AI 中文总结
研究针对三维前沿追踪框架提出积分表面张力方案，在尖锐前沿追踪框架内实现，经多种测试并与多种结果对比，该方案虚假速度与连续表面力法相当，其他测试中精度更高，在多方面有显著改进。
AI 中文摘要
表面张力在许多两相流中至关重要，准确的数值方案对预测其影响必不可少。Popinet和Zaleski（1999）引入的积分公式提供了一种自然离散化方法，能局部和全局守恒动量并直接扩展到可变表面张力，包括马兰戈尼流。但据作者所知，此前仅有二维公式报道，因三维中复杂几何界面的稳健实现具有挑战性。本文提出首个三维积分表面张力方案并在尖锐前沿追踪框架内实现。对静态和移动球形液滴、振荡液滴、热毛细运动及上升气泡进行测试，结果与解析解、实验数据及现有方法对比。该方案产生的虚假速度与连续表面力法相当，但在其他测试中精度更高。在低奥内佐格数下振荡的液滴、可变表面张力流及强烈变形的上升气泡方面改进最大。对于热毛细驱动的液滴，相对于基于平滑的方法，终端速度误差降低多达五个数量级。上升气泡的预测稳态形状也与实验结果更相符，尤其是在低莫顿数时。
英文摘要
Surface tension is central to many two-phase flows, making accurate numerical schemes essential for predicting its effects. The integral formulation introduced by Popinet and Zaleski (1999) provides a natural discretisation that conserves momentum locally and globally and extends directly to variable surface tension, including Marangoni flows. However, to the authors' knowledge, only two-dimensional formulations have been reported, mainly because robust implementation in three dimensions is challenging for interfaces with complex geometries. This work presents the first three-dimensional integral surface tension scheme, implemented within a sharp front-tracking framework. The method is tested for static and translating spherical droplets, oscillating droplets, thermocapillary motion, and rising bubbles. Results are compared with analytical solutions, experimental data, and established approaches, including the continuous surface force (CSF) and smoothing-based methods. The proposed scheme produces spurious velocities comparable to CSF, while providing greater accuracy in all other tests. The largest improvements occur for droplets oscillating at low Ohnesorge numbers, variable-surface-tension flows, and strongly deforming rising bubbles. For a thermocapillary-driven droplet, terminal-velocity errors are reduced by up to five orders of magnitude relative to smoothing-based methods. The predicted steady-state shapes of rising bubbles also agree substantially better with experiments, particularly at low Morton numbers.
