The efficient and accurate solution of continuous thin film flow over surface patterning and past occlusions

The benefits of a spatially and time-adaptive full approximation storage (FAS) multigrid method for the solution of the thin film lubrication equations, as used to model gravity-driven flow over complex submerged topography and past small-scale occlusions, are investigated. Results are presented which demonstrate how flow orientation has a significant effect on the magnitude of the resultant free-surface disturbances and how reduction of the in-plane dimensions of the associated topography increases the computational resources needed to achieve grid-independent solutions. In addition, the ability to automatically restrict fine grid resolution only to those regions in and around small, localized topography is shown to lead to significantly increased computational efficiency over grid-independent solutions obtained on globally fine meshes with the same degree of accuracy. Copyright © 2007 John Wiley & Sons, Ltd