Computing three-dimensional thin film flows including contact lines

We present a computational method for quasi 3D unsteady flows of thin liquid films on a solid substrate. This method includes surface tension as well as gravity forces in order to model realistically the spreading on an arbitrarily inclined substrate. The method uses a positivity preserving scheme to avoid possible negative values of the fluid thickness near the fronts. The "contact line paradox," i.e., the infinite stress at the contact line, is avoided by using the precursor film model which also allows for approaching problems that involve topological changes. After validating the numerical code on problems for which the analytical solutions are known, we present results of fully nonlinear time-dependent simulations of merging liquid drops using both uniform and nonuniform computational grids.