荡现象,本文还给出了平均曲率流算法,可以对界面具有平滑怍用,快速消除界面中达到高曲率部分,减小界面的几何长度,使界面趋于光顺,并尽可能保持LevelSet函数的零等值线的平均位置不变。最后给出了两个LevelSet数值算例,说明了本文方法是有效的。

In a structure of multi-materials, the motion of material interlaces can be abstracted as the evolvement of closed curve or curved surfaces with respect to time. In this paper, the evolvement of material interfaces is described using implicit functions and Hamilton-Jacobi equations satisfied by the evolvement and obtained. To solve the equations, the Godunov scheme with the minimal numerical viscosity and the maximal ability of capturing the singularity of functions is used. The level set algorithm for tracking the motion of material interfaces can be divided into four parts: initialization, velocity expanding, computing of motion for material interfaces and reinitialization. To eliminate the oscillation, We use average curvature flow method that ensures the interfaces to be smooth, eliminates super curvature, reduces the geometric length of interfaces, and maintains the average position of level sets as much as possible. Finally, two numerical examples are computed. Results indicate that the method is effective.