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

Veremieiev, S.; Thompson, H.M.; Gaskell, P.H.

doi:10.1016/j.compfluid.2015.08.016

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

Veremieiev, S.; Thompson, H.M.; Gaskell, P.H.

Authors

Dr Sergii Veremieiev s.veremieiev@durham.ac.uk
Associate Professor

H.M. Thompson

Professor Philip Gaskell p.h.gaskell@durham.ac.uk
Professor

Abstract

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.

Citation

Veremieiev, S., Thompson, H., & Gaskell, P. (2015). Free-surface film flow over topography: full three-dimensional finite element solutions. Computers and Fluids, 122, 66-82. https://doi.org/10.1016/j.compfluid.2015.08.016

Journal Article Type	Article
Acceptance Date	Aug 14, 2015
Online Publication Date	Sep 1, 2015
Publication Date	Nov 20, 2015
Deposit Date	Aug 18, 2015
Publicly Available Date	Sep 1, 2016
Journal	Computers and Fluids
Print ISSN	0045-7930
Publisher	Elsevier
Peer Reviewed	Peer Reviewed
Volume	122
Pages	66-82
DOI	https://doi.org/10.1016/j.compfluid.2015.08.016
Keywords	Liquid film flow, Finite elements, Topography, Long-wave approximation, Navier-Stokes.

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Publisher Licence URL
http://creativecommons.org/licenses/by-nc-nd/4.0/

Copyright Statement
© 2015 This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/