Generation of Non-Isotropic Unstructured Grids via Directional Enrichment

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

MESHING
RESEARCH
CORNER

Institute for Computational Science and Informatics, M.S. 4C7, George Mason University, Fairfax, VA 22030-4444, USA
rlohner@science.gmu.edu

Abstract
The generation of isotropic unstructured grids has reached a fairly mature state, as evidenced by the many publications that have appeared over the last decade on this subject and the widespread use of unstructured grids in industry. The two most widely used techniques are the advancing front technique and the Delaunay triangulation. Hybrid schemes, that combine an advancing front point placement with the Delaunay reconnection have also been used successfully. These isotropic mesh generation techniques tend to fail when attempting to generate highly stretched elements, a key requirement for Reynolds-Averaged Navier Stokes (RANS) calculations with turbulence models that reach into the sublayer.

A number of specialized schemes have been proposed to remedy this situation. The domain to be gridded was divided into isotropic and stretched element regions. In addition, a blending procedure to transition smoothly between these zones was provided. Typically, the stretched mesh region was generated first. Although we have used such an 'advancing layers' scheme for a number of years, we have found several situations in which the requirement of a semi-structured element or point placement close to wetted surfaces is impossible. This is especially the case for points with multiple surface normals, implying that either special procedures have to be invoked or the construction of a grid with non-negative elements is impossible. In view of these difficulties, which tend to surface as the level of geometrical complexity increases, a new procedure was developed, which may be summarized as follows:

• Generate an isotropic mesh; this can be done with any unstructured grid generator;
• Remove all points in regions where stretched elements are to be generated;
• Using a constrained Delaunay technique, introduce points in order to generate highly stretched elements;
• Introduce the points in ascending level of stretching, i.e. from the domain interior to the boundary.

This procedure has the following advantages:

• No surface recovery is required for the Delaunay reconnection, eliminating the most problematic part of this technique;
• Proper meshing of concave ridges/corners is obtained;
• The meshing of concave ridges/corners requires no extra work;
• Meshing problems due to surface curvature are minimized;
• In principle, no CAD representation of the surface is required; and
• It guarantees a final mesh, an essential requirement for automation.

The disadvantages are the following:

• As with any Delaunay technique, the mesh quality is extremely sensitive to point placement.

This new RANS gridding technique has been operational for the last year, and has been used for a number of complex geometries. The present paper reports on improvements and extensions that have been incorporated over the last year. These recent developments have significantly improved the quality of grids generated, as well as the range of applicability of the technique.