This paper establishes an unconditionally bound-preserving and energy-stable scheme for the Cahn-Hilliard equation with degenerate mobility. More specifically, by applying a finite volume method (FVM) with up-wind numerical fluxes to the degenerate Cahn-Hilliard equation rewritten by the scalar auxiliary variable (SAV) approach, we obtain an unconditionally bound-preserving, energy-stable and fully-discrete scheme, which, for the first time, addresses the boundedness of the classical SAV approach under H^{-1}-gradient flow. Furthermore, the dimensional-splitting technique is introduced in high-dimensional spaces, which greatly reduces the computational complexity while preserving original structural properties. Several numerical experiments are presented to verify the bound-preserving and energy-stable properties of the proposed scheme. Moreover, by applying the scheme to the moving interface problem, we have numerically demonstrated that surface diffusion can be modeled by the Cahn-Hilliard equation with degenerate mobility and Flory-Huggins potential at low temperature, which was only shown theoretically by formal matched asymptotics.

翻译：本文为具有退化流动性的Cahn-Hilliard方程式建立了一个无条件约束性、节能稳定的计划。更具体地说,通过对由星际辅助变量(SAV)方法改写的堕落型Cahn-Hilliard方程式采用有上风数字通量的有限量法(FVM),我们获得了一个无条件约束性、能均匀和完全分解的计划,这一计划首次针对H ⁇ -1}梯度流下的经典SAV方程式的界限。此外,在高维空间引入了次元分解技术,大大降低了计算复杂性,同时保留了原有的结构特性。我们提出了数项实验,以核实拟议方程式的约束性、节能和可分配性特性。此外,通过对移动界面问题应用这一计划,我们从数字上表明,表扩散可以通过Cahn-Hilliard方程式进行模拟,该方程式具有退化性流动性,在低温时具有Flory-Huggins潜力,而从理论上说,只有正式的对应性表示。