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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.


Related in: MedlinePlus

Projection of (a) face  onto the plane xγ = 0 (to yield ) and (b) edge  onto the plane xβ = 0 (to yield ).
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fig0010: Projection of (a) face onto the plane xγ = 0 (to yield ) and (b) edge onto the plane xβ = 0 (to yield ).

Mentions: The convex polyhedron defined by the inequality system (1) may be decomposed into n pyramids. Hence its volume can be expressed as(5)V=13∑k=1n∥rk∥Ak,where Ak is the area of face k. Expression (5) is not useful unless a way be found to calculate the face areas. To this end, Lasserre [3] suggested a straightforward projection scheme. If we let denote the area of face k when projected onto the plane xγ = 0, as illustrated in Fig. 2a, we obtain


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

Frenning G - MethodsX (2015)

Projection of (a) face  onto the plane xγ = 0 (to yield ) and (b) edge  onto the plane xβ = 0 (to yield ).
© Copyright Policy - CC BY
Related In: Results  -  Collection

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

fig0010: Projection of (a) face onto the plane xγ = 0 (to yield ) and (b) edge onto the plane xβ = 0 (to yield ).
Mentions: The convex polyhedron defined by the inequality system (1) may be decomposed into n pyramids. Hence its volume can be expressed as(5)V=13∑k=1n∥rk∥Ak,where Ak is the area of face k. Expression (5) is not useful unless a way be found to calculate the face areas. To this end, Lasserre [3] suggested a straightforward projection scheme. If we let denote the area of face k when projected onto the plane xγ = 0, as illustrated in Fig. 2a, we obtain

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.


Related in: MedlinePlus