### 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 |
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Pages (from-to) | 1886-1902 |

Number of pages | 17 |

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

Volume | 225 |

Issue number | C8 |

DOIs | |

Publication status | Published - 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

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

*225*(C8), 1886-1902. https://doi.org/10.1177/0954406211399852