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Special Edition on Unstructured Mesh Generation

Canann, Scott A. Sunil Saigal and Steven J. Owen ed.

International Journal for Numerical Methods in Engineering, Wiley, Vol 1, Num 49, 2000

MESHING
RESEARCH
CORNER

International Journal for Numerical Methods in Engineering Online Publishers Reference

Table of Contents

Preface to Special Edition

A special symposium on unstructured mesh generation was held in conjunction with the 5th US National Congress on Computational Mechanics held at the University of Colorado, Boulder, August 4-6 1999. This special edition of the International Journal for Numerical Methods in Engineering contains eighteen selected papers from the six sessions of the symposium.

Mesh generation plays a vital role in computational field simulation. The mesh can tremendously influence the accuracy and efficiency of a simulation. Automated methods for generating both structured and unstructured meshes have been available for many years. Structured or curvilinear grids, characterized by their regular lattice structure, are ideal for finite difference approaches, where this approach can take advantage of the regular nature of the grid for fast identification of neighboring cells. Unstructured meshes, on the other hand, are ideal for finite element simulation over irregular domains and complex geometry. Automated unstructured mesh generation techniques tend to rely heavily on complex data structures and heuristic computational algorithms. These papers represent the latest research in computational methods for generating unstructured meshes.

Topics addressed in this special edition span a wide range of issues. These include specific computational methods for generating tetrahedral, hexahedral and mixed or hybrid element meshes for solid models. Techniques for meshing parametric surfaces from CAD models as well as application specific methods for viscous flow simulations are also addressed. Also included are techniques for mesh optimization and geometry idealization.

An approach to automatic tetrahedral meshing is presented by Li, Teng and Ungor where a combination of ideas from both advancing front and sphere packing methods are used. Karamete, Beall and Shephard also present a method for triangulating arbitrary polyhedra, a problem frequently arising in mesh adaptation and remeshing.

Various aspects of the hexahedral meshing problem are extensively covered in this issue. A mesh extrusion technique is first introduced by Vassberg, where an elliptic system, typically used in structured grid generation, is used for generating regular quadrilateral and hexahedral meshes. Sweeping techniques are an efficient way of generating all-hexahedral meshes within solid models. With this technique, a mesh is typically swept through the volume from a single source surface to a single target, generating a hexahedral mesh as it is swept. Lai, Benzley and White extend the applicability of sweeping by introducing a method for allowing multiple source and target surfaces. White and Tautges address the issue of automatic recognition of sweepable geometries, providing criteria for when sweeping or other more general algorithms may be applied. When an appropriate mesh generation scheme has been selected, intervals must be assigned to the boundaries before hexahedral meshing methods can proceed. Shepherd, Benzley, and Mitchell introduce an automated technique for assigning appropriate intervals for multiple source and target swept meshes. While sweeping and extrusion methods can be very reliable and efficient, their applicability can be limited. A more general all-hexahedral method is presented by Sheffer and Bercovier that relies on a decomposition of the geometry into an Embedded Voronoi Graph (EVG) representation.

Two hex-dominant approaches are also presented in this special issue. Meshkat and Talmor present a method for transforming an existing tetrahedral mesh into a mixed mesh of hexahedra, pentahedra and tetrahedra by examining the local graph structure and combining elements. Owen and Saigal present a technique that also starts with a tetrahedral mesh. Individual edges and faces of the hexahedra are recovered from the tetrahedral mesh using techniques for edge and face recovery typically used in constrained Delaunay mesh generation.

Surface mesh generation is an important aspect, also represented by several authors in this issue. Borouchaki, Laug and George utilize a combined advancing-front/Delaunay technique for meshing on parametric surfaces. Noel also addresses parametric surface meshing, considering the problem of patch independent meshing over a series of connected trimmed patches, while maintaining a map of element sizes throughout the mesh. Rassineux et al. present a method for meshing or remeshing a surface represented by triangle facets. Hermite diffuse interpolation is used to more accurately represent surface curvature and small features during the remeshing process.

Viscous flow applications frequently require regions of the mesh where elements are highly stretched. Hybrid techniques are often used, where layers of stretched prisms or hexahedra are advanced or offset from the flow boundary and towards the far field. Boundary conforming tetrahedral methods are then used to fill the remaining non-boundary regions. Krause, Strecker and Fichtner present a new approach to the point location problem during the advancing layers process. Khawaja and Kallinderis address the issue of disparate geometric length scales by allowing local variation in the number of prismatic layers. Additional variations on the advancing layers technique are also presented by Garimella and Shephard. An alternate method, presented by Lohner and Cebral, begins with an isotropic teterahedral mesh. The mesh is successively enriched with points using a constrained Delaunay approach to achieve highly stretched elements.

Another important aspect of mesh generation is that of mesh optimization. Freitag and Plassman address this issue by providing an optimization technique for node relocation that will maximize the minimum area of simplicial elements in a local submesh. This technique is ideal for improving or untangling highly distorted meshes.

Very closely related to the mesh generation problem is the idea of geometry idealization. Fine, Remondini and Leon describe a technique where idealizations of the geometry are carried out through a successive vertex removal process. The resulting simplified geometry is more suited to the element size requirements of the mesh generation process.

We would like to thank the many authors who contributed to this special edition on unstructured mesh generation. We would also express appreciation for the timely reviews provided to the authors by numerous experts. In addition, thanks go to the organizers and participants of the 5th US National Congress on Computational Mechanics as well as editor, Professor Ted Belytschko and publisher, John Wiley & Sons for providing the forum for the dissemination of this work.

December, 1999

Scott A. Canann
Sunil Saigal
Steven J. Owen

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