English

A positivity-preserving numerical method for a thin liquid film on a vertical cylindrical fiber

Numerical Analysis 2023-10-18 v1 Numerical Analysis

Abstract

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.

Keywords

Cite

@article{arxiv.2310.10977,
  title  = {A positivity-preserving numerical method for a thin liquid film on a vertical cylindrical fiber},
  author = {Bohyun Kim and Hangjie Ji and Andrea L. Bertozzi and Abolfazl Sadeghpour and Y. Sungtaek Ju},
  journal= {arXiv preprint arXiv:2310.10977},
  year   = {2023}
}