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

Journal article
Authors Frida Svelander
Gustav Kettil
Tomas Johnson
Andreas Mark
Anders Logg
Fredrik Edelvik
Published in Numerical Algorithms
Volume 77
Issue 4
Pages 1029–1068
ISSN 1017-1398
Publication year 2018
Published at Department of Mathematical Sciences
Pages 1029–1068
Language en
Links https://doi.org/10.1007/s11075-017-...
Keywords Cut-cell, Mesh repair, Overlapping triangles, Split hexahedra, Volume fraction
Subject categories Computational Mathematics, Applied mathematics

Abstract

© 2017 The Author(s) 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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