Numerical computation of an immiscible two-phase flow in comparison with experiment

The flow of fluids with interfaces or free surfaces is of great interest in both basic and applied research. Despite enormous efforts to develop numerical methods for solving such flow problems, no undisputed standards have emerged yet. We compare here three different approaches for the problem of a liquid film falling down along a vertical wall under the action of gravity. Due to an instability, waves form on the film surface and a nontrivial flow pattern emerges. This provides a test case for two-phase flow simulation methods under conditions of practical relevance. The methods compared are a moving boundary method and a volume of fluid method implemented in commercial software packages and a new phase field method. A set of experimental data is used as a reference for the comparison. All three methods correctly reproduce the main features of the experiment; however, none are free of quantitative deviations from the data.