Stability and convergence analysis of a dynamics-based collective method for random sphere packing

The simulation of granular materials requires an initial overlap-free packing of spherical particles at high volume packing fractions. In previous work, a dynamics-based collective approach, the Quasi-Dynamics Method (QDM), has been proposed to generate densely distributed spheres in an enclosed container. However, the stability and efficiency of the QDM were not fully addressed. In this paper, the algorithm is reformulated with two control parameters and the impact of these parameters on the algorithm performance is investigated. First, theoretical analyses and numerical verifications for extreme 1-D/2-D packing systems are conducted and the range of the control parameters in which the algorithm is convergent is analytically determined. Then, the analysis is extended to 3-D packing systems and the estimation of the parameter range is verified numerically. Finally, the algorithm is applied to modeling a cylindrical 3-D packing system and the convergence performance at different volume packing fractions is studied. Results show that the QDM is highly efficient in packing spheres at volume packing fractions that are close to the random close packing limit.