FILMPAR: A parallel algorithm designed for the efficient and accurate computation of thin film flow on functional surfaces containing micro-structure

A highly efficient and portable parallel multigrid algorithm for solving a discretised form of the coupled lubrication equations for three-dimensional, gravity-driven, continuous thin film free-surface flow over substrates containing micro-scale topography is presented. Although applicable to problems involving heterogeneous and distributed features, for illustrative purposes the algorithm is benchmarked for the case of flow over a single trench topography; this enables direct comparisons with complementary experimental data and existing serial multigrid solutions. Parallel performance is accessed and shown to lead to super-linear behaviour provided the finest multigrid mesh level employed is sufficiently so.