The accurate modeling of the surface-tension on free surfaces remains a challenging problem in meshfree particle methods. Recently, Matsunaga et al. (2020) have made an important step forward toward addressing this issue by introducing a moving surface mesh to represent the free-surface boundary in 2D. However, the surface mesh makes it difficult to extend this methodology to 3D and to treat topological changes in free surfaces. This study aims to extend this methodology to 3D and restore the capability of the model to simulate topological changes by carefully detecting the free-surface particles. In this situation, the problems regarding fluctuated free-surface boundaries and the dynamic intersection of a free surface with a wall boundary arise. To resolve these problems, a new particle shifting method in the surface normal direction is proposed for the free-surface particles to reduce fluctuations. A new contact angle model is proposed to compute the intersection point of a free surface and a wall boundary. In this manner, an enhanced particle method suitable for simulating the dynamics of liquid droplets with possible topological changes in 3D is developed. Eight numerical examples verified the developed method and demonstrated the enhancement of the new particle shifting technique.

自由表面表面张力的精确建模在无网格粒子方法中仍然是一个具有挑战性的问题。最近，松永等人。(2020) 通过引入移动表面网格来表示 2D 中的自由表面边界，朝着解决这个问题迈出了重要的一步。然而，表面网格使得很难将这种方法扩展到 3D 并处理自由表面的拓扑变化。本研究旨在将这种方法扩展到 3D，并通过仔细检测自由表面粒子来恢复模型模拟拓扑变化的能力。在这种情况下，出现了关于波动的自由表面边界和自由表面与壁边界的动态相交的问题。为了解决这些问题，针对自由表面粒子提出了一种新的表面法线方向粒子偏移方法，以减少波动。提出了一种新的接触角模型来计算交点自由表面和壁面边界。通过这种方式，开发了一种适用于模拟具有 3D 中可能拓扑变化的液滴动力学的增强粒子方法。八个数值例子验证了所开发的方法，并证明了新粒子移动技术的增强。