Adaptive mesh refinement for simulation of thin film flows

We present a robust and accurate numerical method for simulating gravity-driven, thin-film flow problems. The convection term in the governing equation is treated by a semi-implicit, essentially non-oscillatory scheme. The resulting nonlinear discrete equation is solved using a nonlinear full approximation storage multigrid algorithm with adaptive mesh refinement techniques. A set of representative numerical experiments are presented. We show that the use of adaptive mesh refinement reduces computational time and memory compared to the equivalent uniform mesh results. Our simulation results are consistent with previous experimental observations.