Formation and evolution of density singularities in hydrodynamics of inelastic gases

TL;DR

This paper investigates the formation of density singularities in inelastic gases using ideal hydrodynamics, revealing universal finite-time clustering phenomena that resemble shock formation in ideal gases.

Contribution

It introduces a new type of finite-time density blowup in hydrodynamics of inelastic gases, with exact solutions describing cluster formation beyond the blowup.

Findings

Finite-time density blowup occurs with finite pressure.

Exact analytic solutions describe cluster formation.

Hydrodynamics effectively models granular gas clustering.

Abstract

We use ideal hydrodynamics to investigate clustering in a gas of inelastically colliding spheres. The hydrodynamic equations exhibit a new type of finite-time density blowup, where the gas pressure remains finite. The density blowups signal formation of close-packed clusters. The blowup dynamics are universal and describable by exact analytic solutions continuable beyond the blowup time. These solutions show that dilute hydrodynamic equations yield a powerful effective description of a granular gas flow with close-packed clusters, described as finite-mass point-like singularities of the density. This description is similar in spirit to the description of shocks in ordinary ideal gas dynamics.