When a thin liquid film flows down on a vertical fiber, one can observe the complex and captivating interfacial dynamics of an unsteady flow. Such dynamics are applicable in various fluid experiments due to their high surface area-to-volume ratio. Recent studies verified that when the flow undergoes regime transitions, the magnitude of the film thickness changes dramatically, making numerical simulations challenging. In this paper, we present a computationally efficient numerical method that can maintain the positivity of the film thickness as well as conserve the volume of the fluid under the coarse mesh setting. A series of comparisons to laboratory experiments and previously proposed numerical methods supports the validity of our numerical method. We also prove that our method is second-order consistent in space and satisfies the entropy estimate.

翻译：当薄液膜沿竖直纤维向下流动时，可观察到非稳态流动中复杂而引人入胜的界面动力学现象。此类动力学因具有高表面积与体积比而适用于多种流体实验。近期研究证实，当流动经历流型转变时，液膜厚度幅值会发生剧烈变化，给数值模拟带来挑战。本文提出了一种计算高效的数值方法，该方法在粗网格设置下既能保持液膜厚度的正性，又能守恒流体体积。通过与实验室实验及已有数值方法的一系列对比，验证了本方法的有效性。此外，我们证明该方法在空间上具有二阶精度，且满足熵估计条件。