Surface Mesh Generation by Means of Steiner Triangulations
Roque Corral, Jaime Fernández-Castañeda · AIAA Journal · 2001
A method is presented for the efficient and automatic generation of unstructured grids on surfaces. The overall procedure uses a Steiner triangulation where sites are added in arbitrary order and hence the tracking of fronts is not needed in the algorithm. The connectivity of the new points is initially generated by direct subdivision and further improved by using local reconnection. The Lawson's method is used to obtain a Delaunay tessellation but other reconnection criteria may be used with minor modifications (e.g. minimise the maximum angle). The mesh generation procedure uses an approximate physical space grid to define the surface during the grid generation process. At the end the mapped space coordinates are transformed back to the actual surface. The field point distribution is controlled by an element size function obtained from the solution of a Laplace equation whose boundary conditions are derived from the boundary node information. Additional control is possible by prescribing dummy boundaries. The combination of grid smoothing and the elimination of nodes of degree 3, 4, pairs of nodes of degree 5 and nodes of degree higher than 7, as a postprocessing step has proved to be an efficient tool to improve the grid quality. Results are presented which demonstrate that high-quality unstructured grids can be efficiently generated on surfaces using the present method.