论文标题
脱位的cahn--hilliard方程，具有模拟表面扩散的应用
A sturcture-preserving, upwind-SAV scheme for the degenerate Cahn--Hilliard equation with applications to simulating surface diffusion
论文作者
论文摘要
本文为Cahn--Hilliard方程式建立了结构性的数值方案，具有退化的迁移率。首先，通过将有限的卷方法应用于标量辅助变量（SAV）方法重写的退化cahn--hilliard方程式，我们创造性地获得了一种无条件的限制，能量稳定，完全稳定且完全散布的方案，在首次范围内，$ h^$ h^$ h^$ h^y^$ h^n offriptive consection-frestient comploce clocked offersect offersection-h。然后，在高维情况下引入了尺寸分割技术，该技术大大降低了计算复杂性，同时保留了原始结构特性。提出了数值实验，以验证所提出的方案的边界保护和能量稳定的特性。最后，通过应用提出的结构传播方案，我们从数值上证明，Cahn--Hilliard方程可以近似地表面扩散，具有退化的迁移率和florys的潜力 - 当绝对温度足够低时，可以通过形式上分析通过形式上的属性匹配的方式使用形式分析。
This paper establishes a structure-preserving numerical scheme for the Cahn--Hilliard equation with degenerate mobility. First, by applying a finite volume method with upwind numerical fluxes to the degenerate Cahn--Hilliard equation rewritten by the scalar auxiliary variable (SAV) approach, we creatively 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. Then, a dimensional-splitting technique is introduced in high-dimensional cases, which greatly reduces the computational complexity while preserves original structural properties. Numerical experiments are presented to verify the bound-preserving and energy-stable properties of the proposed scheme. Finally, by applying the proposed structure-preserving scheme, we numerically demonstrate that surface diffusion can be approximated by the Cahn--Hilliard equation with degenerate mobility and Flory--Huggins potential when the absolute temperature is sufficiently low, which agrees well with the theoretical result by using formal asymptotic analysis.wn theoretically by formal matched asymptotics.
