Hydrodynamics of granular particles on a line

TL;DR

This paper derives a hydrodynamic model for a granular gas on a line, predicts a steady uniform flow state, and confirms its existence through numerical simulations, linking it to shock phenomena in cooling granular systems.

Contribution

It provides a hydrodynamic description from microscopic dynamics for a lattice granular gas, including finite-size effects, and demonstrates the steady uniform flow state via simulations.

Findings

Existence of a steady uniform longitudinal flow in the model

Hydrodynamic predictions match numerical simulations in the bulk

Connection between the flow state and shock formation in cooling gases

Abstract

We investigate a lattice model representing a granular gas in a thin channel. We deduce the hydrodynamic description for the model from the microscopic dynamics in the large system limit, including the lowest finite-size corrections. The main prediction from hydrodynamics, when finite-size corrections are neglected, is the existence of a steady "uniform longitudinal flow" (ULF), with the granular temperature and the velocity gradient both uniform and directly related. Extensive numerical simulations of the system show that such a state can be observed in the bulk of a finite-size system by attaching two thermostats with the same temperature at its boundaries. The relation between the ULF state and the shocks appearing in the late stage of a cooling gas of inelastic hard rods is discussed.