(249c) An Exact Method for Determining Local Solid Fractions in Discrete Element Method Simulations

A solid fraction algorithm is presented which accounts for the partial volume of a sphere straddling cuboidal measurement bin boundaries. The algorithm accounts for spheres intersecting a single plane (a face) of the bin, two perpendicular planes (an edge), or three mutually perpendicular planes (a corner). Using this algorithm, comparisons are made against the solid fraction calculated using the more common algorithm in which the solid fraction is determined by assigning all of the sphere's volume to the bin in which the sphere's center of volume is located. A curve fit to the exact algorithm calculations is also given in order to improve computational speed while still maintaining acceptable accuracy. Bin size-to-sphere diameter ratios greater than approximately 30 must be used to give errors less than 5% when using the more traditional method when applied to simple cubic and hexagonal close packing static sphere assemblies. Bin size-to-sphere diameter ratios larger than approximately five are required for random sphere packings. Although time averaged solid fraction measurements are similar using either the exact or center of volume solid fraction schemes, the scatter in the center of volume method is much larger than for the exact method.