A unified derivation of Voronoi, power, and finite-element Lagrangian computational fluid dynamics

Lagrangian Voronoi Meshes and Particle Dynamics with Shocks

“…The interest of the partition function is that one can avoid to study in too much details the local geometry of Voronoï cells. In dimension d = 2, it is possible to rely on a local geometrical parametrization of Voronoï cells to calculate the partial derivatives as shown in [16], even if the number of local geometrical configurations to examine can be important. However in dimension d ≥ 3, it seems almost impossible to cover all possible geometrical configurations.…”

“…where f ji and f ri are defined by (7). It is sufficient to use (15)(16)(17) to obtain x∈Ωi R ik (x) ≤ C/β. Similarly…”