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Robust intersection of structured hexahedral meshes and degenerate triangle meshes with volume fraction applications
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  • Original Paper
  • Open Access
  • Published: 01 July 2017

Robust intersection of structured hexahedral meshes and degenerate triangle meshes with volume fraction applications

  • Frida Svelander  ORCID: orcid.org/0000-0002-4448-16061,2,
  • Gustav Kettil1,2,
  • Tomas Johnson1,
  • Andreas Mark1,
  • Anders Logg1,2 &
  • …
  • Fredrik Edelvik1 

Numerical Algorithms volume 77, pages 1029–1068 (2018)Cite this article

  • 952 Accesses

  • 7 Citations

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Abstract

Two methods for calculating the volume and surface area of the intersection between a triangle mesh and a rectangular hexahedron are presented. The main result is an exact method that calculates the polyhedron of intersection and thereafter the volume and surface area of the fraction of the hexahedral cell inside the mesh. The second method is approximate, and estimates the intersection by a least squares plane. While most previous publications focus on non-degenerate triangle meshes, we here extend the methods to handle geometric degeneracies. In particular, we focus on large-scale triangle overlaps, or double surfaces. It is a geometric degeneracy that can be hard to solve with existing mesh repair algorithms. There could also be situations in which it is desirable to keep the original triangle mesh unmodified. Alternative methods that solve the problem without altering the mesh are therefore presented. This is a step towards a method that calculates the solid area and volume fractions of a degenerate triangle mesh including overlapping triangles, overlapping meshes, hanging nodes, and gaps. Such triangle meshes are common in industrial applications. The methods are validated against three industrial test cases. The validation shows that the exact method handles all addressed geometric degeneracies, including double surfaces, small self-intersections, and split hexahedra.

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Acknowledgments

This work was supported in part by the Swedish Governmental Agency for Innovation Systems, VINNOVA, through the FFI Sustainable Production Technology program, and in part by the Sustainable Production Initiative and the Production Area of Advance at Chalmers University of Technology. The support is gratefully acknowledged.

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Authors and Affiliations

  1. Fraunhofer-Chalmers Research Centre for Industrial Mathematics, Göteborg, Sweden

    Frida Svelander, Gustav Kettil, Tomas Johnson, Andreas Mark, Anders Logg & Fredrik Edelvik

  2. Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, Gothenburg, Sweden

    Frida Svelander, Gustav Kettil & Anders Logg

Authors
  1. Frida Svelander
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  2. Gustav Kettil
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  3. Tomas Johnson
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Corresponding author

Correspondence to Frida Svelander.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

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Svelander, F., Kettil, G., Johnson, T. et al. Robust intersection of structured hexahedral meshes and degenerate triangle meshes with volume fraction applications. Numer Algor 77, 1029–1068 (2018). https://doi.org/10.1007/s11075-017-0352-7

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  • Received: 16 May 2016

  • Accepted: 23 May 2017

  • Published: 01 July 2017

  • Issue Date: April 2018

  • DOI: https://doi.org/10.1007/s11075-017-0352-7

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Keywords

  • Cut-cell
  • Volume fraction
  • Mesh repair
  • Overlapping triangles
  • Split hexahedra
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