Automatic mesh sizing specification of complex three dimensional domains using an octree structure

M. Turner, D. Moxey, J. Peiró

24th International Meshing Roundtable (2015)

@inproceedings{turner-2015,
  title = {Automatic mesh sizing specification of complex three dimensional domains using an octree structure},
  booktitle = {24th International Meshing Roundtable},
  author = {Turner, M. and Moxey, D. and Peir\'o, J.},
  year = {2015},
  url = {https://davidmoxey.uk/assets/pubs/2015-imr24.pdf},
  abstract = {A system for automatically specifying a distribution of mesh sizing throughout three dimensional complex domains is presented, which aims to reduce the level of user input required to generate a mesh. The primary motivation for the creation of this system is for the production of suitable linear meshes that are sufficiently coarse for high-order mesh generation purposes. Resolution is automatically increased in regions of high curvature, with the system only requiring three parameters from the user to successfully generate the sizing distribution. This level of automation is achieved through the construction of an octree description of the domain, which targets the curvature of the surfaces and guides the generation of the mesh. After the construction of the octree, an ideal mesh spacing specification is calculated for each octant, based on a relation to the radii of curvature of the domain surfaces and mesh gradation criteria. The system is capable of accurately estimating the number of elements that will be produced prior to the generation process, so that the meshing parameters can be altered to coarsen the mesh before effort is wasted generating the actual mesh.}
}

Generating a mesh normally requires a good deal of manual specification of how fine it should be and where. This paper builds an octree description of a three-dimensional domain and derives a target spacing for each octant from the local surface curvature, needing only three parameters from the user. The number of elements can be estimated before generation, so the settings can be adjusted before the effort of meshing is spent.