Advances in co-volume mesh generation and mesh optimisation techniques

This paper introduces developments in modified techniques for the generation of unstructured, non-uniform, dual orthogonal meshes which are suitable for use with co-volume solution schemes. Two new mesh generation techniques, a modified advancing front technique and an octree-Delaunay algorithm, are coupled with a mesh optimisation algorithm. When using a Delaunay–Voronoi dual, to construct mutually orthogonal meshes for co-volume schemes, it is essential to minimise the number of Delaunay elements which do not contain their Voronoi vertex. These new techniques provide an improvement over previous approaches, as they produce meshes in which the number of elements that do not contain their Voronoi vertex is reduced. In particular, it is found that the optimisation algorithm, which could be applied to any mesh cosmetics problem, is very effective, regardless of the quality of the initial mesh. This is illustrated by applying the proposed approach to a number of complex industrial aerospace geometries.