A Voronoi-Based Hybrid Meshing Method

In this research note we introduce a method to build volumetric hybrid meshes suitable for finite element computations. Our work is motivated by meshing problems encountered in geological modeling. Geological models are multimaterial models that can have a high number of interfaces, these interfaces can come close to each other in certain zones and intersect at low-angles defining thin features that may have an impact on large scale numerical simulations. Generating a mesh that captures these thin features while controlling the number and quality of its elements is of crucial importance for many applications such as assessing natural resources or evaluating environmental risks and natural hazards. We propose to adapt the elements of a tetrahedral dominant mesh to the local model configuration by generalizing the Voronoi-Delaunay dual relationship. The volume, defined by a set of triangulated surfaces, is sampled with a given number of points that optimize a function based on Centroidal Voronoi Tessellation (Sect. 3). From the Voronoi diagram of these points we identify the zones that can be meshed with their Delaunay triangulation, and the thin sections that cannot. The latter are filled with triangular prisms, square pyramids, and tetrahedra (Sect. 4). Some examples of hybrid meshes generated by the method are given in Sect. 5.