Finite particle methods for computing interfacial curvature in volume of fluid simulations

The volume of fluid (VOF) method is a useful tool for multiphase flow simulation. However, smallscale interfacial structures introduce significant computational challenges. One difficulty is determining interface curvature at low resolutions-a requirement in turbulent spray simulation. In this work we evaluate two finite particle schemes for computing curvature of poorly resolved interfaces in the context of VOF simulations. Curvature is computed from the convolved VOF in the first scheme and directly from the VOF in the second scheme. Both cell-centered and interface-centered calculations are considered in the first scheme, while only cell-centered calculations are considered in the second scheme. The methods are evaluated via the L₂ and L_∞ error norms corresponding to the curvature of spheres. Results yield L₂ errors less than 1% and L_∞ errors less than 3% for nearly all resolutions considered. Additionally, a hybrid implementation of the first scheme demonstrates greater accuracy than a contemporary variant of the height function method for resolutions relevant to spray simulations. The results suggest the finite particle method to be a valuable tool for computing interfacial curvature in flows with a poorly resolved dispersed phase.