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SUMMARYA method is described which constructs three-dimensional unstructured tetrahedral meshes using the Delaunay triangulation criterion. Several automatic point creation techniques will be highlighted and an algorithm will be presented which can ensure that, given an initial surface triangulation which bounds a domain, a valid boundary conforming assembly of tetrahedra will be produced. Statistics of measures of grid quality are presented for several grids. The efficiency of the proposed procedure reduces the computer time for the generation of realistic unstructured tetrahedral grids to the order of minutes on workstations of modest computational capabilities.

A procedure for generating curved meshes, suitable for high-order finite element analysis, is described. The strategy adopted is based upon curving a generated initial mesh with planar edges and faces by using a linear elasticity analogy. The analogy employs boundary loads that ensure that nodes representing curved boundaries lie on the true surface. Several examples, in both two and three dimensions, illustrate the performance of the proposed approach, with the quality of the generated meshes being analysed in terms of a distortion measure. The examples chosen involve geometries of particular interest to the computational fluid dynamics community, including anisotropic meshes for complex three dimensional configurations.

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