Voronoi Fluid Particles & Tessellation Fluid Dynamics

We formalize the concept of fluid particle that it is heuristically introduced in textbooks of fluid mechanics. Fluid particles are regarded as portions of fluid that move along the flow field and they have an extension. A natural way of assigning an extension to a set of points is through a tessellation. With a minimum of physical input information a well-defined discrete fluid particle model emerges. In the process, discrete differential operators based on the volume associated to the fluid particles appear. We identify a set of basic properties that the volume of the fluid particle should satisfy in order for these discrete operators to be exact when applied to linear fields, for arbitrary arrangements of the particles. The Voronoi volume and the Smoothed Particle Hydrodynamic volume are investigated, and a further option based on the volume of the “Delaunay cell” is proposed. We show how the Voronoi fluid particle model can be used to study features of turbulence, and suggests its usefulness for the modeling of complex fluids.