Globally Conservative Surface Tension Modeling in Volume-of-Fluid Simulations

Multiphase flow simulations often rely on the Continuum Surface Force (CSF) model to calculate the contribution of surface tension to the conservation of momentum. The CSF model uses the interface curvature, the surface tension coefficient, and the discrete volume fraction gradient to convert the surface tension force into a volumetric momentum source. While powerful and widely used, the CSF model suffers from a number of issues. Notably, it can result in closed interfaces being subject to a non-zero net force, i.e. is not globally conservative. On the other hand, The Continuum Surface Stress (CSS) model is globally momentum conservative, but requires a smooth representation of the interface, enabling the reliable calculation of interface tangents at the cell faces. We present a method that uses VOF interface segments to create a smooth interface approximation, which is then utilized to calculate conservative surface tension forces. This method allows for the direct inclusion of variable surface tension resulting from temperature gradients or surfactants. Performance will be assessed on two-dimensional Laplace equilibrium and capillary wave test cases.