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

Naire

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


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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.

Acceptance Date Feb 11, 2019
Publication Date Aug 15, 2019
Publicly Available Date Mar 29, 2024
Journal Journal of Computational and Applied Mathematics
Print ISSN 0377-0427
Publisher Elsevier
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
Publisher URL https://doi.org/10.1016/j.cam.2019.02.010

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