Toward Automatic Grid Generation

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Toward Automatic Grid Generation
Si Loi Leung
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University of Hawaii
Mechanical Engineering
Mentor Dr. Nathan Prewitt
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Project Goals

• Write a program to generate shape structure
  graphs for any given boundaries
• Investigate how it could possibly be employed in
  automatic grid generation of any arbitrary
  boundaries

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Outline

• How to create shape structure graphs
• Evaluation of the shape structure graphs
• A look at the medial axis

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Grid Generation
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Getting Complicated
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Multi-Block Topology
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Shape Structure Graphs

• Idea started from an article by Vitaly Ablavsky
  in the C/C Users Journal

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Voronoi Diagram
The Voronoi diagram of a collection of nodes is
a partition of space into cells, where any point
within a cell is closer to its respective node
than to any others.
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Voronoi in Action
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Medial Axis
The medial axis is the collection of center
points of circles that touch the boundary at
least twice.
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Medial Axis in Action
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Medial Axis in Action
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Shape Structure Graph
The shape structure graph is a meta-graph with
respect to the medial axis and retains only the
interesting vertices.
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Shape Structure Graph
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Easymesh/Showmesh

• Easymesh
• Bojan Niceno
• Generates two-dimensional unstructured meshes
• Showmesh is a graphical interface to show the
  results

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Input
5 0 0 0 5 1 1 5 0
5 1 2 5 2.5 5 2 3 3.5
4 5 2 4 0 4 5 1
x y scale marker 5 0 0 1 1 1
1 2 2 2 2 3 3 3 3 4 4 4
4 0 5 a b marker
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Output
3 0 0 3 4 -1 -1 1 5 6
4 2.5000 .25000 -1 1 0 2 3
2 -1 0 4 2 1 2.4167 1.4167
-1 2 3 1 2 -1 1 -1 3
1 0 1.7500 2.0000 -1 ---------------------
--------------------------------------------------
- e i, j, k, ei, ej, ek, si, sj,
sk xV, yV sign
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samples
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Evaluation

• Shape structure graph?
• Medial axis graph?

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TopMaker

• By David L. Rigby, QSS Group
• Technique to generate multi-block topologies
  using the medial axis

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How to Divide
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Creating the Multi-block Topology
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Something Like This
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Conclusion

• Work in progress
• What I learned
• C/C
• Linux
• CFD
• Acknowledgement
• Dr. Nathan Prewitt
• PET staff
• PET interns

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Thank You