A height function based numerical scheme has been developed to apply contact angle in the parallel computational framework of 3D volume-of-fluid method. Given that most of the reported height function methods are implemented in 2D, the differences between the implementations of 2D and 3D height function methods are first focused. Then, a novel scheme is proposed to preserve the accuracy and consistency of height function for the calculation of interface curvature near the contact line. Finally, the extension to parallel computation is presented in details because it is not a trivial task as it appears, e.g., the information transmission among the cells neighboring two intersecting boundaries requires careful treatment. Numerical tests reveal that with the proposed scheme, accurate estimations of interface curvature and normal vector are obtained for a spherical interface, and such a numerical strategy allows the spurious currents to decrease to machine accuracy for a 3D stationary droplet. Moreover, by simulating a droplet spreading on a solid wall with 3D Cartesian grid, either from a static state driven by capillary force or with an initial impact velocity, the numerical results verify that the contact line can maintain an axi-symmetric shape during the dynamic spreading.

已经开发了基于高度函数的数值方案，以在3D流体体积方法的并行计算框架中应用接触角。鉴于大多数报告的高度函数方法是在2D中实现的，因此首先要关注2D和3D高度函数方法的实现之间的差异。然后，提出了一种新的方案来保持高度函数的准确性和一致性，以用于计算接触线附近的界面曲率。最后，详细介绍了对并行计算的扩展，因为它看起来并不容易，例如，与两个相交边界相邻的单元之间的信息传输需要仔细处理。数值测试表明，采用该方案，对于球形界面，可以获得界面曲率和法向矢量的准确估计，并且这种数值策略允许将杂散电流减小到3D固定液滴的机器精度。此外，通过模拟由3D笛卡尔网格在固体壁上散布的液滴（从毛细作用力驱动的静态或初始冲击速度），数值结果验证了接触线在动态过程中可以保持轴对称形状传播。