Hydrodynamic theory for granular gases

A granular gas subjected to a permanent injection of energy is described by means of hydrodynamic equations derived from a moment expansion method. The method uses as reference function not a Maxwellian distribution $f_M$ but a distribution $f_0=\Phi f_M,$ such that $\Phi$ adds a fourth cumulant $\kappa$ to the velocity distribution. The formalism is applied to a stationary conductive case showing that the theory fits extraordinarily well the results coming from our Newtonian molecular dynamic simulations once we determine $\kappa$ as a function of the inelasticity of the particle–particle collisions. The shape of $\kappa$ is independent of the size N of the system.