A paraboloid fitting technique for calculating curvature from piecewise-linear interface reconstructions on 3D unstructured meshes

摘要

We present a novel method for calculating interface curvature on 3Dunstructured meshes from piecewise-linear interface reconstructions typicallygenerated in the volume of fluid method. Interface curvature is a necessaryquantity to calculate in order to model surface tension driven flow. Curvatureneeds only to be computed in cells containing an interface. The approachrequires a stencil containing only neighbors sharing a node with a target cell,and calculates curvature from a least-squares paraboloid fit to the interfacereconstructions. This involves solving a 6x6 symmetric linear system in eachmixed cell. We present verification tests where we calculate the curvature of asphere, an ellipsoid, and a sinusoid in a 3D domain on regular Cartesianmeshes, distorted hex meshes, and tetrahedral meshes. For both regular andunstructured meshes, we find in all cases the paraboloid fitting method forcurvature to converge between first and second order with grid refinement.