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CAGD techniques in grid generation

The objective of this study is to develop the algorithms for static and dynamic grid generation applicable to complex industrial configurations by utilizing Computer Aided Geometry Design (CAGD) techniques. The Non-Uniform Rational BSpline (NURBS) is used as a basis for the geometric definition and in the development of grid generation schemes. The algorithms which bridge the gap between CAD/CAM systems and grid generation systems have been developed by utilizing the IGES (Initial Graphics Exchange Specification) file format, which is the output of the CAD/CAM systems. The IGES and NASA/IGES prescribed geometric entities have been supported by developing algorithms which transfer all geometric entities into a common NURBS data structure. These robust transformation algorithms developed in this study provide enhancements and generalizations to the existing CAGD techniques pertinent to the grid generation process. The algorithms to interactively construct NURBS curves, surfaces and volumes widely applicable to CFD configurations are presented. Projection and inversion techniques applicable to an interpolated sculptured discretized data set are developed and validated. The reparameterization algorithms to overcome the influence of NURBS geometric characteristics on the quality of the resulting grids have been developed. These algorithms have been cast into a computer software CAGI (Computer Aided Grid Interface) to facilitate the geometric modeling and surface preparations associated with the grid generation process. The CAGI software provides a menu driven interactive environment based on the FORMS and GL graphics libraries. The interactive graphics capabilities of CAGI have been applied to initiate the surface grid generation associated with trimmed surface entity (IGES entity 144). The NURBS based griding algorithms have been applied to construct dynamic grids associated with complex solution adaptive and temporally deforming configurations. Computational examples demonstrating the success of these algorithms in allowing the treatment of CAD/IGES files, formulating very concise NURBS control polygon (control net or control volume) associated with industrial geometries, and addressing grid redistribution, solution adaptation and dynamically deforming grids are exercised. The algorithms developed in this study along with efficient computer memory requirement and fast evaluation of NURBS entities make the CAGI program very attractive for addressing grid generation needs associated with complex industrial configurations efficiently and economically.