Yet another hexahedral dominant meshing algorithm: HexDom

• Published in: Finite elements in analysis and design Vol. 136; pp. 1 - 17
• Main Authors: Karamete, B. Kaan, Aubry, Romain, Mestreau, Eric L., Dey, Saikat
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 15.11.2017; Elsevier BV
• Subjects: Algorithms; Boundary layer; Boundary layers; Cavity meshing; Hexahedral volume meshing; Manifolds; Meshing; Robustness (mathematics); Solvers; Tetrahedra; Tetrahedra; Hexahedral volume meshing; Boundary layers; Cavity meshing
• ISSN: 0168-874X; 1872-6925
• DOI: 10.1016/j.finel.2017.07.009

In this paper, we describe a robust meshing algorithm for obtaining a mixed mesh with large number of hexahedral/prismatic elements grown over the domain boundary respecting the user imposed anisotropic metric where physics matter the most and in areas where it is required to have the least number of elements. The inner section away from the boundaries is filled with the terminal octants of a non-conformal octree. The remaining unmeshed portion of the domain within the hexahedral/prismatic faces is filled with narrow bands of tetrahedra. The novel idea of the meshing algorithm is the formation of the cavity as slim as possible between the exposed faces of the outer most boundary layers and the octant faces of the inner most terminal octants, in such a way that the length scales of the cavity mesh spacings would allow the frontal tetrahedral meshing algorithm robustly succeeding to fill the cavity respecting its boundary faces without recovery issues. The algorithm could be applied to non-cubical, arbitrary geometries that can also be non-manifold. Each domain region is meshed recursively and within which, the tetrahedral filling algorithm constructs as many manifold cavity shells as the problem constrains are imposed by the boundary layers and the mesh size settings. The final hexahedral dominant mesh is exported to a face-based finite volume format (OpenFoam) so that the non-manifold nature of the mesh is captured by flux based numerical solvers consistently and accurately. •Due to the ability to discretize large volumes with fewer elements when compared to tetrahedra, hexahedral meshing of the volume in such applications offers computational savings over a purely tetrahedral approach.•For applications of interest here, flow fields generally impose greater gradients around the boundaries than anywhere else in the domain.•Alternatively, the gradients do not change as much in the bulky interior regions of the problem domain.•Therefore, fine and gradient compatible directional resolution in the mesh are needed to capture the solution gradients around the boundaries for accuracy, and fewer elements are desired to fill the space in the interior to save from the computational effort.•For both accounts, the use of hexahedral/prismatic elements make sense more than the tetrahedra. Hence, based on these observations, our intent in this study is to come up with a fast and robust algorithm of generating hexahedra dominant (HexDom) meshes where it makes sense for the numerics of the computational physics simulation.