Sebastiano Pennisi

An 18 Moments Model for Dense Gases: Entropy and Galilean Relativity Principles without Expansions

The 14 moments model for dense gases, introduced in the last few years by Arima, Taniguchi, Ruggeri and Sugiyama, is here extended up to 18 moments. They have found the closure of the balance equations up to a finite order with respect to equilibrium; it is also possible to impose for that model the entropy and Galilean relativity principles up to whatever order with respect to equilibrium, but by using Taylor’s expansion. Here, the exact solution is found, without expansions, but a bigger number of moments has to be considered and reasons will be shown suggesting that this number is at least 18.

Extended thermodynamics of charged gases with many moments: An alternative closure

In 2011, a macroscopic extended model with many moments for the description of relativistic gases under the influence of an external electromagnetic field has been proposed. An exact closure of this model, up to whatever order with respect to thermodynamical equilibrium, has been found. Such closure is given in terms of the entropy density at equilibrium and the expression for the higher order terms involves a family of arbitrary constants. It allows to know the value of the constitutive functions up to every desired degree of approximation, but paying the cost of a large amount of arbitrary terms. Moreover, if one wants to use the closure for applications it is necessary to cut it at a chosen order with respect to thermodynamical equilibrium. In this paper, we propose a different method to find the closure that, starting from a fixed order with respect to thermodynamical equilibrium, allows to obtain univocally all the lower order terms in terms of two arbitrary functions depending on a scalar variable a...

Entropy Principle and Galilean Relativity for Dense Gases, the General Solution without Approximations

The many moments model for dense gases and macromolecular fluids is considered here, where the upper order moment is chosen in accordance to the suggestions of the non-relativistic limit of the corresponding relativistic model. The solutions of the restrictions imposed by the entropy principle and that of Galilean relativity were, until now, obtained in the literature by using Taylor expansions around equilibrium and without proving convergence. Here, an exact solution without using expansions is found. The particular case with only 14 moments has already been treated in the literature in a completely different way. Here, it is proven that this particular closure is included in the presently more general one.

On some remarkable properties of an extended thermodynamic model for dense gases and macromolecular fluids

Recently, the 14 moments model of extended thermodynamics for dense gases and macromolecular fluids has been considered and an exact solution, of the restrictions imposed by the entropy principle and that of Galilean relativity, has been obtained without using Taylors expansions. Here, we prove the uniqueness of the above solution and exploit other pertinent conditions such as the convexity of the function h′ related to the entropy density, the problem of subsystems and the fact that the flux in the conservation law of mass must be the moment of order 1 in the conservation law of momentum. The results present interesting aspects which were not suspected when only approximated solutions of this problem were known.

Extended thermodynamics of charged gases with many moments

Recently a model with many moments for the description of relativistic gases has been studied and an exact closure has been found, depending on an arbitrary set of single variable functions. In the case of a charged gas and when the electromagnetic field acts as an external force, the exploitation of the entropy principle produces an additional condition. A closure compatible with this further condition has been found, when the highest order moment has an even number of free indexes. It amounts in restrictions on the arbitrary single variable functions appearing in the general case. They are polynomials of increasing degree with respect to equilibrium, which coefficients are arbitrary constants. When the highest order moment has an odd number M of free indexes the further condition is different from that appearing in the case M even and alternative techniques must be used to find a closure compatible with it. In this paper we take into account this last model and we find a closure compatible with the furt...

An exact fluid model for relativistic electron beams: The many moment case

An interesting and satisfactory fluid model has been proposed in literature for the description of relativistic electron beams. It was obtained with 14 independent variables by imposing the entropy principle and the relativity principle. Here the case is considered with an arbitrary number of independent variables, still satisfying the above mentioned two principles; these lead to conditions whose general solution is here found. We think that the results satisfy also a certain ordering with respect to a smallness parameter ϵ measuring the dispersion of the velocity about the mean; this ordering generalizes that appearing in literature for the 14 moments case.

Extended Thermodynamics for Dense Gases up to Whatever Order and with Only Some Symmetries

Extended Thermodynamics of dense gases is characterized by two hierarchies of field equations, which allow one to overcome some restrictions on the generality of the previous models. This idea has been introduced by Arima, Taniguchi, Ruggeri and Sugiyama. In the case of a 14-moment model, they have found the closure of the balance equations up to second order with respect to equilibrium. Here, the closure is obtained up to whatever order and imposing only the necessary symmetry conditions. It comes out that the first non-symmetric parts of the higher order fluxes appear only at third order with respect to equilibrium, even if Arima, Taniguchi, Ruggeri and Sugiyama found a non-symmetric part proportional to an arbitrary constant also at first order with respect to equilibrium. Consequently, this constant must be zero, as Arima, Taniguchi, Ruggeri and Sugiyama assumed in the applications and on an intuitive ground.

The model with many moments for relativistic electron beams: A simplified solution

In the 1980s, Amendt and Weitzner proposed an interesting model capable to describe relativistic electron beams. It concerned 14 independent variables and the closure was obtained by using the entropy and the Einstein relativity principles. As we know from literature, an extension to many moments allows to achieve an improvement in the results. Three years ago, we exhibited a macroscopic model with an arbitrary but fixed number of moments for relativistic extended thermodynamics. Such model was more general than those previously appeared in literature, so it was applicable even to materials different from an electron beam. Subsequently, we found the closure of such model consistent with the entropy and the Einstein relativity principles, up to whatever order with respect to equilibrium. The solution was determined in terms of a family of arbitrary single variable functions arising from integration. Those results have a very complex shape and are very difficult to handle so a simplification is necessary. I...

An exact macroscopic extended model with many moments for ultrarelativistic gases

Extended Thermodynamics is a very important theory: for example, it predicts hyperbolicity, finite speeds of propagation waves as well as continuous dependence on initial data. Therefore, it constitutes a significative improvement of ordinary thermodynamics. Here its methods are applied to the case of an arbitrary, but fixed, number of moments. The kinetic approach has already been developed in literature; then, the macroscopic approach is here considered and the constitutive functions appearing in the balance equations are determined up to whatever order with respect to thermodynamical equilibrium. The results of the kinetic approach are a particular case of the present ones.

Relativistic Eulerian rarefied gas with internal structure

Recently Pennisi and Ruggeri [Ann. Phys. 377, 414 (2017)] proposed a casual hyperbolic model for a dissipative relativistic gas with internal structure. In this paper, we consider the particular case of the model when dissipation is negligible (Eulerian gas). We study in particular the energy behavior in comparison with the Synge energy which is valid for monatomic gas and we evaluate the characteristic velocities proving the hyperbolicity of the differential system. The second part of the paper is devoted to the ultra-relativistic limit of the model and we prove that there exists a critical value of the degree of freedom such that for smaller values of this quantity the ultra-relativistic limit of the energy of a gas with structure is the same as the Synge energy, while for larger degrees of freedom the energy increases with the degree of freedom itself.