A phase-field method for unstructured grids that is accurate, conservative, and robust is proposed in this work. The proposed method also results in bounded transport of volume fraction, and the interface thickness adapts automatically to local grid size. In addition to this, we present a novel formulation for two-phase flows on collocated grids that is provably energy stable, which is a critical feature for robust simulations of two-phase turbulent flows. The proposed method is first evaluated on canonical test cases, including scenarios like drop advection and drop in a shear flow. The accuracy of the proposed method in the presence of grid transitions, which is important for simulations in complex geometries using unstructured grids, is also evaluated. We assess the robustness of our method by performing simulations of a drop in homogeneous isotropic turbulence at infinite Reynolds number with varying density ratios. Furthermore, as a step toward verification and validation, simulations of test cases in complex geometries and conditions, such as, a damped surface wave, infinitesimal interface distortion on a liquid jet, and the atomization of a liquid jet from the engine combustion network's Spray A nozzle are presented. These simulations illustrate the accuracy, robustness, and applicability of the proposed method in various kinds of complex two-phase flow applications of engineering interest.

中文翻译：

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非结构化网格上两相流的鲁棒相场方法

本文提出了一种精确、保守且鲁棒的非结构化网格相场方法。所提出的方法还导致体积分数的有界传输，并且界面厚度自动适应局部网格尺寸。除此之外，我们还提出了一种新的并置网格上的两相流公式，该公式可证明能量稳定，这是两相湍流鲁棒模拟的关键特征。所提出的方法首先在典型的测试用例上进行评估，包括液滴平流和剪切流中的液滴等场景。还评估了所提出的方法在存在网格过渡的情况下的准确性，这对于使用非结构化网格进行复杂几何形状的模拟非常重要。我们通过模拟不同密度比的无限雷诺数下均匀各向同性湍流的下降来评估我们方法的稳健性。此外，作为验证和确认的一个步骤，在复杂的几何形状和条件下模拟测试用例，例如阻尼表面波、液体射流上的无穷小的界面变形以及来自发动机燃烧网络的喷雾 A 的液体射流的雾化喷嘴被提出。这些模拟说明了所提出的方法在工程领域的各种复杂两相流应用中的准确性、鲁棒性和适用性。