A Frontal Approach for Internal Node Generation in Delaunay Triangulations

The past decade has known an increasing interest in the solution of the Euler equations on unstructured grids due to the simplicity with which an unstructured grid can be tailored around very complex geometries and be adapted to the solution. It is desirable that the mesh can be generated with minimum input from the user, ideally, just specifying the boundary geometry and, perhaps, a function to prescribe some desired mesh size. The internal nodes should then be found automatically by the grid generation code. The approach we propose here combines the Delaunay triangulation with ideas from the advancing front method of Peraire et al. and Lijhner et al. Both methods are briefly reviewed in Section 1. Our method uses a background grid to interpolate local mesh size parameters that is taken from the triangulation of the given boundary nodes. Geometric criteria are used to find a set of nodes in a frontal manner. This set is subsequently introduced into the existing mesh, thus providing an updated Delaunay triangulation. The procedure is repeated until no more improvement of the grid can be achieved by inserting new nodes.