Viscous flows in corner regions: Singularities and hidden eigensolutions

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Colleges, School and Institutes

Abstract

Numerical issues arising in computations of viscous flows in corners formed by a liquid fluid free surface and a solid boundary are considered. It is shown that on the solid a Dirichlet boundary condition, which removes multivaluedness of velocity in the 'moving contact-line problem' and gives rise to a logarithmic singularity of pressure, requires a certain modification of the standard finite-element method. This modification appears to be insufficient above a certain critical value of the corner angle where the numerical solution becomes mesh-dependent. As shown, this is due to an eigensolution, which exists for all angles and becomes dominant for the supercritical ones. A method of incorporating the eigensolution into the numerical method is described that makes numerical results mesh-independent again. Some implications of the unavoidable finiteness of the mesh size in practical applications of the finite-element method in the context of the present problem are discussed. Copyright (C) 2009 John Wiley & Sons, Ltd.

Details

Original languageEnglish
Pages (from-to)372-382
Number of pages11
JournalInternational Journal for Numerical Methods in Fluids
Volume65
Issue number4
Publication statusPublished - 10 Feb 2011