Assessing a Hydrodynamic Description for Instabilities in Highly Dissipative, Freely Cooling Granular Gases

TL;DR

This study evaluates a modified hydrodynamic model for highly dissipative granular gases, demonstrating its improved accuracy over standard models in predicting clustering and vortex instabilities through stability analysis and molecular dynamics simulations.

Contribution

The paper introduces and validates a modified-Sonine approximation for granular gas hydrodynamics, showing enhanced agreement with simulations in highly dissipative regimes.

Findings

Modified theory accurately predicts critical length scales for instabilities.

Standard theory fails to match MD results at high dissipation.

Cluster sizes can remain stable or halve depending on parameters.

Abstract

An intriguing phenomenon displayed by granular flows and predicted by kinetic-theory-based models is the instability known as particle "clustering," which refers to the tendency of dissipative grains to form transient, loose regions of relatively high concentration. In this work, we assess a modified-Sonine approximation recently proposed [Garz\'o et al., Physica A 376, 94 (2007)] for a granular gas via an examination of system stability. In particular, we determine the critical length scale associated with the onset of two types of instabilities -vortices and clusters- via stability analyses of the Navier-Stokes-order hydrodynamic equations by using the expressions of the transport coefficients obtained from both the standard and the modified-Sonine approximations. We examine the impact of both Sonine approximations over a range of solids fraction \phi <0.2 for small restitution coefficients e=0.25--0.4, where the standard and modified theories exhibit discrepancies. The theoretical predictions for the critical length scales are compared to molecular dynamics (MD) simulations, of which a small percentage were not considered due to inelastic collapse. Results show excellent quantitative agreement between MD and the modified-Sonine theory, while the standard theory loses accuracy for this highly dissipative parameter space. The modified theory also remedies a (highdissipation) qualitative mismatch between the standard theory and MD for the instability that forms more readily. Furthermore, the evolution of cluster size is briefly examined via MD, indicating that domain-size clusters may remain stable or halve in size, depending on system parameters.