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.
Original language | English |
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Pages (from-to) | 372-382 |
Number of pages | 11 |
Journal | International Journal for Numerical Methods in Fluids |
Volume | 65 |
Issue number | 4 |
DOIs | |
Publication status | Published - 10 Feb 2011 |