Extended thermodynamics of granular media

A thirteen moments model for dilute granular gases will be presented in the context of Rational Extended Thermodynamics. We will introduce and discuss a quasi-linear PDEs system consisting of 13 field equations for the 13 field variables, in which constitutive relations are determined by using universal physical principles such as the entropy principle and the principle of relativity. The hyperbolicity property of this macroscopic model will be analysed and preliminary studies of some special cases will also be illustrated. In particular, the homogeneous case will be discussed in order to study the dependence of the model on the restitution coefficient and to compare its solutions with Haff’s law. The stationary 1D cases and their validity will be presented as well. Finally, it will be shown that the entropy principle limits the acceptability of some kinds of solutions.