  We developed a sharp interface level-set approach for two-phase immiscible
flow with moving contact lines. The Cox-Voinov model is used to describe the
moving contact line. A piecewise linear interface method is used to construct
the signed distance function and to implement the contact angle boundary
condition. Spurious currents are studied in the case of static and moving fluid
interfaces, which show convergence behavior. Pressure and the surface tension
force are balanced up to machine precision for static parabolic interfaces,
while the velocity error decreases steadily with grid refinement when the
interface is advected in a uniform flow field. The moving contact line problem
is studied and validated through comparison with theory and experiments for an
advancing interface and capillary rise in a tube.
