A Systematic Expansion Method in Granular Hydrodynamics

TL;DR

This paper introduces a systematic expansion method for granular hydrodynamics, effectively describing the asymptotic states of small, freely evolving granular fluids with inhomogeneities.

Contribution

It presents a novel systematic expansion technique for granular hydrodynamics applicable to small systems, providing quantitative descriptions of inhomogeneities and decay laws.

Findings

Accurately describes flow profiles and inhomogeneities

Quantifies decay law of temperature and energy

Validates the method for inelastic hard sphere systems

Abstract

We propose a systematic expansion method which is applied to freely evolving granular fluids contained in sufficiently small systems. Restricting ourselves to small systems, we show that there exists a small parameter which characterizes a typical size of density and temperature inhomogeneities. A solution of the hydrodynamic equations for a fluid of inelastic hard spheres is expanded in the small parameter. It is shown that our method quantitatively describes the asymptotic state of the system, such as flow profiles, density and temperature inhomogeneities, and the decay law of the global temperature and the energy per particle.