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Free-surface film flow over topography : full three-dimensional finite element solutions.

Veremieiev, S. and Thompson, H.M. and Gaskell, P.H. (2015) 'Free-surface film flow over topography : full three-dimensional finite element solutions.', Computers and fluids., 122 . pp. 66-82.


An efficient Bubnov-Galerkin finite element formulation is employed to solve the Navier-Stokes and continuity equations in three-dimensions for the case of surface-tension dominated film flow over substrate topography, with the free-surface location obtained using the method of spines. The computational challenges encountered are overcome by employing a direct parallel multi-frontal method in conjunction with memory-efficient out-of-core storage of matrix co-factors. Comparison is drawn with complementary computational and experimental results for low Reynolds number flow where they exist, and a range of new benchmark solutions provided. These, in turn, are compared with corresponding solutions, for non-zero Reynolds number, from a simplified model based on the long-wave approximation; the latter is shown to produce comparatively acceptable results for the free-surface disturbance experienced, when the underpinning formal restrictions on geometry and capillary number are not exceeded.

Item Type:Article
Additional Information:Liquid film flow, Finite elements, Topography, Long-wave approximation, Navier-Stokes.
Full text:(AM) Accepted Manuscript
Available under License - Creative Commons Attribution Non-commercial No Derivatives.
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Publisher statement:© 2015 This manuscript version is made available under the CC-BY-NC-ND 4.0 license
Date accepted:14 August 2015
Date deposited:21 August 2015
Date of first online publication:01 September 2015
Date first made open access:01 September 2016

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