Robust Intersection of Structured Hexahedral Meshes and Degenerate Triangle Meshes with Volume Fraction Applications
Artikel i vetenskaplig tidskrift, 2017

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.


Frida Svelander

Göteborgs universitet

Chalmers, Matematiska vetenskaper

Gustav Kettil

Chalmers, Matematiska vetenskaper

Göteborgs universitet

Tomas Johnson

Anders Logg

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Fredrik Edelvik

Numerical Algorithms

1017-1398 (ISSN)

Vol. July


Building Futures




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