Automatic Parallel Generation of Three-dimensional Unstructured Grids for Computational Mechanics

Unstructured mesh techniques take an important place in grid generation. The main feature of unstructured grids consists, in contrast to structured grids, in a nearly absolute absence of any restrictions on grid cells, grid organization, or grid structure. It allows placing the grid nodes locally irrespective of any coordinate direction, so that complex geometries with curved boundaries can be meshed easily and local regions in which solution variations are large can be resolved with a selective insertion of new points without unduly affecting the resolution in other parts of the physical domain. Unstructured grid methods were originally developed in solid mechanics. Nowadays these methods influence many other fields of applications beyond solid modeling, in particular, computational fluid dynamics, where they are becoming widespread. At the present time the methods of unstructured grid generation have reached the stage where three-dimensional domains with complex geometry can be successfully meshed. The most spectacular theoretical and practical achievements have been connected with the techniques for generating tetrahedral grids. There are at least two basic approaches that have been used to generate these meshes: Delaunay [1] and advancing front [2]. In this paper we are dealing with Delaunay approaches only. Delaunay property means that the hypersphere of each ndimensional simplex defined by n + 1 points is void of any other points of the triangulation (fig. 1). This empty circum-circle property gives us some grounds to expect that the grid cells of a Delaunay triangulation are not too deformed [3]. The most famous Delaunay triangulation algorithms are the “Divide & Conquer” paradigm algorithm [4] and the incremental insertion algorithm [5].