The algorithm for surface modeling and volume grid generation using parametric Non-Uniform Rational B-splines (NURBS) geometric representation are presented. The enhanced re-parameterization algorithm which can yield a desired physical distribution on the curve, surface, and volume is also presented. This approach bridges the gap between computer aided design surface/volume definition and surface/volume grid generation

Benjamin, Ted

Soni, Bharat K.

Williams, Robert

Yu, Tzuyi

English

NASA Technical Reports Server

Surface and Volume grid generation
in parametric form
by
Tzuyi Yu, Bharat K. Soni
NSF/ERC For Computational Field Simulation
Mississippi State University, MS39762
Ted Benjamin, Robert Williams
Marshall Space Flight Center, AL 35812
ABSTRACT
The algorithms for surface modeling and volume grid generation using parametric NURBS geometric
representation are presented. The enhanced re-parameterization algorithm which can yield a desired
physical distribution on the curve, surface and volume is also presented. This approach bridges the gap
between CAD surface / volume definition and surface / volume grid generation.
INTRODUCTION
Surface grid generation is the most labor intensive part of the overall complex three dimensional
grid generation process. Also, a significant amount of effort is required in changing the resolutions (grid
sizes) and / or the distribution of the grid while maintaining geometry fidelity. In the last few years, vari-
ous researchers have concentrated on utilizing the Computer Aided Geometry Design (CAGD) techniques
to expedite the overall surface generation process. In this presentation, a parametric formula which has
been used in CAD system is extended with re-parameterization approach to numerical grid generation for
modeling the surface as well as the volume grid.
There are many parametric approaches for representing sculptured geometry, such as rational or
non-rational Bezier, cubic splines, rational or non-rational B-spines ..... etc. Among these representation,
the Non-Uniform Rational B-Splines (NURBS) has been widely accepted among these researchers.
NURBS has been widely utilized to represent and design geometry in the CAD/CAM and the graphics
community due to its powerful features, such as the local control property, variation diminishing, convex
hull and affine invariance [Ref 1,2]. Also the geometry tool kits, such as curve/surface interpolation, data
reduction, degree elevation, knot insertion and splitting, are well-developed [Ref 1,2,]. These properties
have made NURBS representation very popular in recent developments in CAD/CAM. However, the dis-
tribution requirements in CFD application are much complicated than those in CAD system. Hence, the
NURBS must be cooperated with re-parameterization algorithm so that it can be more useful in grid gen-
eration. Computational examples associated with practical configurations are shown in Figure 1 and 2.
The re-parameterization approach described in many research [Ref 2,3] is implemented by iteration pro-
cess, which needs a lot of computation time. The more efficient and robust approach presented here needs
only one interpolation process.
The development of the software based on NURBS representation package: CAGI (Computer
Aided Grid Interface) was initiated by authors under the sponsorship of NASA Marshall Space Flight
Center. The purpose of this presentation is to present the progress realized in enhancing the NURBS
based curve / surface grid generation techniques into a 3D volume grid generation technique. To this end,
various options for generating 3D volume geometry-grid are discussed. A reparameterization scheme
has been developed to achieve desired distribution in physical space. Computational examples for model-
ing practical configurations have been exercised using the volume options and the reparameterization
scheme.
1119
https://ntrs.nasa.gov/search.jsp?R=19960029272 2020-06-16T04:21:35+00:00Z
Figure 1" Propulsional example.
3D NURBS control patches model
the missile (with fins) geometry.
Figure 2:
3D NURBS control patches model
the single rotation propfan.
References
[1 ] Piegl, L., - 'On NURBS: A survey' IEEE Computer Graphics & Applications, Vol 11, No 1, pp 57 -
71, January, 1991.
[2] FARIN, G. "NURB curves and surfaces: from projective geometry to practical use," First Edition,
A K Peters, Ltd., 1995.
[3] Yu, T.Y. and Soni, B.K.,"Geometry Transformer and NURBS in grid Generation," 4th International
Conference on Numerical Grid Generation in CFD and Related Fields, Swansea, UK., April 6-8,
1994.
[4] Yu, T.Y., Soni, B.K., and Shih M. H. "CAGI: Computer Aided Grid Interface," AIAA-95-0243,
33nd Aerospace Sciences Meeting & Exhibit., Reno, Nevada January 09-12,1995.
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Surface and Volume Grid Generation in Parametric Form

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