A paraboloid fitting technique for calculating curvature from piecewiselinear interface reconstructions on 3D unstructured meshes
Abstract
In this work, we present a novel method for calculating interface curvature on 3D unstructured meshes from piecewiselinear 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 leastsquares 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.
 Authors:

 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Publication Date:
 Research Org.:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org.:
 USDOE National Nuclear Security Administration (NNSA)
 OSTI Identifier:
 1477652
 Report Number(s):
 LAUR1730548
Journal ID: ISSN 08981221
 Grant/Contract Number:
 AC5206NA25396
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Computers and Mathematics with Applications (Oxford)
 Additional Journal Information:
 Journal Name: Computers and Mathematics with Applications (Oxford); Journal Volume: 78; Journal Issue: 2; Journal ID: ISSN 08981221
 Publisher:
 Elsevier
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; Volume of fluid; VOF; Curvature; Interface reconstruction; PLIC; Leastsquares fit
Citation Formats
Jibben, Zechariah Joel, Carlson, Neil N., and Francois, Marianne M. A paraboloid fitting technique for calculating curvature from piecewiselinear interface reconstructions on 3D unstructured meshes. United States: N. p., 2018.
Web. doi:10.1016/j.camwa.2018.09.009.
Jibben, Zechariah Joel, Carlson, Neil N., & Francois, Marianne M. A paraboloid fitting technique for calculating curvature from piecewiselinear interface reconstructions on 3D unstructured meshes. United States. https://doi.org/10.1016/j.camwa.2018.09.009
Jibben, Zechariah Joel, Carlson, Neil N., and Francois, Marianne M. Thu .
"A paraboloid fitting technique for calculating curvature from piecewiselinear interface reconstructions on 3D unstructured meshes". United States. https://doi.org/10.1016/j.camwa.2018.09.009. https://www.osti.gov/servlets/purl/1477652.
@article{osti_1477652,
title = {A paraboloid fitting technique for calculating curvature from piecewiselinear interface reconstructions on 3D unstructured meshes},
author = {Jibben, Zechariah Joel and Carlson, Neil N. and Francois, Marianne M.},
abstractNote = {In this work, we present a novel method for calculating interface curvature on 3D unstructured meshes from piecewiselinear 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 leastsquares 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.},
doi = {10.1016/j.camwa.2018.09.009},
journal = {Computers and Mathematics with Applications (Oxford)},
number = 2,
volume = 78,
place = {United States},
year = {2018},
month = {9}
}
Web of Science