In this paper we consider a level set reinitialization technique based on a high-order, local discontinuous Galerkin method on unstructured triangular meshes. A finite volume based subcell stabilization is used to improve the nonlinear stability of the method. Instead of the standard hyperbolic level set reinitialization, the flow of time Eikonal equation is discretized to construct an approximate signed distance function. Using the Eikonal equation removes the regularization parameter in the standard approach which allows more predictable behavior and faster convergence speeds around the interface. This makes our approach very efficient especially for banded level set formulations. A set of numerical experiments including both smooth and non-smooth interfaces indicate that the method experimentally achieves design order accuracy.

翻译：在本文中,我们考虑一个基于高阶、局部不连续的Galerkin法的设定重新初始化技术。 使用量基子细胞的有限稳定性来提高该方法的非线性稳定性。 与标准的双曲水平重新初始化相比, Eikonal 等式的时间流被分离, 以构建大致的签名距离函数。 使用 Eikonal 等式删除了标准方法中的正规化参数, 使界面周围的行为更可预测, 并更快的趋同速度。 这使得我们的方法非常高效, 特别是对于带宽的立式配方。 一组数字实验, 包括光滑和非线性界面, 表明该方法在实验中实现了设计顺序的准确性 。