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 volume-conservation constraints. In this framework, we avoid reinitialization that is 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 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 the methodology to predict equilibrium shapes over both structured and realistic rough surfaces is demonstrated.

开发了一种鲁棒的数值方法来预测任意固体表面上的平衡界面。所提出方法的核心是距离正则化水平集方程（DRLSE），其中包含了无穿透和体积守恒约束的技术。在此框架中，我们避免了传统级别集方法中通常使用的重新初始化。由于仅求解一个对流方程，因此可以使用更有效的算法，并且避免了与重新定标步骤相关的数值误差。规定了基于谐波均值的新型表面张力分布，以使零位组具有正确的液固表面张力值。这导致更精确的三重接触点位置。该方法使用了二阶中心差分方案，该方案便于并行实现，并且通过与经典的标准集方法进行比较来验证了该方法。该方法在吉布斯自由能最小化的背景下获得液体-空气界面的应用已针对现有的分析解决方案进行了验证。证明了该方法能够预测结构化和实际粗糙表面上的平衡形状的能力。