Unstructured grid generation

This chapter introduces the two basic approaches to the generation of unstructured grids, Delaunay triangulation, and the Advancing Front method. The presentation in the chapter is confined to two dimensions, but the extension of these methods to three dimensions is straightforward in principle. In most cases, results for triangles in two dimensions can be generalized to tetrahedra in three dimensions. The principal objective of the chapter is to represent the two-dimensional solution domain of a problem by a set of triangles. Delaunay triangulation, the method discussed in the chapter, was first presented by Dirichlet in terms of connecting an arbitrary set of points together, thus producing a set of triangles, in such a way that the resulting triangulation was as near uniformly equilateral as possible. An important feature of a Delaunay triangulation is the Circumcircle Property: this guarantees that in a Delaunay triangulation, none of the points (vertices) of a triangle can lie within the circumcircle of any other triangle. The advancing front technique is an unstructured grid generation method that preserves boundary integrity and has the capacity to create the clustering of high aspect-ratio triangles in boundary-layer regions.