  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.
