When boundary conditions arising from the usual hydrodynamic assumptions are applied, analyses of dynamic wetting processes lead to a well-known nonintegrable stress singularity at the dynamic contact line, necessitating new ways to model this problem. In this paper, numerical simulations for a set of representative problems are used to explore the possibility of providing material boundary conditions for predictive models of inertialess moving contact line processes. The calculations reveal that up to Capillary number Ca=0.15, the velocity along an arc of radius 10Li (Li is an inner, microscopic length scale! from the dynamic contact line is independent of the macroscopic length scale a for a.103Li , and compares well to the leading order analytical ‘‘modulated-wedge’’ flow field [R. G. Cox, J. Fluid Mech. 168, 169 (1986)] for Capillary number Ca,0.1. Systematic deviations between the numerical and analytical velocity field occur for 0.1168, 169 (1986)] is used as a boundary condition along an arc of radius R=10-2a from the dynamic contact line, agree well with those using two inner slip models for Ca<0.1, with a breakdown at higher Ca. Computations in a cylindrical geometry reveal the role of azimuthal curvature effects on velocity profiles in this vicinity of dynamic contact lines. These calculations show that over an appropriate range of Ca, the velocity field and the meniscus slope in a geometry-independent region can potentially serve as material boundary conditions for models of processes containing dynamic contact lines.