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

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)1886-1902
Number of pages17
JournalProceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science
Volume225
Issue numberC8
DOIs
Publication statusPublished - 2011

Keywords

  • thin film flow
  • droplet spreading
  • computational fluid dynamics
  • lubrication theory
  • numerical methods
  • LIQUID-FILMS
  • INCLINED PLANE
  • DIFFUSION
  • EVAPORATION
  • TOPOGRAPHY
  • EQUATIONS
  • DROPLETS

Cite this

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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.",
keywords = "thin film flow, droplet spreading, computational fluid dynamics, lubrication theory, numerical methods, LIQUID-FILMS, INCLINED PLANE, DIFFUSION, EVAPORATION, TOPOGRAPHY, EQUATIONS, DROPLETS",
author = "Cowling, {N. P.} and Gaskell, {P. H.} and Lee, {Y. C.} and Thompson, {H. M.}",
year = "2011",
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language = "English",
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pages = "1886--1902",
journal = "Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science",
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TY - JOUR

T1 - Towards the efficient numerical solution of three-dimensional thin film flows on real surfaces: an evaluation of finite-difference-based schemes

AU - Cowling, N. P.

AU - Gaskell, P. H.

AU - Lee, Y. C.

AU - Thompson, H. M.

PY - 2011

Y1 - 2011

N2 - 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.

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.

KW - thin film flow

KW - droplet spreading

KW - computational fluid dynamics

KW - lubrication theory

KW - numerical methods

KW - LIQUID-FILMS

KW - INCLINED PLANE

KW - DIFFUSION

KW - EVAPORATION

KW - TOPOGRAPHY

KW - EQUATIONS

KW - DROPLETS

U2 - 10.1177/0954406211399852

DO - 10.1177/0954406211399852

M3 - Article

VL - 225

SP - 1886

EP - 1902

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

SN - 0954-4062

IS - C8

ER -