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

Artikel i vetenskaplig tidskrift
Författare Frida Svelander Gustav Kettil Tomas Johnson Andreas Mark Anders Logg Fredrik Edelvik Numerical Algorithms 77 4 1029–1068 1017-1398 2018 Institutionen för matematiska vetenskaper 1029–1068 en https://doi.org/10.1007/s11075-017-... Cut-cell, Mesh repair, Overlapping triangles, Split hexahedra, Volume fraction Beräkningsmatematik, Tillämpad matematik

## Sammanfattning

© 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.