We analyze numerical approximations for axisymmetric two-phase flow in the arbitrary Lagrangian-Eulerian (ALE) framework. We consider a parametric formulation for the evolving fluid interface in terms of a one-dimensional generating curve. For the two-phase Navier-Stokes equations, we introduce both conservative and nonconservative ALE weak formulations in the 2d meridian half-plane. Piecewise linear parametric elements are employed for discretizing the moving interface, which is then coupled to a moving finite element approximation of the bulk equations. This leads to a variety of ALE methods, which enjoy either an equidistribution property or unconditional stability. Furthermore, we adapt these introduced methods with the help of suitable time-weighted discrete normals, so that the volume of the two phases is exactly preserved on the discrete level. Numerical results for rising bubbles and oscillating droplets are presented to show the efficiency and accuracy of these introduced methods.

翻译：本文分析了任意拉格朗日-欧拉（ALE）框架下轴对称两相流的数值逼近方法。我们针对演化的流体界面，采用基于一维生成曲线的参数化表述。对于两相Navier-Stokes方程，我们在二维子午半平面上引入了守恒型和非守恒型ALE弱形式。采用分段线性参数单元离散移动界面，并将其与体方程的移动有限元逼近相耦合，由此导出若干满足等分布性质或无条件的稳定性的ALE方法。此外，我们借助合适的时间加权离散法向量对这些方法进行改进，以确保在离散层面上精确保持两相体积。针对上升气泡和振荡液滴的数值结果展示了所提出方法的效率与精度。