Solution Strategies for Thin Film Rimming Flow Modelling

Abstract

This paper explores the role of surface tension, grid resolution, inertia term representation and temporal discretisation scheme in the numerical simulation of shear-driven thin-film rimming flows. An ideal film formulation and solution strategy, suitable for the simulation of smooth, shock and pool solutions is presented. Shock and pool solution stability is shown to be dependent on the provision of sufficient grid refinement to resolve key flow features present in the solution such as steep fronts and small wavelength capillary waves. A minimum grid refinement criterion is proposed based on the findings from a parametric study. A previously established dependence of solution stability on surface tension is shown to be linked to the sensitivity of the wavelengths of disturbances in the capillary zone on the surface tension coefficient. Solution strategies utilising un-physically high surface tension values to guarantee stability, are explored and shown to enhance stability by modifying the solution in the capillary zone to one that is resolvable on the available grid. The role of inertia in solution stability is also investigated and simplified inertia representations are shown to primarily affect accuracy but not stability.