Global models for moving contact lines.

We consider thin film flows driven by surface tension and gravity. Within the framework of the lubrication approximation, we study the contact line motion using global models where either precursor film or slip are allowed. We show that completely wetting films can be simulated under both conditions without requiring direct tracking of the contact line interface. We perform a comparative study of standard and positivity preserving numerical methods for these problems in one space dimension, with the ultimate goal of choosing the best method applicable to two-dimensional problems. We find a considerable computational advantage of the precursor film model over the slipping models.