An adaptive moving mesh method for two-dimensional thin film flow equations with surface tension

Alharbi, Abdulghani; Naire, Shailesh

Abstract

In this paper, we extend our previous work [A. Alharbi and S. Naire, An adaptive moving mesh method for thin film flow equations with surface tension, J. Computational and Applied Mathematics, 319 (2017), pp. 365-384.] on a one-dimensional r-adaptive moving mesh technique based on a mesh density function and moving mesh partial differential equations (MMPDEs) to two dimensions. As a test problem, we consider the gravitydriven thin film flow down an inclined and pre-wetted plane including surface tension and a moving contact line. This technique accurately captures and resolves the moving contact line and associated fingering instability. Moreover, the computational effort is hugely reduced in comparison to a fixed uniform mesh.

Citation

Alharbi, A., & Naire, S. (2019). An adaptive moving mesh method for two-dimensional thin film flow equations with surface tension. Journal of Computational and Applied Mathematics, 365, 219-230. https://doi.org/10.1016/j.cam.2019.02.010

• Journal Article Type: Article
• Acceptance Date: Feb 11, 2019
• Online Publication Date: Feb 22, 2019
• Publication Date: Aug 15, 2019
• Publicly Available Date: May 26, 2023
• Journal: Journal of Computational and Applied Mathematics
• Print ISSN: 0377-0427
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 365
• Pages: 219-230
• DOI: https://doi.org/10.1016/j.cam.2019.02.010
• Keywords: Thin film flows, Surface tension, Fingering instability, Adaptive moving mesh, r-adaptive method, Moving Mesh PDEs (MMPDEs), applied mathematics, numerical and computational mathematics, electrical and electronic engineering
• Public URL: https://keele-repository.worktribe.com/output/412693
• Publisher URL: https://doi.org/10.1016/j.cam.2019.02.010