Abstract
When the discrete element method (DEM) is used to simulate confined compression of granular materials, the need arises to estimate the void space surrounding each particle with Voronoi polyhedra. This entails recurring Voronoi tessellation with small changes in the geometry, resulting in a considerable computational overhead. To overcome this limitation, we propose a method with the following features:•A local determination of the polyhedron volume is used, which considerably simplifies implementation of the method.•A linear approximation of the polyhedron volume is utilised, with intermittent exact volume calculations when needed.•The method allows highly accurate volume estimates to be obtained at a considerably reduced computational cost.
Highlights
When the discrete element method (DEM) is used to simulate confined compression of granular materials, the need arises to estimate the void space surrounding each particle with Voronoi polyhedra
We describe a method to approximate the volume of Voronoi polyhedra in situations where recurring updates are needed for small changes in the geometry, as during simulations of confined compression of granular materials with the discrete element method (DEM) [1]
The method utilises a linear approximation of the volume, with intermittent exact volume calculations when needed
Summary
We describe a method to approximate the volume of Voronoi polyhedra in situations where recurring updates are needed for small changes in the geometry, as during simulations of confined compression of granular materials with the discrete element method (DEM) [1] (see section ‘Additional information: background’). Where x denotes the spatial coordinates, R is an n  3 matrix whose kth row equals rk and f is an n dimensional array with components f k 1⁄4 krkk2:. It is clear from (1) and (2) that the polyhedron, and its volume V, is a function of R. The gradient determination, described in section ‘Gradient calculation’, utilises formulae derived by Muller et al [2] and Lasserre [4]
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