Abstract
This chapter provides a brief review of some algorithms used to construct model granular media (packings of spheres), together with a comparison of results obtained on tessellations of those packings. The computational algorithms involve several techniques, including: a Random Sequential Adsorption approach (RSA), an Event-Driven model (ED), a Molecular Dynamics code (MD), a Smoothed Particle Hydrodynamics approach (SPH) and the classical static algorithm for dense packings of spheres. These techniques model static or dynamic interactions between the particles and give different geometries even for the same mean solid fraction. These numerical methods can apply to two or three-dimensional packings.
Different methods can generate full tessellation of the two and three-dimensional spaces (a tessellation is a random geometrical foam). The classical Voronoi tessellation is well known and deals only with points or the coordinates of the particle centers. In this case, the particles have finite radii and generate a minimal exclusion area. The radical and “navigation” tessellations both account for particle size and give the same result if the packing is monosize but give different results if the particles are of different diameters.
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Oger, L., Troadec, J.P., Gervois, A., Medvedev, N.N. (1999). Computer Simulations and Tessellations of Granular Materials. In: Sadoc, J.F., Rivier, N. (eds) Foams and Emulsions. NATO ASI Series, vol 354. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9157-7_31
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