(367i) Predicting Clustering Instabilities in Granular Materials: Kinetic-Theory Simulations Vs. Molecular Dynamics Simulations

Instabilities in freely cooling granular materials have been widely observed via kinetic-theory-based models and molecular dynamics (MD) simulations. Recently, the quantitative ability of kinetic-theory-based predictions for the onset of instabilities was previously assessed through comparison with MD simulations [Mitrano et al. 2011, Mitrano et al. 2012]. However, the ability of kinetic-theory descriptions to accurately predict the evolution of instabilities has not previously been addressed.  In this work, we carry out such an assessment via a direct comparison between (i) transient simulation using kinetic theory, (ii) a linear stability analysis of the same theory, and (iii) MD simulation.  The results reveal two important findings.  First, an excellent agreement is obtained between the transient theoretical predictions and MD simulations for the critical clustering length scale.  This agreement is somewhat surprising given the small-Knudsen (small-gradient) assumption of the Navier-Stokes-order theory coupled with the presence of large gradients in the unstable system.  However, it is also encouraging as it implies that the range of validity of the theory is wider than expected from a strict interpretation of its assumptions.  Second, the predictions of the same length scale from the linear stability analysis over-estimate those of MD and transient simulations.  This result confirms earlier work indicating the important role of nonlinear mechanisms in the evolution of instabilities.