Non-Simplicial Unstructured Mesh Generation

Dissertation, Department of Civil and Environmental Engineering, Carnegie Mellon University, April 1999

MESHING
RESEARCH
CORNER

Abstract
New automatic methods and algorithms are presented for the generation of unstructured meshes comprised primarily of non-simplicial (non-triangular or non-tetrahedral) elements. Within this context, four specific areas are addressed: (1) Element Sizing: Natural Neighbor Interpolation is proposed as a new method for providing sizing information to a surface mesh generator. Several applications of sizing control are provided. (2) Quadrilateral Mesh Generation: A new method, known as Q-Morph, for quadrilateral mesh generation on arbitrary surfaces is presented. The algorithm begins with a triangular mesh, over which systematic transformations are performed on the triangles working from the boundary towards the interior. A boundary-aligned all-quadrilateral mesh with few irregular internal nodes is produced. (3) Hexahedral- Dominant Mesh Generation: H-Morph, the three-dimensional extension of the Q- Morph algorithm is proposed as a method for generating a boundary conforming, hex-dominant mesh for arbitrary volumes. Beginning with a boundary constrained tetrahedral mesh, tetrahedra are methodically transformed and replaced with hexahedral elements. Regions that cannot be filled with hexahedra are left with tetrahedra. (4) Pyramid Element Formation: Pyramid shaped elements are proposed as a convenient mechanism for interfacing tetrahedral elements with hexahedra. Several methods are proposed for their construction and their performance is evaluated.

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