Bubbles and solid structures in a vibrated bed of granular materials

Modern graphics processing units (GPUs) are able to perform high-precision simulations for scientific applications. As a demonstration example, large-scale, three-dimensional computer simulations were performed on a single GPU to produce bubbles and solid structures in a tiny, annular container, partially filled with a granular material, shaken vertically. The dynamics of the gas above and within the shaken granular material was solved using large-eddy simulations (LES) while the grains were treated with molecular dynamics. A feature of the results is that bubbles form when peak acceleration relative to gravity exceeds a critical value Γb. This is in qualitative agreement with experiments [H.P. Pak, P.R. Behringer, Nature 371 (1994) 231]. An interesting finding is that Γbfor glass particles depends primarily on the coefficient of friction,μ, as well as on the coefficients which characterize the viscoelastic response of the granular material.