用于轴对称几何中强各向异性固态去湿的 Willmore 正则化锐界面模型：建模与模拟
Willmore regularized sharp-interface model for strongly anisotropic solid-state dewetting with axisymmetric geometry: modeling and simulation
AI总结：
针对强各向异性表面能导致的锐界面模型不适定问题，引入 Willmore 能量正则化自由能并推导轴对称三维固态去湿模型，构造保体积守恒与能量稳定的数值格式，显著改善长期模拟中的网格质量。
摘要：
在本工作中，我们考虑具有强各向异性表面能的三维固态去湿问题，并假设薄膜呈轴对称形貌。然而，当表面能表现出强各向异性时，某些取向可能会从平衡形状中缺失，这将导致控制方程不适定。通过引入 Willmore 能量，我们定义了一个正则化的总自由能，并基于热力学变分严格推导了一个锐界面模型。我们进一步为该锐界面模型发展了一种数值格式，该格式能够保持两个重要的结构性质，包括体积守恒律和能量稳定性律。最后，我们给出了一系列数值模拟，以说明其准确性和结构保持性质。更重要的是，大量数值模拟清楚地表明，我们的格式能够显著提高网格质量，这有利于长期计算。
英文摘要：
In this work, we consider the three-dimensional solid-state dewetting with strongly anisotropic surface energy, assuming an axisymmetric morphology of the thin film. However, when surface energy exhibits strong anisotropy, certain orientations may be missing from the equilibrium shapes, which will lead to an ill-posed governing equation. By incorporating the Willmore energy, we define a regularized total free energy and rigorously derive a sharp-interface model based on thermodynamic variations. We further develop a numerical scheme for the sharp-interface model that can preserve two important structural properties, including both the volume-conservation and energy-stability laws. We conclude by presenting a series of numerical simulations that illustrate the accuracy and structure-preserving properties. More importantly, extensive numerical simulations clearly demonstrate that our schemes can significantly enhance mesh quality, which is beneficial for long-term computations.
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