Multi-Block Mesh Extrusion Driven by a Globally Elliptic System

2nd Symposium on Trends in Unstructured Mesh Generation, University of Colorado, Boulder, August 1999

MESHING
RESEARCH
CORNER

Geometricon, LLC and Hydro-Aero Consulting Group
jcv@hydroaero.com

Abstract
The application of nonlinear computational methods typically require that a mesh be generated throughout the domain of interest. For consideration to the accuracy of the computed solution, the boundaries of these meshes are usually required to be body conforming, clustered in regions of high gradients and adhere to acceptable limits on skewness, aspect-ratio, etc. In two dimensions, these qualities can be maintained through use of conformal transformations. However in three dimensions, the utilization of conformal transformations is limited to planar cross sections of the domain.

Over the past 15 years, several techniques have been developed which address the generation of structured grids for three-dimensional problems. These include elliptic equations[1], trans-finite interpolation and marching schemes based on either hyperbolic[2] or locally-elliptic equations. Yet to mesh even a semi-complex domain, some level of unstructured coarse-grain decomposition is usually required, whether it be point match, zonal or over-set regions.

Fully unstructured-mesh techniques have dramatically streamlined the grid- generation process[3], especially for complex geometrical cases. Unfortunately, not all problems are conducive to employing an unstructured mesh.

Generating a volume mesh using stencil-based elliptic equations or trans-finite interpolation requires that the user first define a surface mesh on all six boundaries of each block. While these "fill-in" techniques are fairly robust, the quality of the resulting mesh depends on the nature of the user- generated surface grids at the block boundaries. Additionally, this process is very time consuming by the shear number of surface meshes the user must manually generate.

The prospect of extruding a mesh from one boundary outward was first achieved through use of hyperbolic equations, then later refined with locally-elliptic smoothing. Due to the nature of these techniques, the advancing front is driven only by the mesh behind it and oblivious to possibly pertinent information about the domain ahead of it. As a result, these methods are generally not as robust as the "fill-in" techniques.

The present work develops a 3-D extrusion technique based on a globally elliptic system which encodes all of the information about the domain boundaries in such a manner that the advancing front is equally cognizant of the domain ahead of it as it is of that behind it. The quality of the resulting volume mesh rivals that of two-dimensional meshes based on conformal mappings.

References

[1] J.F.Thompson, Z.U.A.Warsi and C.W.Mastin, 'Numerical Grid Generation, Foundations and Applications', North-Holland, New York, 1985.

[2] J.Q.Cordova and T.J.Barth, 'Grid Generation for General 2-D Regions Using Hyperbolic Equations', AIAA Paper 88-0520, January 1988.

[3] T.J.Baker and J.C.Vassberg, 'Tetrahedral Mesh Generation and Optimization', Proc. 6th Int. Conf. Numerical Grid Generation, (ed. M.Cross), Greenwich, UK, July 1998, pp 337-349