A Height Function Method for the Simulation of Capillary Driven Multiphase Flows in Complex Domains

Multiphase flows play a considerable role in many physical phenomena as well as manufacturing processes, such as potting and lacquering. Particularly in small geometries, these flows are dominated by surface tension forces, which act singularly on the phase interface and are dependent on its geometry. Additionally, the dynamics at the triple line, thus at the intersection of the interface with a solid boundary are governed by complex, multiscale effects.
In order to facilitate the simulation of industrial applications, this work introduces a novel curvature-estimation approach for the volume of fluid method, which incorporates the boundary geometry into the height function methodology. In combination with a well-balanced, cell-centered, finite volume solver, the novel curvature schemes yield new possibilities for industrial applications, as shown in numerous analytical and realistic test cases.