2017/12/14 by Zechariah Jibben, Jibben, Z., Neil Carlson +3 · 1 citation
Computer Science · Engineering · Materials Science · #Computational Physics (physics.comp-ph) #Computer Graphics and Visualization Techniques #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Heat Transfer #Surface Modification and Superhydrophobicity
paper · pdf · doi:10.48550/arxiv.1712.05467
openalex publication_date 2017/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a novel method for calculating interface curvature on 3D unstructured meshes from piecewise-linear interface reconstructions typically generated in the volume of fluid method. Interface curvature is a necessary quantity to calculate in order to model surface tension driven flow. Curvature needs only to be computed in cells containing an interface. The approach requires a stencil containing only neighbors sharing a node with a target cell, and calculates curvature from a least-squares paraboloid fit to the interface reconstructions. This involves solving a 6x6 symmetric linear system in each mixed cell. We present verification tests where we calculate the curvature of a sphere, an ellipsoid, and a sinusoid in a 3D domain on regular Cartesian meshes, distorted hex meshes, and tetrahedral meshes. For both regular and unstructured meshes, we find in all cases the paraboloid fitting method for curvature to converge between first and second order with grid refinement.