  Molecular dynamics (MD) and continuum simulations are carried out to
investigate the influence of shear rate and surface roughness on slip flow of a
Newtonian fluid. For weak wall-fluid interaction energy, the nonlinear
shear-rate dependence of the intrinsic slip length in the flow over an
atomically flat surface is computed by MD simulations. We describe laminar flow
away from a curved boundary by means of the effective slip length defined with
respect to the mean height of the surface roughness. Both the magnitude of the
effective slip length and the slope of its rate-dependence are significantly
reduced in the presence of periodic surface roughness. We then numerically
solve the Navier-Stokes equation for the flow over the rough surface using the
rate-dependent intrinsic slip length as a local boundary condition. Continuum
simulations reproduce the behavior of the effective slip length obtained from
MD simulations at low shear rates. The slight discrepancy between MD and
continuum results at high shear rates is explained by examination of the local
velocity profiles and the pressure distribution along the wavy surface. We
found that in the region where the curved boundary faces the mainstream flow,
the local slip is suppressed due to the increase in pressure. The results of
the comparative analysis can potentially lead to the development of an
efficient algorithm for modeling rate-dependent slip flows over rough surfaces.
