Towards a continuum theory of clustering in a freely cooling inelastic gas

TL;DR

This paper investigates the clustering instability in a freely cooling inelastic gas using molecular dynamics simulations, revealing that late-time behavior can be described by the Burgers equation with coarsening dynamics.

Contribution

It introduces a continuum theory for clustering in inelastic gases, connecting molecular dynamics results to the Burgers equation framework.

Findings

Shear stress becomes negligible as the gas cools.

Finite-time singularities are arrested by cluster formation.

Late-time dynamics follow the Burgers equation with coarsening behavior.

Abstract

We performed molecular dynamics simulations to investigate the clustering instability of a freely cooling dilute gas of inelastically colliding disks in a quasi-one-dimensional setting. We observe that, as the gas cools, the shear stress becomes negligibly small, and the gas flows by inertia only. Finite-time singularities, intrinsic in such a flow, are arrested only when close-packed clusters are formed. We observe that the late-time dynamics of this system are describable by the Burgers equation with vanishing viscosity, and predict the long-time coarsening behavior.