Abstract
A freely cooling granular gas without any external force evolves from the initial homogeneous state to the inhomogeneous clustering state, at which the energy decay deviates from the Haff’s law. The asymptotic behavior of energy in the inelastic hard sphere model have been predicted by several theories, which are based on the mode coupling theory or extension of inelastic hard rods gas. In this study, we revisited the clustering regime of freely evolving granular gas via large-scale molecular dynamics simulation with up to 16.7 million inelastic hard disks. We found novel regime regarding on collisions between “clusters” spontaneously appearing after clustering regime, which can only be identified more than a few million particles system. The volumetric dilatation pattern of semicircular shape originated from density shock propagation are well characterized on the appearing of “cluster impact” during the aggregation process of clusters.
Highlights
Clustering in the granular gas is one of the fascinating phenomena in the granular physics [1,2,3]
A freely cooling granular gas with an inelastic hard sphere (IHS) model is known to evolve from the initial homogeneous equilibrium state to the inhomogeneous clustering state, at which the energy decay deviates from so-called “Haff’s law” [4]
We confirmed that the theories seem to be consistent in relatively dilute and small system, we found the new regime regarding on collisions between “clusters” spontaneously after the clustering regime in dense case
Summary
Clustering in the granular gas is one of the fascinating phenomena in the granular physics [1,2,3]. [5,6,7,8], we have investigated the macroscopic statistical properties on the freely evolving quasi-elastic IHS model by performing a large-scale event-driven molecular dynamics with mainly 5122 [5], 40962 [7] in two-dimensional system (2D) and 1283 [8] in three dimensional system (3D) These extensive numerical simulations have revealed a quite similarity with fluid Navier-Stokes turbulence, such as enstrophy cascade (Kraichnan-Leith-Bachelor theory), Kolmogorov scaling and Bose-Einstein condensation, which are well-known concept in the fluid turbulence [9]. We performed large-scale and long-time event-based molecular dynamics simulation [13, 14] in IHS model with up to 16.7 million particles to clarify the validity of asymptotic behaviors predicted by these theories, and especially focus on inhomogeneous clustering regimes in the dense systems, at which the theoretical approach cannot be resolved
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