Parallel computing as a vehicle for engineering design of complex functional surfaces

Thin liquid film flow over surfaces containing complex multiply connected topography is modelled using lubrication theory. The resulting time dependent nonlinear coupled set of governing equations for film thickness and pressure is solved on different parallel computing platforms using a purpose written portable and scalable parallel multigrid algorithm in order to achieve the fine-scale resolution required to guarantee mesh independent solutions. The robustness of the approach is demonstrated via the solution of three problems: one to establish the convergence characteristics viz. the partitioning and message passing strategies adopted, taking flow over a well-defined trench topography as a benchmark against existing experimental and corresponding numerical predictions; two, flow through a sparsely distributed set of occlusions with computations performed on different parallel architectures; three, free-surface planarisation with respect to flow over complex topography – the first an engineered functional substrate, the second a naturally occurring surface.