Positivity-preserving numerical method for thin liquid films on vertical cylindrical fibers

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 used in various applications due to their high surface area to volume ratio. Recent experiments indicate that when the flow undergoes regime transitions, the magnitude of the film thickness changes dramatically making it difficult to develop a numerical method accounting for the changes. 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.