We seek to assess the key aspects of two modern moving mesh approaches for simulating two-phase flows where a thin explicit interface separates the two fluids within the context of “one-fluid” formulation. Both methods discretize the fluid equations through the Finite Element (FE) method using the Arbitrary Lagrangian-Eulerian (ALE) framework, therefore a complex moving mesh scheme is achieved. These methods are supported by a spatial Heaviside function which locates the interface between fluids in the domain of interest. Despite a sharp geometrical definition of the tracked interface, one methodology requires a smooth regularization of the Heaviside function to avoid undesirable numerical instabilities. On the other hand, the second method bypass such an artificial requirement but an advanced remeshing algorithm is demaded to maintain the simulation. Several important test cases are used as benchmark to assess the capabilities of both approaches such as the oscillating drop and the Zalesak’s disk test where fundamental parameters are evaluated and more challenging two-phase flows such as the rising of single bubbles and microscale flows in capillaries. A comparison is then made to evaluate the important aspects of each model and an accurate analysis is made to quantify the errors associated to important parameters in two-phase flows such as surface tension, liquid film thickness, interfacial waves, interface deformation and bubble/drop shape.

我们试图评估用于模拟两相流的两种现代移动网格方法的关键方面，其中薄显式界面在“单一流体”公式的背景下将两种流体分开。这两种方法都使用任意拉格朗日-欧拉 (ALE) 框架通过有限元 (FE) 方法离散流体方程，因此实现了复杂的移动网格方案。这些方法得到空间 Heaviside 函数的支持，该函数定位感兴趣域中流体之间的界面。尽管被跟踪界面的几何定义很清晰，但一种方法需要对 Heaviside 函数进行平滑的正则化，以避免出现不希望的数值不稳定性。另一方面，第二种方法绕过了这种人为的要求，但需要使用先进的重新网格划分算法来维持模拟。几个重要的测试用例被用作评估这两种方法的能力的基准，例如振荡下降和 Zalesak 圆盘测试，其中评估基本参数和更具挑战性的两相流，例如单气泡的上升和毛细管中的微尺度流动。然后进行比较以评估每个模型的重要方面，并进行准确分析以量化与两相流中重要参数相关的误差，例如表面张力、液膜厚度、界面波、界面变形和气泡/液滴形状。几个重要的测试用例被用作评估这两种方法的能力的基准，例如振荡下降和 Zalesak 圆盘测试，其中评估基本参数和更具挑战性的两相流，例如单气泡的上升和毛细管中的微尺度流动。然后进行比较以评估每个模型的重要方面，并进行准确分析以量化与两相流中重要参数相关的误差，例如表面张力、液膜厚度、界面波、界面变形和气泡/液滴形状。几个重要的测试用例被用作评估这两种方法的能力的基准，例如振荡下降和 Zalesak 圆盘测试，其中评估基本参数和更具挑战性的两相流，例如单气泡的上升和毛细管中的微尺度流动。然后进行比较以评估每个模型的重要方面，并进行准确分析以量化与两相流中重要参数相关的误差，例如表面张力、液膜厚度、界面波、界面变形和气泡/液滴形状。