Viscous flows in corner regions: Singularities and hidden eigensolutions

Details Viscous flows in corner regions: Singularities and hidden eigensolutions Viscous flows in corner regions: Singularities and hidden eigensolutions

2009-06-18

arxiv.org/abs/0906.3462v1

Physics

Fluid Dynamics

Submitted to the International Journal for Numerical Methods in Fluids

Scientific paper

10.1002/fld.2187

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.

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