Relativistic extended thermodynamics of polyatomic gases in the Landau and Lifshitz description

2021 ◽  
pp. 103756
Author(s):  
M.C. Carrisi ◽  
S. Pennisi
Keyword(s):  
Extended Thermodynamics ◽  
Polyatomic Gases

scholarly journals Molecular Extended Thermodynamics of Rarefied Polyatomic Gases with a New Hierarchy of Moments

Fluids ◽  
2021 ◽  
Vol 6 (2) ◽  
pp. 62
Author(s):  
Takashi Arima ◽  
Tommaso Ruggeri
Keyword(s):  
Degrees Of Freedom ◽  
Maximum Entropy Principle ◽  
Extended Thermodynamics ◽  
Moment Equations ◽  
Field Equations ◽  
Polyatomic Gases ◽  
Moment System ◽  
Rarefied Polyatomic Gases ◽  
Entropy Principle ◽  
Internal Degrees Of Freedom

The aim of this paper is to construct the molecular extended thermodynamics for classical rarefied polyatomic gases with a new hierarchy, which is absent in the previous procedures of moment equations. The new hierarchy is deduced recently from the classical limit of the relativistic theory of moments associated with the Boltzmann–Chernikov equation. The field equations for 15 moments of the distribution function, in which the internal degrees of freedom of a molecule are taken into account, are closed with the maximum entropy principle. It is shown that the theory contains, as a principal subsystem, the previously polyatomic 14 fields theory, and in the monatomic limit, in which the dynamical pressure vanishes, the differential system converges, instead of to the Grad 13-moment system, to the Kremer 14-moment system.

scholarly journals Consistent Order Approximations in Extended Thermodynamics of Polyatomic Gases

2021 ◽  
Vol 1 (2) ◽  
pp. 12-21
Author(s):  
Sebastiano Pennisi
Keyword(s):  
Maximum Entropy ◽  
Arbitrary Number ◽  
Maximum Entropy Principle ◽  
Extended Thermodynamics ◽  
The Other ◽  
Balance Equations ◽  
Polyatomic Gases ◽  
New Model ◽  
Independent Variables ◽  
Entropy Principle

In this article the known models are considered for relativistic polyatomic gases with an arbitrary number of moments, in the framework of Extended Thermodynamics. These models have the downside of being hyperbolic only in a narrow domain around equilibrium, called "hyperbolicity zone". Here it is shown how to overcome this drawback by presenting a new model which satisfies the hyperbolicity requirement for every value of the independent variables and without restrictions. The basic idea behind this new model is that hyperbolicity is limited in previous models by the approximations made there. It is here shown that hyperbolicity isn't limited also for an approximated model if terms of the same order are consistently considered, in a new way never used before in literature. To design and complete this new model, well accepted principles are used such as the "Entropy Principle" and the "Maximum Entropy Principle". Finally, new trends are analized and these considerations may require a modification of the results published so far; as a bonus, more manageable balance equations are obtained. This allows to obtain more stringent results than those so far known. For example, we will have a single quantity (the energy e) expressed by an integral and all the other constitutive functions will be expressed in terms of it and its derivatives with respect to temperature. Another useful consequence is its easier applicability to the case of diatomic and ultrarelativistic gases which are useful, at least for testing the model in simple cases.

A Study of Linear Waves Based on Extended Thermodynamics for Rarefied Polyatomic Gases

2014 ◽  
Vol 132 (1) ◽  
pp. 15-25 ◽  
Author(s):  
Takashi Arima ◽  
Shigeru Taniguchi ◽  
Tommaso Ruggeri ◽  
Masaru Sugiyama
Keyword(s):  
Extended Thermodynamics ◽  
Polyatomic Gases ◽  
Linear Waves ◽  
Rarefied Polyatomic Gases

Dispersion relation for sound in rarefied polyatomic gases based on extended thermodynamics

2012 ◽  
Vol 25 (6) ◽  
pp. 727-737 ◽  
Author(s):  
Takashi Arima ◽  
Shigeru Taniguchi ◽  
Tommaso Ruggeri ◽  
Masaru Sugiyama
Keyword(s):  
Dispersion Relation ◽  
Extended Thermodynamics ◽  
Polyatomic Gases ◽  
Rarefied Polyatomic Gases

scholarly journals A Numberable Set of Exact Solutions for the Macroscopic Approach to Extended Thermodynamics of Polyatomic Gases with Many Moments

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Maria Cristina Carrisi ◽  
Rita Enoh Tchame ◽  
Marcel Obounou ◽  
Sebastiano Pennisi
Keyword(s):  
Exact Solutions ◽  
Fixed Number ◽  
Extended Thermodynamics ◽  
Relativity Principle ◽  
Polyatomic Gases ◽  
New Model ◽  
Galilean Relativity ◽  
Entropy Principle ◽  
Macroscopic Approach ◽  
Particular Solution

A new model for Polyatomic Gases with an arbitrary but fixed number of moments has been recently proposed and investigated in the framework of Extended Thermodynamics; the arbitrariness of the number of moments is linked to a numberNand the resulting model is called anN-Model. This model has been elaborated in order to take into account the entropy principle, the Galilean relativity principle, and some symmetry conditions. It has been proved that the solution for all these conditions exists, but it has not been written explicitly because hard notation is necessary; it has only been shown how the theory is self-generating in the sense that if we know the closure of theN-Model, then we will be able to find that of(N+1)-Model. Up to now only a single particular solution has been found in this regard. Instead of this, we find here a numberable set of exact solutions which hold for every fixed numberN.

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