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Inertial thin film flow on planar surfaces featuring topography

Veremieiev, S.; Thompson, H.M.; Lee, Y.C.; Gaskell, P.H.

Inertial thin film flow on planar surfaces featuring topography Thumbnail


H.M. Thompson

Y.C. Lee


A range of problems is investigated, involving the gravity-driven inertial flow of a thin viscous liquid film over an inclined planar surface containing topographical features, modelled via a depth-averaged form of the governing unsteady Navier–Stokes equations. The discrete analogue of the resulting coupled equation set, employing a staggered mesh arrangement for the dependent variables, is solved accurately using an efficient full approximation storage (FAS) algorithm and a full multigrid (FMG) technique; together with error-controlled automatic adaptive time-stepping and proper treatment of the associated nonlinear convective terms. An extensive set of results is presented for flow over both one- and two-dimensional topographical features, and errors quantified via detailed comparisons drawn with complementary experimental data and predictions from finite element analyses where they exist. In the case of one-dimensional (spanwise) topography, moderate Reynolds numbers and shallow/short topographical features, the results obtained are in close agreement with corresponding finite element solutions of the full free-surface problem. For the case of flow over two-dimensional (localised) topography, it is shown that the free-surface disturbance is influenced significantly by the presence of inertia leading, as in the case of spanwise topography, to an increase in the magnitude and severity of the resulting capillary ridge and trough formations: the effect of inclination angle and topography aspect ratio are similarly explored.


Veremieiev, S., Thompson, H., Lee, Y., & Gaskell, P. (2010). Inertial thin film flow on planar surfaces featuring topography. Computers and Fluids, 39(3), 431-450.

Journal Article Type Article
Acceptance Date Sep 9, 2009
Online Publication Date Sep 15, 2009
Publication Date Mar 1, 2010
Deposit Date Sep 18, 2013
Publicly Available Date Aug 21, 2015
Journal Computers and Fluids
Print ISSN 0045-7930
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 39
Issue 3
Pages 431-450


Accepted Journal Article (2.7 Mb)

Copyright Statement
NOTICE: this is the author’s version of a work that was accepted for publication in Computers and Fluids. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Computers and Fluids, 39, 3, March 2010, 10.1016/j.compfluid.2009.09.007.

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