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SPECIAL ISSUE PAPERS

Conformal Refinement and Coarsening of Unstructured Hexahedral Meshes

[+] Author and Article Information
Steven E. Benzley

 Brigham Young University, Provo, UTseb@byu.edu

Nathan J. Harris

 Brigham Young University, Provo, UTnjh33@byu.edu

Michael Scott

 Brigham Young University, Provo, UTmas88@byu.edu

Michael Borden

 Sandia National Laboratories, Albuquerque, NMmborden@sandia.gov

Steven J. Owen

 Sandia National Laboratories, Albuquerque, NMsjowen@sandia.gov

J. Comput. Inf. Sci. Eng 5(4), 330-337 (Jun 28, 2005) (8 pages) doi:10.1115/1.2052848 History: Received October 07, 2004; Revised June 28, 2005

This paper describes recently developed procedures for local conformal refinement and coarsening of all-hexahedral unstructured meshes. Both refinement and coarsening procedures take advantage of properties found in the dual or “twist planes” of the mesh. A twist plane manifests itself as a conformal layer or sheet of hex elements within the global mesh. We suggest coarsening techniques that will identify and remove sheets to satisfy local mesh density criteria while not seriously degrading element quality after deletion. A two-dimensional local coarsening algorithm is introduced. We also explain local hexahedral refinement procedures that involve both the placement of new sheets, either between existing hex layers or within an individual layer. Hex elements earmarked for refinement may be defined to be as small as a single node or as large as a major group of existing elements. Combining both refinement and coarsening techniques allows for significant control over the density and quality of the resulting modified mesh.

Copyright © 2005 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

A stack of hexahedrons represented by a dual chord (black line)

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Figure 2

A sheet of hexahedrons represented by a dual “twist plane”

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Figure 3

A meshed cylinder and the corresponding dual

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Figure 4

An all-hex mesh (a) and single sheet (b)

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Figure 5

Uniform removal of numerous sheets along a specified curve

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Figure 6

A hex triad (a), coarsened element (b)

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Figure 7

User selected elements (a), applied grid structure (b), transition element insertion (c)

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Figure 8

Using a surface to define the shrink region

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Figure 9

Mesh of airfoil before and after refinement

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Figure 10

Using a line to define a shrink region

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Figure 11

Meshed shaft before and after refinement, the line shown defines the shrink region

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Figure 12

Cross-section views of refinement to shaft mesh

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Figure 13

Using a point to define the shrink region

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Figure 14

2D mesh with target element selected (a) and the chords that define the mesh (b)

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Figure 15

A single chord-loop insertion (a) and resulting mesh (b); multiple chord-loop insertion (c) and resulting mesh (d)

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Figure 16

An extracted sheet showing a single direction of refinement on the target center hex (a) and the mesh after three directions of refinement (b)

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Figure 17

Single hex sheet refinement templates

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Figure 18

Concavity issues

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Figure 19

Concavity adjustment

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Figure 20

Single sheet operations: Original mesh (a), selected elements (b), selected curve and vertex (c), selected surface (d)

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Figure 21

Additional hex sheet templates

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Figure 22

Combination refinement: parallel sheet refinement (a and c) followed by multiple directions of single sheet refinement (b and d)

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Figure 23

Single node refinement: refined mesh (a), smoothed mesh (b)

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Figure 24

Combination refinement: Original mesh (a), selected edges (b), and selected faces (c)

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Figure 25

Quality comparison (a) original mesh, (b) single sheet refinement, (c) combination refinement

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Figure 26

A single direction of refinement, i.e., a “stint”

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Figure 27

Variable single sheet refinement example

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