A Systematic Expansion Method in Granular Hydrodynamics
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.