Simulation of the vertical flow of a thin, wavy film using a finite-element method

The Navier-Stokes equations for a two-dimensional liquid film which is drained down a vertical wall in laminar flow are formulated in terms of the Lagrangian velocities and solved by a finite-element method. Excellent agreement is obtained between simulated results for wave celerity and wave form, and the corresponding experimental results. The momentum and mass balances, discretized in terms of the nodal point values for the velocities and the pressure, are solved by Galerkin's method. To avoid distortion of the network for increasing integration time a rezoning procedure has been developed. This overcomes a major deficiency of the Lagrangian formulation, and allows integration to proceed until a stationary wave profile is reached.