  The conventional no-slip boundary condition leads to a non-integrable stress
singularity at a contact line. This is a main challenge in numerical
simulations of two-phase flows with moving contact lines. We derive a
two-dimensional hydrodynamic model for the velocity field at a contact point
moving with constant velocity over a curved wall. The model is a perturbation
of the classical Huh and Scriven hydrodynamic solution [11], which is only
valid for flow over a flat wall. The purpose of the hydrodynamic model is to
investigate the macroscopic behavior of the fluids close to a contact point. We
also present an idea for how the hydrodynamic solution could be used to
prescribe macroscopic Dirichlet boundary conditions for the velocity in the
vicinity of a moving contact point. Simulations demonstrate that the velocity
field based on the non-singular boundary conditions is capable of accurately
advecting the contact point.
