Walkley, M.A., Gaskell, P.H., Jimack, P.K., Kelmanson, M.A. and Summers, J.L. (2005) Adaptive finite element simulation of threedimensional surface tension dominated freesurface flow problems. Australian and New Zealand Industrial and Applied Mathematics Journal, 46 (E). C558C571. ISSN 14468735

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Abstract
An arbitrary LagrangianEulerian finite element method is described for the solution of timedependent, threedimensional, freesurface flow problems. Many flows of practical significance involve contact lines, where the free surface meets a solid boundary. This contact line may be pinned to a particular part of the solid but is more typically free to slide in a manner that is characterised by the dynamic contact angle formed by the fluid. We focus on the latter case and use a model that admits spatial variation of the contact angle: thus permitting variable wetting properties to be simulated.
The problems are driven by the motion of the fluid free surface (under the action of surface tension and external forces such as gravity) hence the geometry evolves as part of the solution, and mesh adaptivity is required to maintain the quality of the computational mesh for the physical domain. Continuous mesh adaptivity, in the form of a pseudoelastic mesh movement scheme, is used to move the interior mesh nodes in response to the motion of the fluid's free surface. Periodic, discrete remeshing stages are also used for cases in which the fluid volume has grown, or is sufficiently distorted, by the freesurface motion. Examples are given of a droplet sliding on an inclined uniform plane and of a droplet spreading on a surface with variable wetting properties.
Item Type:  Article 

Copyright, Publisher and Additional Information:  © Copyright 2005 Australian Mathematical Society. Text freely available from the journal web site. 
Institution:  The University of Leeds 
Academic Units:  The University of Leeds > Faculty of Engineering (Leeds) > School of Computing (Leeds) The University of Leeds > Faculty of Maths and Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) The University of Leeds > Faculty of Engineering (Leeds) > School of Mechanical Engineering (Leeds) > Institute of Engineering Thermofluids, Surfaces & Interfaces (iETSI) (Leeds) 
Depositing User:  Repository Assistant 
Date Deposited:  15 Dec 2006 
Last Modified:  06 Jun 2014 18:34 
Published Version:  http://anziamj.austms.org.au/V46/CTAC2004/Walk/hom... 
Status:  Published 
Publisher:  Australian Mathematical Society 
Refereed:  Yes 
Related URLs:  
URI:  http://eprints.whiterose.ac.uk/id/eprint/1765 