A FRONTAL APPROACH FOR INTERNAL NODE GENERATION IN DELAUNAY TRIANGULATIONS

The past decade has known an increasing interest in the solution of th e Euler equations on unstructured grids due to the simplicity with whi ch 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 t he boundary geometry and, perhaps, a function to prescribe some desire d mesh size. The internal nodes should then be found automatically by the grid generation code. The approach we propose here combines the De launay triangulation with ideas from the advancing front method of Per aire et al. and Lohner et al. Both methods are briefly reviewed in Sec tion 1. Our method uses a background grid to interpolate local mesh si ze parameters that is taken from the triangulation of the given bounda ry nodes. Geometric criteria are used to find a set of nodes in a fron tal manner. This set is subsequently introduced into the existing mesh , thus providing an updated Delaunay triangulation. The procedure is r epeated until no more improvement of the grid can be achieved by inser ting new nodes.