薄膜固态去湿问题是材料科学领域中被广泛关注的一类由系统总能量减少所驱动的界面演化问题，表面扩散流、移动接触线和界面能的各向异性是该问题的几个重要特征。实验发现，固态去湿现象对界面能的各向异性和衬底的曲率高度敏感，且去湿的过程中往往伴随着复杂的拓扑结构变化。已建立的固态去湿问题的尖锐界面模型需要显式追踪界面的演化踪迹，且基于参数化有限元方法在数值求解时存在网格畸变的困难。而相场模型的方法具有不需要显式捕获界面踪迹的天然优势，容易处理复杂的结构变化，并且空间离散时不存在网格畸变的困难。因此，本项目计划利用相场模型来研究薄膜固态去湿问题，其主要内容包括：（1）发展界面能为弱各向异性情形的相场模型及其保结构格式；（2）发展界面能为强各向异性情形的相场模型及其保结构格式；（3）基于相场模型研究界面能的各向异性和衬底的曲率对薄膜固态去湿现象的演化过程和平衡态的影响。

The solid-state dewetting problem is a class of interface evolution problem driven by the reduction of the total energy of the system, which is widely concerned in the field of material science. Surface diffusion flow, moving contact line and anisotropic surface energy are several important characteristics of the problem. The experiments found that the solid-state dewetting phenomenon is highly sensitive to the anisotropy of the surface energy and the curvature of the substrate, and the evolution of dewetting is often accompanied by complex topological structure changes. The sharp-interface model of the established solid-state dewetting problem needs to explicitly track the evolution of the interface, and the numerical approach based on the parametric finite element method can lead to grid distortion. Because the phase-field method has the natural advantage of not needing to capture the interface trace explicitly, it is easy to handle complex structural changes, and there is no grid distortion problem in space discrete. Therefore, this project plans to use the phase-field model to study the solid-state dewetting of thin films. The main contents include: (1) developing a phase-field model with weakly anisotropic surface energy and its structure-preserving scheme; (2) developing a phase-field model with strong anisotropic and its structure-preserving scheme; (3) Based on the phase-field model, the influence of the anisotropy of the surface energy and the curvature of the substrate on the evolution and equilibrium state of the solid-state dewetting of thin film was studied.