文档介绍：PHYSICAL REVIEW E VOLUME 54, NUMBER 1 JULY 1996
Model ic equation for low-density granular flow
J. J. Brey and F. Moreno
Fı´sica Teo´rica, Universidad de Sevilla, Apartado de Correos 1065, E-41080, Sevilla, Spain
James W. Dufty
Department of Physics, University of Florida, Gainesville, Florida 32611
͑Received 6 October 1995; revised manuscript received 26 February 1996͒
A model ic equation is proposed to describe the time evolution of a posed of particles which
collide inelastically. Dissipation in collisions is described by means of a parameter which is related to the
coefficient of restitution, ⑀. The ic equation can be solved exactly for the homogeneous cooling state,
providing explicit expressions for both the time-dependent ‘‘temperature’’ and the velocity distribution func-
tion. In contrast to the Maxwellian for fluids with energy conservation, this distribution exhibits algebraic
decay for large velocities. Hydrodynamic equations are derived by expanding in the gradients of the hydro-
dynamic fields around the homogeneous cooling state, without the limitation to ⑀ asymptotically close to unity.
The equation for the energy density contains, in addition to a source term describing the energy lost in
collisions, a contribution to the heat flux which is proportional to the gradient of the density. The linear
stability of the homogeneous cooling state is investigated by analyzing the hydrodynamic modes of the system.
The shear modes are found to decay slowly at long wavelengths, in the sense that spatial perturbations of the
macroscopic flow field decay slower than the cooling rate for the thermal velocity of the reference homoge-
neous state. On the other hand, the heat mode is always stable. ͓S1063-651X͑96͒02107-1͔
PACS number͑s͒: , , ,
I. INTRODUCTION puter simulations ͓3–5͔. The stability of two particular states
corresponding to different physical situations has been inves-
The study of