H-Morph: An Indirect Approach to Advancing Front Hex Meshing

2nd Symposium on Trends in Unstructured Mesh Generation, University of Colorado, Boulder, August 1999

MESHING
RESEARCH
CORNER

Steve J. Owen
ANSYS Inc., 275 Technology Drive, Canonsburg PA 15317
steve.owen@ansys.com

Sunil Saigal
Department of Civil and Environmental Engineering, Carnegie Mellon University, PA 15317
saigal+@cmu.edu

Abstract
H-Morph is a new automatic algorithm for the generation of a hexahedral-dominant finite element mesh for arbitrary volumes. As an extension of the ideas initially introduced in the Q-Morph algorithm [1] for quadrilateral surface meshing, the H-Morph method starts with an initial tetrahedral mesh and systematically transforms and combines tetrahedra into hexahedra. Input to the algorithm is a set of quadrilateral surface facets. The quad facets are first split into triangles and sent to a tetrahedral mesh generator. H-Morph is an advancing front method where the initial front consists of the quadrilateral surface facets, and where each quadrilateral is associated with two triangle faces of the internal tetrahedral mesh. Fronts are individually processed by recovering each of the six quadrilateral faces of a hexahedron from the tetrahedral mesh. Recovery techniques similar to those used in boundary constrained Delaunay mesh generation [2] are used. Tetrahedra internal to the six hexahedral faces are then removed and a hexahedron is formed. A state- machine approach similar to that used by plastering [3], a direct advancing front hex meshing algorithm, is used to determine the priority for processing fronts. The procedure continues until no tetrahedra remain within the volume, or tetrahedra remain which cannot be transformed or combined into valid hexahedral elements. Any remaining tetrahedra are typically towards the interior of the volume, generally a less critical region for analysis. Transition from tetrahedra to hexahedra in the final mesh is accomplished through pyramid shaped elements [4].

Several advantages of the proposed algorithm over existing methods will be illustrated. Some of these advantages include: (1) its ability to conform to an existing surface mesh; (2) costly surface intersection calculations needed when using a direct advancing front method are eliminated; and (3) at any time during the procedure, a valid mixed tetrahedra-hexahedra mesh is defined. The proposed method has been implemented and successfully tested on a limited number of cases. Example test cases and performance will be presented.

References

[1] Owen, Steven J., Matthew L. Staten, Scott A. Canann and Sunil Saigal 'Q-Morph: An Indirect Approach to Advancing Front Quad Meshing', International Journal for Numerical Methods in Engineering. Vol 44. No. 9 (1999) 1317-1340

[2] George, P. L., F. Hecht and E. Saltel 'Automatic Mesh Generator With Specified Boundary', Computer Methods in Applied Mechanics and Engineering, Vol. 92 (1991) 269-288

[3] Hipp, Jim and Randy Lober 'Plastering: Automated All-Hexahedral Mesh Generation Through Connectivity-Resolution' Proceedings, 3rd International Meshing Roundtable (1994)

[4] Owen, Steven J., Scott A. Canann and Sunil Saigal 'Pyramid Elements for Maintaining Tetrahedra to Hexahedra Conformability', Trends in Unstructured Mesh Generation, AMD-Vol. 220 (1997) 123-129