A geometric algorithm based on tetrahedral meshes to generate a dense polydisperse sphere packing

In the discrete element method, the packing generation of polydisperse spheres with a high packing density value is a major concern. Among the methods already developed, few algorithms can generate sphere packing with a high density value. The aim of this paper is to present a new geometric algorithm based on tetrahedral meshes to generate dense isotropic arrangements of non-overlapping spheres. The method consists of first filling in every tetrahedron with spheres in contact (i.e., hard-sphere clusters). Then, the algorithm increases the packing density value by detecting the large empty spaces and filling them with new spheres. This new geometric algorithm can also generate a complex shape structure.