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异性的自由表面流的 Sharp Interface 方法：分解和聚结


许多自由表面流（液滴/气泡破裂或聚结以及薄膜/片材破裂）的一个共同特征是流体动力学奇点的出现。鉴于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，这需要捕获在 5-6 个数量级的不同长度尺度上发生的动力学。在液滴破裂中，必须模拟形成并最终夹断的流体线的细化，直到线的半径约为 10 nm。当两个液滴彼此接近时，分隔它们的液膜厚度必须低于 10 nm，然后才能说发生了聚结。如果初始液滴半径为 1 mm，则仿真必须忠实于物理场，因为螺纹半径或薄膜厚度从 10-3 m 下降到 10-8 m 以下。在这里，我们回顾了由锐利界面算法引领的具有流体动力学奇点的界面流的重要发现。这些多维算法可以实现迄今为止只有使用简单的 1D 进化方程才能实现的分辨率。