Volume of fluid(VOF) method is a sharp interface method employed for simulations of two phase flows. Interface in VOF is usually represented using piecewise linear line segments in each computational grid based on the volume fraction field. While VOF for cartesian coordinates conserve mass exactly, existing algorithms do not show machine-precision mass conservation for axisymmetric coordinate systems. In this work, we propose analytic formulae for interface reconstruction in axisymmetric coordinates, similar to those proposed by Scardovelli and Zaleski (J. Comput. Phys. 2000) for cartesian coordinates. We also propose modifications to the existing advection schemes in VOF for axisymmetric coordinates to obtain higher accuracy in mass conservation.

流体体积 (VOF) 方法是一种用于模拟两相流的锐界面方法。VOF 中的界面通常使用基于体积分数场的每个计算网格中的分段线性线段来表示。虽然笛卡尔坐标的 VOF 精确守恒质量，但现有算法并未显示轴对称坐标系的机器精度质量守恒。在这项工作中，我们提出了轴对称坐标中界面重建的解析公式，类似于 Scardovelli 和 Zaleski (J. Comput. Phys. 2000) 为笛卡尔坐标提出的解析公式。我们还建议修改 VOF 中现有的轴对称坐标对流方案，以获得更高的质量守恒精度。