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Efficient Voronoi volume estimation for DEM simulations of granular materials under confined conditions.

Frenning G - MethodsX (2015)

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: Department of Pharmacy, Uppsala University, P.O. Box 580, SE-751 23 Uppsala, Sweden.

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.

No MeSH data available.


Average and maximal relative errors of the volume changes as a function of the relative volume change for (a) ϵ = 0.1% and (b) ϵ = 1%. The insets in (a) and (b) show the initial and final particle arrangements.
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fig0025: Average and maximal relative errors of the volume changes as a function of the relative volume change for (a) ϵ = 0.1% and (b) ϵ = 1%. The insets in (a) and (b) show the initial and final particle arrangements.

Mentions: The results from the small-scale DEM simulations are summarised in Fig. 5, which displays the average and maximal relative errors of the volume changes as a function of the magnitude of the volume change, expressed as /ΔV/V0/. The insets in Fig. 5a and b show the initial and final particle arrangements. As can be clearly seen, the magnitude of the relative errors of the volume changes (Fig. 5) are considerably larger than the magnitude of the relative errors of the Voronoi volumes (Fig. 3). Moreover, the relative errors increase when /ΔV/V0/ decreases and may, for sufficiently small values of /ΔV/V0/, exceed unity. This behaviour is not unexpected but is rather a consequence of the nature of the approximation. Using matrix notation and expanding the volume to second order, one obtains


Efficient Voronoi volume estimation for DEM simulations of granular materials under confined conditions.

Frenning G - MethodsX (2015)

Average and maximal relative errors of the volume changes as a function of the relative volume change for (a) ϵ = 0.1% and (b) ϵ = 1%. The insets in (a) and (b) show the initial and final particle arrangements.
© Copyright Policy - CC BY
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4487340&req=5

fig0025: Average and maximal relative errors of the volume changes as a function of the relative volume change for (a) ϵ = 0.1% and (b) ϵ = 1%. The insets in (a) and (b) show the initial and final particle arrangements.
Mentions: The results from the small-scale DEM simulations are summarised in Fig. 5, which displays the average and maximal relative errors of the volume changes as a function of the magnitude of the volume change, expressed as /ΔV/V0/. The insets in Fig. 5a and b show the initial and final particle arrangements. As can be clearly seen, the magnitude of the relative errors of the volume changes (Fig. 5) are considerably larger than the magnitude of the relative errors of the Voronoi volumes (Fig. 3). Moreover, the relative errors increase when /ΔV/V0/ decreases and may, for sufficiently small values of /ΔV/V0/, exceed unity. This behaviour is not unexpected but is rather a consequence of the nature of the approximation. Using matrix notation and expanding the volume to second order, one obtains

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: Department of Pharmacy, Uppsala University, P.O. Box 580, SE-751 23 Uppsala, Sweden.

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.

No MeSH data available.