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

Journal Article · 27 September 2018 · Computers and Mathematics with Applications (Oxford)

DOI: https://doi.org/10.1016/j.camwa.2018.09.009 · OSTI ID:1477652

Jibben, Zechariah Joel  ^[1]; Carlson, Neil N.  ^[1]; Francois, Marianne M.  ^[1]

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1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

In this work, 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 6 × 6 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. Lastly, 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.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA)
• Grant/Contract Number: AC52-06NA25396
• OSTI ID: 1477652
• Report Number(s): LA-UR-17-30548
• Journal Information: Computers and Mathematics with Applications (Oxford), Vol. 78, Issue 2; ISSN 0898-1221
• Publisher: ElsevierCopyright Statement
• Country of Publication: United States
• Language: English