A 16 moments model in relativistic extended thermodynamics of rarefied polyatomic gas

A model with 16 moments is here presented in the framework of RET of polyatomic gases. It furnishes as principal subsystem the relativistic counterpart of a work by Arima T., Ruggeri T., Sugiyama M.; this is present in literature and treats the non relativistic case which incorporates relaxation processes of molecular rotation and vibration. Another principal subsystem is the natural extension of the 14 moments model by Pennisi S. and Ruggeri T.; this is also present in literature in the relativistic framework but where the trace of the third balance equation is neglected. Its extension is found here for the case when this trace isn’t neglected.

     

Wave speeds in the macroscopic relativistic extended model with many moments

An exact macroscopic extended model for relativistic gases, with an arbitrary number of moments, is present in the literature. It is determined except for a numberable family $\mathcal {F}$ of single variable functions whose physical meaning remains an open problem; a possibility is that it allows to apply the theory to a wider set of materials. Other models appearing in literature are particular cases of this macroscopic one when all these arbitrary functions are zero. Here we exploit equations determining wave speeds for that model. We find interesting results; for example, the whole system for their determination can be divided into independent subsystems which are expressed by linear combinations, through scalar coefficients, of tensors all of the same order. As expected, these wave speeds for the macroscopic model depend on $\mathcal {F}$ . Moreover, some wave speeds (but not all of them) are expressed by square roots of rational numbers.     

The Lagrangian View-Point Compared with the Eulerian One,in the Framework of Extended Thermodynamics

The salient points of Extended Thermodynamics are here revised according to the Lagrangian view-point. The conservation laws of mass, momentum and energy, from the Lagrangian view-point, have already been treated in literature. Here a similar procedure is followed for all the balance laws of Extended Thermodynamics with an arbitrary number of moments. It is also shown how the Galilean Relativity Principle and some symmetry condition, which are present in the Eulerian view-point, can be “translated” in the Lagrangian view-point, where they are no more so self-evident.     

Some open problems in non-linear extended thermodynamics and their possible solutions

In this article we aim to furnish arguments for further considerations on some procedures commonly used in Extended Thermodynamics, such as the Taylor’s expansions around equilibrium or the transition to subsystems. The initial impulse for these considerations lies in the fact that we have found, for a 14 moments model, the exact closure to the conditions arising from the entropy principle and the material objectivity principle, without using Taylor’s expansions. These generated some problems; one of these concerns the relationship between system and subsystems, another one concerns the convexity of entropy and hyperbolicity; a third problem deals with the correct moments to be used as independent variables, those suggested by the classical limit of the relativistic moment theory. We will give suggestions for the solution of these problems.