Quad-Dominant Semistructured Grid Generation Using A Parabolic MarchingScheme
by
David S. Thompson
MSU/NSF Engineering Research Center
Coauthors: B. K. Soni

The effectiveness of utilizing systems of partial differential equations to generate node distributions for discrete solutions of field equations is well documented. Elliptic and hyperbolic systems have been used extensively to generate meshes for a wide variety of configurations. In this paper, we describe a parabolic marching scheme for generating semi-structured grids based on the initial work of Nakamura later refined and extended by Noack and Parpia for structured grids. Grids generated using parabolic methods can be obtained in times competitive with those generated using hyperbolic schemes and the presence of dissipative terms in the generating equations ensures a smooth grid point distribution.

In the parabolic method, a reference grid is utilized to make the marching problem well-posed. In this work, the reference grid is generated algebraically to be locally orthogonal. The application of the parabolic Poisson equation can be thought of as a smoothing of the reference grid. The resulting smoothed grid still exhibits many of the characteristics of the reference grid. In practice, it has been found that reducing the grid point movement induced by the smoothing by an order of magnitude results in a grid that is sufficiently smooth. Typically, this requires the equivalent of four to five iterations of an elliptic solver. Domains containing strongly non-convex regions require additional iteration.

Included in our method is the capability to delete or insert nodes as the marching scheme advances. This is possible because of the data structure we employ. The reference grid generated for each marching level consists of three levels of structured data. The node deletion/insertion process occurs after the grid has been smoothed using the parabolic equations. No information regarding previous levels is necessary once the initial data line for the next marching level has been established. The algorithm we use for node deletion is based on cell aspect ratio. Because of the node-deletion rules, cells may be generated with four, five, six, or seven sides. For grids appropriate for viscous simulations, the number of four-sided cells typically exceeds 95% of the total number of cells. Node insertion has been demonstrated but has not been thoroughly tested.

The method described here is directly extendable to three dimensions. The parabolic marching scheme has been previously demonstrated in three dimensions and three-dimensional analogies exist for the data structure and node deletion algorithm.

References

S. Nakamura, ``Noniterative Grid Generation Using Parabolic Partial Differential Equations, '' Numerical Grid Generation, Ed. J. F. Thompson, Elsevier Science Publishing Company, Inc., New York, 1982.

R. W. Noack, and I. H. Parpia, ``Solution Adaptive Parabolic Grid Generation in Two and Three Dimensions'', Numerical Grid Generation in Computational Fluid Dynamics and Related Fields, Eds. A. S.-Arcilla, J. Hauser, P. R. Eiseman, and J. F. Thompson, Elsevier Science Publishing Company, New York, 1991.

Date received: April 14, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacr-65.