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An improved particle correction procedure for the particle level set method

机译：用于粒子水平设定方法的改进的粒子校正程序

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The particle level set method [D. Enright, R. Fedkiw, J. Ferziger, I. Mitchell, A hybrid particle level set method for improved interface capturing, J. Comput. Phys. 183 (2002) 83-116.] can substantially improve the mass conservation property of the level set method by using Lagrangian marker particles to correct the level set function in the under-resolved regions. In this study, the limitations of the particle level set method due to the errors introduced in the particle correction process are analyzed, and an improved particle correction procedure is developed based on a new interface reconstruction scheme. Moreover, the zero level set is "anchored" as the level set functions are reinitialized; hence the additional particle correction after the level set reinitialization is avoided. With this new scheme, a well-defined zero level set can be obtained and the disturbances to the interface are significantly reduced. Consequently, the particle reseeding operation will barely result in the loss of interface characteristics and can be applied as frequently as necessary. To demonstrate the accuracy and robustness of the proposed method, two extreme particle reseeding strategies, one without reseeding and the other with reseeding every time step, are applied in several benchmark advection tests and the results are compared with each other. Three interfacial flow cases, a 2D surface tension driven oscillating droplet, a 2D gas bubble rising in a quiescent liquid, and a 3D drop impact onto a liquid pool are simulated to illustrate the advantages of the current method over the level set and the original particle level set methods with regard to the smoothness of geometric properties and mass conservation in real physical applications.
机译：粒子水平设定方法[D． Enright，R。Fedkiw，J。Ferziger，I。Mitchell，一种用于改进界面捕获的混合粒子水平集方法，J。Comput。物理183（2002）83-116。]可以通过使用拉格朗日标记颗粒校正欠溶解区域中的水平设定功能来实质上改善水平设定方法的质量守恒性质。在这项研究中，分析了由于粒子校正过程中引入的误差而导致的粒子水平集方法的局限性，并基于新的界面重构方案开发了一种改进的粒子校正程序。此外，随着级别设置功能的重新初始化，“级别”设置为“零”。因此避免了在水平集重新初始化之后的额外粒子校正。使用这种新方案，可以获得定义明确的零电平集，并且可以大大减少对接口的干扰。因此，粒子重播操作几乎不会导致界面特性的损失，并且可以根据需要频繁地应用。为了证明所提方法的准确性和鲁棒性，在几种基准对流试验中采用了两种极端的粒子播种策略，一种是不播种，另一种是每步都播种，并将结果进行比较。模拟了三种界面流动情况，2D表面张力驱动的振荡液滴，2D气泡在静态液体中上升以及3D液滴撞击液体池的过程，以说明当前方法相对于水平集和原始粒子的优势在实际物理应用中有关几何特性的平滑度和质量守恒的水平设置方法。

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