Three-dimensional thin film and droplet flows over and past surface features with complex physics

This paper describes, in the main, the benefits of using a general Newton globally convergent solver within an adaptive multigrid framework for solving discretised forms of lubrication models of three-dimensional, free-surface flow over and/or past substrate topography, involving complex physics. The two illustrative gravity-driven problems considered address solute mixing in a continuous thin film flow and droplet migration down an inclined substrate. The computational price paid for the flexibility offered by the solver is investigated alongside the overall benefits of adaptive local mesh refinement and multigridding.