A common feature of many free surface flows—drop/bubble breakup or coalescence and film/sheet rupture—is the occurrence of hydrodynamic singularities. Accurately computing such flows with continuum mechanical, multidimensional free surface flow algorithms is a challenging task given these problems’ multiscale nature, which necessitates capturing dynamics occurring over disparate length scales across 5–6 orders of magnitude. In drop breakup, the thinning of fluid threads that form and eventually pinch-off must be simulated until the thread's radius is about 10 nm. When two drops approach one another, the thickness of the fluid film separating them must fall below 10 nm before coalescence is said to have occurred. If the initial drop radii are 1 mm, simulations must remain faithful to the physics as thread radius or film thickness falls from 10−3 m to below 10−8 m. Here we review significant findings in interfacial flows with hydrodynamic singularities spearheaded by sharp interface algorithms. These multidimensional algorithms can achieve resolution that to date has only been possible with the use of simple 1D evolution equations.

中文翻译：

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用于模拟和分析具有奇点的自由表面流的锐接口方法：破碎和合并

许多自由表面流（液滴/气泡破裂或聚结以及薄膜/片材破裂）的一个共同特征是出现流体动力学奇点。考虑到这些问题的多尺度性质，使用连续机械、多维自由表面流算法准确计算此类流动是一项具有挑战性的任务，这需要捕获跨 5-6 个数量级的不同长度尺度上发生的动力学。在液滴破碎过程中，必须模拟形成的流体线的变细以及最终的夹断，直到线的半径约为 10 nm。当两滴彼此接近时，分离它们的流体膜的厚度必须降至 10 nm 以下，才能发生聚结。如果初始下降半径为 1 毫米，当螺纹半径或薄膜厚度从 10 下降时，模拟必须忠实于物理原理。−3米至10以下−8米。在这里，我们回顾了由尖锐的界面算法带头的具有流体动力学奇点的界面流动的重要发现。这些多维算法可以实现迄今为止只能通过使用简单的一维演化方程才能实现的分辨率。