The paper describes a novel implementation of the piecewise linear interface-capturing volume-of-fluid method (PLIC-VOF) in axisymmetric cylindrical coordinates. The principal innovative feature involved in this work is that both the forward and inverse reconstruction problems are solved analytically, resulting in an appreciable speed-up in computing time in comparison with an iterative approach. All reconstruction formulae are introduced explicitly, and an example illustrating their derivation is included for clarity. The numerical implementation of the PLIC-VOF interface tracking method developed here is described in detail, as well as its coupling with the 3D incompressible Navier-Stokes solver PSI-BOIL, which features a finite-volume approach based on a fixed, rectangular grid. This coupling includes a method to calculate the surface tension force within an axisymmetric VOF framework by means of height functions. The method is first verified to ensure its correct implementation in the code, and to evaluate its performance, and several advection tests are employed to demonstrate successful solution of the basic transport problem. It is shown that convergence to equilibrium may be achieved for static problems, involving the control of parasitic currents, for a variety of grid arrangements, and for different material properties. Several axisymmetric dam-break and rising bubble problems, for which high-quality measured data are available, are also presented to serve as validation tests. In all cases, very good agreement of simulation results with experimental data has been recorded, and the dynamics of the problem well reproduced.

本文描述了一种在轴对称圆柱坐标系中分段线性界面捕获流体体积方法（PLIC-VOF）的新颖实现。这项工作涉及的主要创新特征是，可以通过解析方式解决正向和逆向重构问题，与迭代方法相比，可以显着加快计算时间。明确介绍了所有重建公式，为清楚起见，还包括一个示例说明它们的推导过程。详细介绍了此处开发的PLIC-VOF接口跟踪方法的数值实现方式，以及与3D不可压缩的Navier-Stokes求解器PSI-BOIL的耦合，PSI-BOIL具有基于固定矩形网格的有限体积方法。这种耦合包括一种通过高度函数计算轴对称VOF框架内的表面张力的方法。首先对该方法进行验证，以确保其在代码中的正确实现并评估其性能，并通过多次对流测试演示了基本运输问题的成功解决方案。结果表明，对于静态问题，包括对寄生电流的控制，对于各种网格布置，以及对于不同的材料特性，都可以实现收敛到平衡。还提供了一些轴对称的溃坝和上升气泡问题，这些问题都可获得高质量的测量数据，以用作验证测试。在所有情况下，都记录了模拟结果与实验数据的良好一致性，