Comparison of methods for curvature estimation from volume fractions

Abstract

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. A shape-independent test of the curvature estimation is introduced through the use of randomly oriented and shaped paraboloids as reference interfaces. The coupling of the curvature estimation, interface transport, and Navier–Stokes surface tension force is evaluated through the measurement of spurious velocities in simulations of stationary and translating droplets. These studies 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 when errors are introduced in the volume fraction field either artificially or through the interface advection and reconstruction steps.