一种用于粗糙表面润湿的高效阈值动力学方法
An efficient threshold dynamics method for wetting on rough surfaces
AI总结：
本文提出一种高效体积保持阈值动力学方法，用于模拟粗糙表面的润湿过程，该方法基于扩展域内加权表面积功能的最小化，具有O(N log N)复杂度且稳定可靠。
摘要：
由Merriman、Bence和Osher开发的阈值动力学方法（MBO方法）是模拟均向曲率流动的一种高效方法，当界面远离固体边界时。直接将MBO型方法扩展到具有界面与固体边界相交的润湿问题并不容易，因为求解具有润湿边界条件的通用领域热方程效率不如原始MBO方法。接触点的动力学也遵循与界面远离边界时不同的规律。本文开发了一种高效的体积保持阈值动力学方法，用于模拟粗糙表面的润湿过程。该方法基于在包含固体相的扩展域内最小化加权表面积泛函。该方法简单、稳定，具有O(N log N)的每时间步复杂度，并且不敏感于固体边界的不均匀性或粗糙度。
英文摘要：
The threshold dynamics method developed by Merriman, Bence and Osher (MBO) is an efficient method for simulating the motion by mean curvature flow when the interface is away from the solid boundary. Direct generalization of MBO-type methods to the wetting problem with interfaces intersecting the solid boundary is not easy because solving the heat equation in a general domain with a wetting boundary condition is not as efficient as it is with the original MBO method. The dynamics of the contact point also follows a different law compared with the dynamics of the interface away from the boundary. In this paper, we develop an efficient volume preserving threshold dynamics method for simulating wetting on rough surfaces. This method is based on minimization of the weighted surface area functional over an extended domain that includes the solid phase. The method is simple, stable with $O(N \log N)$ complexity per time step and is not sensitive to the inhomogeneity or roughness of the solid boundary.
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