Free-surface thin-film flows over uniformly heated topography

The long-wave (lubrication) approximation governing the evolution of a thin film over a uniformly heated topographical substrate is solved numerically. We study the initial-value problem for a variety of governing dimensionless parameters and topographical substrates. We demonstrate that the dynamics is characterized by a slow relaxation process with continuous coarsening of drops up to a large time where coarsening is terminated and the interface organizes into a series of drops each of which is located in a trough in topography.