An Improved Curvature Estimation Method Based on Height Function and Volume Preserving Mean Curvature Motion

Abstract

We present an improved height function technique aimed at obtaining smooth curvature in three dimensions. The new approach is designed for estimating curvature from the volume of fluid (VOF) field. Motivated by the volume-preserved mean curvature (VPMC) motion, an iterative procedure is implemented to eliminate oscillations from the curvature field while simultaneously ensuring consistency with the VOF field. To validate the new method, the curvature of 2D and 3D drops is considered. Numerical tests demonstrate the efficient elimination of high-frequency errors in the local curvature, and the total volume enclosed by the interface is preserved. Considering the equilibrium of the static droplet problem, the spurious current is also effectively suppressed. The proposed method is further extended to an adaptive mesh and validated through the free oscillation of a 2D droplet. Finally, the accuracy and efficiency of the improved height function technique applied to 3D problems are confirmed through the simulation of a liquid droplet impact onto a deep liquid pool.