Toward Automatic Grid Generation

Si Loi Leung

Mechanical Engineering

Mentor: Dr. Nathan Prewitt

University of Hawaii

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

Outline

• How to create shape structure graphs

• Evaluation of the shape structure graphs

• A look at the medial axis

Grid Generation

Getting Complicated

Multi-Block Topology

Shape Structure Graphs

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

Voronoi DiagramThe 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.

Voronoi in Action

Medial AxisThe medial axis is the collection of center points of circles that touch the boundary at least twice.

Medial Axis in Action

Medial Axis in Action

Shape Structure Graph

The shape structure graph is a meta-graph with respect to the medial axis and retains only the “interesting” vertices.

Shape Structure Graph

Easymesh/Showmesh

Easymesh

• Bojan Niceno

• Generates two-dimensional unstructured meshes

• Showmesh is a graphical interface to show the results

Input

50: 0 0 5 11: 5 0 5 1 2: 5 2.5 5 2 3: 3.5 4 5 24: 0 4 5 1# x y scale marker

50: 0 1 11: 1 2 22: 2 3 33: 3 4 44: 4 0 5# a b marker

Output3

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

samples

Evaluation

• Shape structure graph?

• Medial axis graph?

TopMaker

• By David L. Rigby, QSS Group

• Technique to generate multi-block topologies using the medial axis

How to Divide

Creating the Multi-block Topology

Something Like This

Conclusion

• Work in progress• What I learned

– C/C++

– Linux

– CFD

• Acknowledgement– Dr. Nathan Prewitt

– PET staff

– PET interns

Thank You