Damages due to pitting corrosion of metals cost industry billions of dollars per year and can put human lives at risk. The design and implementation of an adaptive moving mesh method is provided for a moving boundary problem related to pitting corrosion. The adaptive mesh is generated automatically by solving a mesh PDE coupled to the nonlinear potential problem. The moving mesh approach is shown to enable initial mesh generation, provide mesh recovery and is able to smoothly tackle changing pit geometry. Materials with varying crystallography are considered. Changing mesh topology due to the merging of pits is also handled. The evolution of the pit shape, the pit depth and the pit width are computed and compared to existing results in the literature.

翻译：金属点蚀造成的损伤每年给工业界带来数十亿美元的损失，并对人类生命安全构成威胁。本文针对点蚀相关的移动边界问题，提出并实现了一种自适应移动网格方法。该方法通过求解与非线性电位问题耦合的网格偏微分方程来自动生成自适应网格。研究表明，移动网格方法能够实现初始网格生成、提供网格恢复能力，并平滑处理点蚀几何外形的变化。研究还考虑了不同晶体学特性的材料，并成功处理了因点蚀合并导致的网格拓扑变化。计算了点蚀形态、点蚀深度和点蚀宽度的演化过程，并与现有文献结果进行了对比。