  A main challenge in numerical simulations of moving contact line problems is
that the adherence, or no-slip boundary condition leads to a non-integrable
stress singularity at the contact line. In this report we perform the first
steps in developing the macroscopic part of an accurate multiscale model for a
moving contact line problem in two space dimensions. We assume that a micro
model has been used to determine a relation between the contact angle and the
contact line velocity. An intermediate region is introduced where an analytical
expression for the velocity exists. This expression is used to implement
boundary conditions for the moving contact line at a macroscopic scale, along a
fictitious boundary located a small distance away from the physical boundary.
Model problems where the shape of the interface is constant thought the
simulation are introduced. For these problems, experiments show that the errors
in the resulting contact line velocities converge with the grid size $h$ at a
rate of convergence $p\approx 2$.

Fluid Dynamics