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

Jibben, Zechariah Joel; Carlson, Neil N.; Francois, Marianne M.

doi:10.1016/j.camwa.2018.09.009

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

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Abstract

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.

Authors:

^[1];

^[1]

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

Publication Date:: 2018-09-27

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):: LA-UR-17-30548
Journal ID: ISSN 0898-1221

Grant/Contract Number:: AC52-06NA25396

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 0898-1221

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; Volume of fluid; VOF; Curvature; Interface reconstruction; PLIC; Least-squares fit

Citation Formats


                    Jibben, Zechariah Joel, Carlson, Neil N., and Francois, Marianne M. A paraboloid fitting technique for calculating curvature from piecewise-linear interface reconstructions on 3D unstructured meshes.  United States: N. p., 2018. 
Web.  doi:10.1016/j.camwa.2018.09.009.

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                    Jibben, Zechariah Joel, Carlson, Neil N., & Francois, Marianne M. A paraboloid fitting technique for calculating curvature from piecewise-linear interface reconstructions on 3D unstructured meshes.  United States.  https://doi.org/10.1016/j.camwa.2018.09.009

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                    Jibben, Zechariah Joel, Carlson, Neil N., and Francois, Marianne M. Thu .  
"A paraboloid fitting technique for calculating curvature from piecewise-linear 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.

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@article{osti_1477652,

  title        = {A paraboloid fitting technique for calculating curvature from piecewise-linear 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 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.},

  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}

}

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