发表机构
School of Mathematics and Statistics, Henan University; Center for Applied Mathematics of Henan Province, Henan University; School of Artificial Intelligence, Wuhan University（河南大学数学与统计学院; 河南省应用数学中心; 武汉大学人工智能学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对固态去湿相场模拟中的虚假粗化问题，提出结合对数势、拉格朗日乘子与迎风有限体积的保结构格式，保证有界性、守恒与耗散，并抑制虚假收缩。
AI 中文摘要
基于多项式势的固态去湿相场模拟可能表现出虚假的体扩散粗化，这与以表面扩散为主的物理机制不一致。为解决此问题，我们构建了一个具有对数Flory--Huggins势和动态接触线边界条件的退化Cahn--Hilliard模型，用于薄膜-基底-蒸气三相接触点。对数势垒将相变量限制在其物理范围内，并在连续层面抑制虚假粗化。我们开发了一种全离散、保结构的格式，该格式结合了拉格朗日乘子方法与迎风有限体积离散化，并严格保证了逐点有界性、质量守恒和能量耗散，无需人工截断或投影。维度分裂策略进一步降低了计算成本，同时在每个一维扫描中保持这些性质。我们还推导了由自发薄膜收缩引起的平衡半径收缩的显式估计，表明对数势产生的虚假收缩弱于多项式势。数值实验证实了分析结果，并表明对于较小的温度参数，所提出的格式抑制了虚假粗化和颈缩，同时准确再现了以表面扩散为主的动力学以及向平衡岛状结构的弛豫过程。
英文摘要
Phase-field simulations of solid-state dewetting based on polynomial potentials may exhibit spurious bulk-diffusion coarsening, inconsistent with the surface-diffusion-dominated physics. To address this issue, we formulate a degenerate Cahn--Hilliard model with the logarithmic Flory--Huggins potential and dynamic contact line boundary conditions for the film--substrate--vapor triple junction. The logarithmic barrier confines the phase variable to its physical range and suppresses spurious coarsening at the continuum level. We develop a fully discrete, structure-preserving scheme that combines a Lagrange multiplier approach with an upwind finite-volume discretization and rigorously guarantees pointwise boundedness, mass conservation, and energy dissipation without artificial cut-offs or projections. A dimensional-splitting strategy further reduces computational cost while preserving these properties in each one-dimensional sweep. We also derive an explicit estimate of the equilibrium radius contraction caused by spontaneous film shrinking, showing that the logarithmic potential produces weaker spurious shrinkage than the polynomial potential. Numerical experiments confirm the analysis and demonstrate that, for small temperature parameters, the proposed scheme suppresses spurious coarsening and pinch-off while accurately reproducing surface-diffusion-dominated dynamics and relaxation toward equilibrium island structures.
