预测任意固体表面平衡界面的无需重新初始化的变分水平集方法
A variational level set methodology without reinitialization for the prediction of equilibrium interfaces over arbitrary solid surfaces
摘要：
发展了一种预测任意固体表面平衡界面的数值方法。该方法的核心是距离正则化水平集方程（DRLSE）的技术，将无穿透和质量守恒的约束。在这个框架中，我们避免了传统水平集方法中通常使用的重新初始化。这允许更有效的算法，因为仅求解一个平流方程，并且避免了与重新定距步骤相关联的数值误差。一种新的表面张力分布，基于调和平均值，规定，使零水平集具有正确的液-固表面张力值。这导致更准确的三重接触点位置。该方法使用二阶中心差分格式，便于并行实现，并通过与传统的水平集方法的典范问题进行了比较验证。该方法的应用，在吉布斯自由能最小化的背景下，以获得液体-空气界面对现有的解析解进行验证。我们目前的方法来预测结构化和现实的粗糙表面的平衡形状的能力被证明。
英文摘要：
A robust numerical methodology to predict equilibrium interfaces over arbitrary solid surfaces is developed. The kernel of the proposed method is the distance regularized level set equations (DRLSE) with techniques to incorporate the no-penetration and mass-conservation constraints. In this framework, we avoid reinitialization typically used in traditional level set methods. This allows for a more efficient algorithm since only one advection equation is solved, and avoids numerical error associated with the re-distancing step. A novel surface tension distribution, based on harmonic mean, is prescribed such that the zero level set has the correct the liquid-solid surface tension value. This leads to a more accurate triple contact point location. The method uses second-order central difference schemes which facilitates easy parallel implementation, and is validated by comparing to traditional level set methods for canonical problems. The application of the method, in the context of Gibbs free energy minimization, to obtain liquid-air interfaces is validated against existing analytical solutions. The capability of our current methodology to predict equilibrium shapes over both structured and realistic rough surfaces is demonstrated.
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