Abstract
Alternative lubrication and depth-averaged formulations of the unsteady Navier–Stokes equations are used to explore the problem of gravity-driven inertial thin film flow on substrates containing topography that is either fully submerged or protrudes through the film. The resulting discrete form of the equation sets are solved using a multigrid strategy incorporating automatic adaptive time-stepping, enabling accurate mesh independent solutions to be generated very efficiently. Two benchmark test problems are solved revealing the extent of the free surface disturbance that ensues, together with the effect of inertia on the same.
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Acknowledgments
S. Veremieiev gratefully acknowledges the financial support of the European Union Marie Curie Action, contract MEST-CT-2005-020599.
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Veremieiev, S., Gaskell, P.H., Lee, Y.C., Thompson, H.M. (2011). Predicting Three-Dimensional Inertial Thin Film Flow over Micro-Scale Topography. In: Kuzmin, A. (eds) Computational Fluid Dynamics 2010. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17884-9_105
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DOI: https://doi.org/10.1007/978-3-642-17884-9_105
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