Reinitialization is essential to maintaining the accuracy of the level set method at capturing interfaces. In this paper, a high-order reinitialization method for the level set function which has previously been developed for structured grids was extended to unstructured grids. The proposed method involves constructing a stencil of an unstructured grid to define a high-order polynomial that approximates a piecewise segment of the interface. Then, the closest point method is adopted to estimate the signed distance function at grid points. The proposed method was validated by solving some benchmark problems of static cases and then the evolution of moving interfacial problems subject to prescribed velocity fields for various grid resolutions consisting of triangular elements. The accuracy of the proposed method was evaluated for computing geometric quantities such as the normal vector and curvature field. The proposed method proved to have high-order accuracy for estimating not only the signed distance function but also geometric quantities for a smooth interface. Finally, a local correction procedure was developed to apply the proposed method to level set problems involving the interface with kinks. The proposed method can accurately estimate normal vector and curvature fields including singularities both for static cases and for dynamic cases where an interface experiences topological changes.

重新初始化对于保持水平集方法在捕获接口时的准确性至关重要。在本文中，将先前为结构化网格开发的水平集函数的高阶重新初始化方法扩展到非结构化网格。所提出的方法包括构造一个非结构化网格的模板来定义一个近似于界面分段的高阶多项式。然后，采用最近点法估计网格点的有符号距离函数。所提出的方法通过解决一些静态情况的基准问题，然后对由三角形元素组成的各种网格分辨率的规定速度场的移动界面问题的演变进行了验证。所提出的方法的准确性被评估为计算几何量，如法向量和曲率场。所提出的方法被证明具有高阶精度，不仅可以估计有符号距离函数，还可以估计光滑界面的几何量。最后，开发了一个局部校正程序，将所提出的方法应用于涉及具有扭结的界面的水平集问题。所提出的方法可以准确地估计法向量和曲率场，包括静态情况和界面经历拓扑变化的动态情况的奇异性。开发了一种局部校正程序，以将所提出的方法应用于涉及具有扭结的界面的水平集问题。所提出的方法可以准确地估计法向量和曲率场，包括静态情况和界面经历拓扑变化的动态情况的奇异性。开发了一种局部校正程序，以将所提出的方法应用于涉及具有扭结的界面的水平集问题。所提出的方法可以准确地估计法向量和曲率场，包括静态情况和界面经历拓扑变化的动态情况的奇异性。