On the computation of viscous terms for incompressible two-phase flows with Level Set/Ghost Fluid Method
On the computation of viscous terms for incompressible two-phase flows with Level Set/Ghost Fluid Method
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DOI：
10.1016/j.jcp.2015.08.036
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发表时间：
2015-11
期刊：
影响因子：
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通讯作者：
Benjamin Lalanne;L. R. Villegas;S. Tanguy;Frédéric Risso
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文献类型：
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作者：
Benjamin Lalanne;L. R. Villegas;S. Tanguy;Frédéric Risso
本文详细分析了在LevelSet/GhostFluid方法框架下，当粘性在界面上不连续时，不可压缩两相流粘性项的计算。关于这个主题的两篇开创性论文，Kang等人。[10]和Sussman等人。[26]，提出了两种不同的方法来处理粘性项。然而，目前还没有对它们各自效率的确切评估。在本文中，我们从理论论证和数值模拟证实，这两种方法是等效的，从连续的角度来看，我们比较它们的精度在相关的测试用例。我们还提出了一个新的中间方法，它使用的性质，前两种方法。这种新的方法使一个简单的实施的隐式时间离散的粘性条款。此外，还评估了Delta函数方法[24]的效率，并与前三种方法进行了比较，这使我们能够对所有可用方法的准确性进行总体概述。所选的测试案例涉及的配置，其中粘度起着重要作用，无论是理论结果或实验数据可作为参考解决方案：模拟球形上升气泡，形状振荡气泡和变形上升气泡在低雷诺数。
In this paper, we present a detailed analysis of the computation of the viscous terms for the simulation of incompressible two-phase flows in the framework of Level Set/Ghost Fluid Method when viscosity is discontinuous across the interface. Two pioneering papers on the topic, Kang et al. [10] and Sussman et al. [26], proposed two different approaches to deal with viscous terms. However, a definitive assessment of their respective efficiency is currently not available. In this paper, we demonstrate from theoretical arguments and confirm from numerical simulations that these two approaches are equivalent from a continuous point of view and we compare their accuracies in relevant test-cases. We also propose a new intermediate method which uses the properties of the two previous methods. This new method enables a simple implementation for an implicit temporal discretization of the viscous terms. In addition, the efficiency of the Delta Function method [24] is also assessed and compared to the three previous ones, which allow us to propose a general overview of the accuracy of all available methods. The selected test-cases involve configurations wherein viscosity plays a major role and for which either theoretical results or experimental data are available as reference solutions: simulations of spherical rising bubbles, shape-oscillating bubbles and deformed rising bubbles at low Reynolds numbers.