On the generation of curvilinear meshes through subdivision of isoparametric elements

D. Moxey, M. D. Green, S. J. Sherwin, J. Peiró

New Challenges in Grid Generation and Adaptivity for Scientific Computing, pp. 203–215 (2015)

@inbook{moxey-2015d,
  title = {On the generation of curvilinear meshes through subdivision of isoparametric elements},
  author = {Moxey, D. and Green, M. D. and Sherwin, S. J. and Peir\'o, J.},
  booktitle = {New Challenges in Grid Generation and Adaptivity for Scientific Computing},
  pages = {203--215},
  year = {2015},
  publisher = {Springer},
  doi = {10.1007/978-3-319-06053-8_10},
  url = {https://davidmoxey.uk/assets/pubs/2014-tet.pdf},
  abstract = {Recently, a new mesh generation technique based on the isoparametric representation of curvilinear elements has been developed in order to address the issue of generating high-order meshes with highly stretched elements.  Given a valid coarse mesh comprising of a prismatic boundary layer, this technique uses the shape functions that define the geometries of the elements to produce a series of subdivided elements of arbitrary height.  The purpose of this article is to investigate the range of conditions under which the resulting meshes are valid, and additionally to consider the application of this method to different element types. We consider the subdivision strategies that can be achieved with this technique and apply it to the generation of meshes suitable for boundary-layer fluid problems.}
}

A companion to our isoparametric boundary-layer meshing work, asking when the technique actually produces valid meshes. Starting from a valid coarse prismatic mesh, the shape functions that define the elements are used to subdivide them into layers of arbitrary height; this paper works out the range of conditions under which the result stays valid, and considers how the method applies to different element types.