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

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Abstract

We present an adaptive moving mesh method for the numerical solution of thin liquid film spreading flows with surface tension. We follow the r-adaptive moving mesh technique which utilises a mesh density function and moving mesh partial differential equations (MMPDEs) to adapt and move the mesh coupled to the PDE(s) describing the thin film flow problem. Numerical experiments are performed on two one dimensional thin film flow equations to test the accuracy and efficiency of the method. This technique accurately resolves the multiple one-dimensional structures observed in these test problems. Moreover, it reduces the computational effort in comparison to the numerical solution using the finite difference scheme on a fixed uniform mesh.

Acceptance Date Jan 16, 2017
Publication Date Jan 25, 2017
Publicly Available Date Mar 28, 2024
Journal Journal of Computational and Applied Mathematics
Print ISSN 0377-0427
Publisher Elsevier
Pages 365-384
DOI https://doi.org/10.1016/j.cam.2017.01.019
Keywords Thin film flows; Surface Tension; Adaptive moving mesh; r-adaptive method; moving mesh PDEs (MMPDEs); Mesh density function
Publisher URL https://doi.org/10.1016/j.cam.2017.01.019

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