Towards the efficient numerical solution of three-dimensional thin film flows on real surfaces: an evaluation of finite-difference-based schemes

N. P. Cowling; P. H. Gaskell; Y. C. Lee; H. M. Thompson

doi:10.1177/0954406211399852

Towards the efficient numerical solution of three-dimensional thin film flows on real surfaces: an evaluation of finite-difference-based schemes

N. P. Cowling^*, P. H. Gaskell, Y. C. Lee, H. M. Thompson

^*Corresponding author for this work

School of Engineering, Computing and Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

The comparative efficiency of time-splitting and multigrid schemes for the solution of lubrication models of three-dimensional (3D), thin film flow is demonstrated via detailed comparisons for benchmark gravity-driven continuous film and droplet spreading problems. Data are presented which show the effect of (1) problem formulation (either as a single fourth-order partial differential equation for the film thickness or two coupled second-order equations for film thickness and pressure) and (2) grid density on the choice of fixed time-step, CPU time per time-step and overall efficiency of each scheme. On the basis of these findings, recommendations are given as to the most efficient combination of problem formulation and numerical scheme for solving 3D thin film free surface flows over practical, engineering surfaces.

Original language	English
Pages (from-to)	1886-1902
Number of pages	0
Journal	Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science
Volume	225
Issue number	8
Early online date	25 May 2011
DOIs	https://doi.org/10.1177/0954406211399852
Publication status	Published - Aug 2011

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Cowling, N. P., Gaskell, P. H., Lee, Y. C., & Thompson, H. M. (2011). Towards the efficient numerical solution of three-dimensional thin film flows on real surfaces: an evaluation of finite-difference-based schemes. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 225(8), 1886-1902. https://doi.org/10.1177/0954406211399852

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title = "Towards the efficient numerical solution of three-dimensional thin film flows on real surfaces: an evaluation of finite-difference-based schemes",

abstract = " The comparative efficiency of time-splitting and multigrid schemes for the solution of lubrication models of three-dimensional (3D), thin film flow is demonstrated via detailed comparisons for benchmark gravity-driven continuous film and droplet spreading problems. Data are presented which show the effect of (1) problem formulation (either as a single fourth-order partial differential equation for the film thickness or two coupled second-order equations for film thickness and pressure) and (2) grid density on the choice of fixed time-step, CPU time per time-step and overall efficiency of each scheme. On the basis of these findings, recommendations are given as to the most efficient combination of problem formulation and numerical scheme for solving 3D thin film free surface flows over practical, engineering surfaces. ",

author = "Cowling, {N. P.} and Gaskell, {P. H.} and Lee, {Y. C.} and Thompson, {H. M.}",

year = "2011",

month = aug,

doi = "10.1177/0954406211399852",

language = "English",

volume = "225",

pages = "1886--1902",

journal = "Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science",

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Cowling, NP, Gaskell, PH, Lee, YC & Thompson, HM 2011, 'Towards the efficient numerical solution of three-dimensional thin film flows on real surfaces: an evaluation of finite-difference-based schemes', Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, vol. 225, no. 8, pp. 1886-1902. https://doi.org/10.1177/0954406211399852

Towards the efficient numerical solution of three-dimensional thin film flows on real surfaces: an evaluation of finite-difference-based schemes. / Cowling, N. P.; Gaskell, P. H.; Lee, Y. C. et al.
In: Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, Vol. 225, No. 8, 08.2011, p. 1886-1902.

Research output: Contribution to journal › Article › peer-review

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AB - The comparative efficiency of time-splitting and multigrid schemes for the solution of lubrication models of three-dimensional (3D), thin film flow is demonstrated via detailed comparisons for benchmark gravity-driven continuous film and droplet spreading problems. Data are presented which show the effect of (1) problem formulation (either as a single fourth-order partial differential equation for the film thickness or two coupled second-order equations for film thickness and pressure) and (2) grid density on the choice of fixed time-step, CPU time per time-step and overall efficiency of each scheme. On the basis of these findings, recommendations are given as to the most efficient combination of problem formulation and numerical scheme for solving 3D thin film free surface flows over practical, engineering surfaces.

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JO - Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science

JF - Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science

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Cowling NP, Gaskell PH, Lee YC, Thompson HM. Towards the efficient numerical solution of three-dimensional thin film flows on real surfaces: an evaluation of finite-difference-based schemes. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science. 2011 Aug;225(8):1886-1902. Epub 2011 May 25. doi: 10.1177/0954406211399852

Towards the efficient numerical solution of three-dimensional thin film flows on real surfaces: an evaluation of finite-difference-based schemes

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