{"paper":{"title":"A Paraboloid Fitting Technique for Calculating Curvature from Piecewise-Linear Interface Reconstructions on 3D Unstructured Meshes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.flu-dyn"],"primary_cat":"physics.comp-ph","authors_text":"M. M. Francois, N. N. Carlson, Z. Jibben","submitted_at":"2017-12-14T22:24:26Z","abstract_excerpt":"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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.05467","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}