This paper evaluates and compares the accuracy and robustness of curvature
estimation methods for three-dimensional interfaces represented implicitly by
discrete volume fractions on a Cartesian mesh. The height function (HF) method
is compared to three paraboloid fitting methods: fitting to the piecewise
linear interface reconstruction centroids (PC), fitting to the piecewise linear
interface reconstruction volumetrically (PV), and volumetrically fitting (VF)
the paraboloid directly to the volume fraction field. The numerical studies
presented in this work find that while the curvature error from the VF method
converges with second-order accuracy as with the HF method for static
interfaces represented by exact volume fractions, the PV method best balances
low curvature errors with low computational cost for dynamic interfaces when
the interface reconstruction and advection are coupled to a two-phase
Navier-Stokes solver