Page 303 - Computational Fluid Dynamics for Engineers

References 293

Fig. 9.20. Advancing Front technique for unstructured grid generation.

the new third node or an existing node to form the new triangle based on which
will form the best triangle. Also required are intersection checks to ensure that
triangles do not overlap as opposing fronts advance towards each other. A sizing
function can also be denned in this method to control element sizes. At each
step, the front is updated. This front is a dynamic data structure that changes
continuously during the generation process. Any straight line segment available
to form an element side is termed active. Any segment no longer active is re-
moved from the front. The grid generation is complete when the front is empty.
Lohner [12] proposed using a coarse Delaunay mesh of selected boundary nodes
over which the sizing function could be quickly interpolated.
In the advancing front method nodes and elements are added simultaneously,
with smooth mesh point placement. The method is boundary conforming since
the initial front is the boundary. It can fail when there are large variations in grid
spacing. The need to search for nearby nodes and edges/faces and the complex
intersection checking make the advancing front method slow. In addition, it
is better to add points rather than elements because there are, on average,
two triangles per point in two dimensions. The Delaunay triangulation method,
which adds points, has less searching to perform, and has much simpler geometry
checking. It is much faster than the advancing front method and is the preferred
method in three-dimensional unstructured grid generation. A more complete
overview of the "advancing front" method is given in [13].

References

[1] Thompson, J. F., Warsi, Z. U. A. and Mastin, C. W., Numerical Grid Generation, Foun-
dations and Applications, North Holland, 1985.
[2] Smith, R. E. and Weigel, B.L., "Analytic and Approximate Boundary Fitted Coordi-
nate Systems for Fluid Flow Solutions", AIAA Paper No. 80-0192