scholarly journals Relativistic Rational Extended Thermodynamics of Polyatomic Gases with a New Hierarchy of Moments

Entropy ◽  
2021 ◽  
Vol 24 (1) ◽  
pp. 43
Author(s):  
Takashi Arima ◽  
Maria Cristina Carrisi ◽  
Sebastiano Pennisi ◽  
Tommaso Ruggeri
Keyword(s):  
Bulk Viscosity ◽  
Maximum Entropy Principle ◽  
Entropy Density ◽  
Extended Thermodynamics ◽  
Bgk Model ◽  
Rest Energy ◽  
Polyatomic Gases ◽  
The Cauchy Problem ◽  
Entropy Principle ◽  
Rational Extended Thermodynamics

A relativistic version of the rational extended thermodynamics of polyatomic gases based on a new hierarchy of moments that takes into account the total energy composed by the rest energy and the energy of the molecular internal mode is proposed. The moment equations associated with the Boltzmann–Chernikov equation are derived, and the system for the first 15 equations is closed by the procedure of the maximum entropy principle and by using an appropriate BGK model for the collisional term. The entropy principle with a convex entropy density is proved in a neighborhood of equilibrium state, and, as a consequence, the system is symmetric hyperbolic and the Cauchy problem is well-posed. The ultra-relativistic and classical limits are also studied. The theories with 14 and 6 moments are deduced as principal subsystems. Particularly interesting is the subsystem with 6 fields in which the dissipation is only due to the dynamical pressure. This simplified model can be very useful when bulk viscosity is dominant and might be important in cosmological problems. Using the Maxwellian iteration, we obtain the parabolic limit, and the heat conductivity, shear viscosity, and bulk viscosity are deduced and plotted.

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.

scholarly journals Rational extended thermodynamics of dense polyatomic gases incorporating molecular rotation and vibration

2020 ◽  
Vol 378 (2170) ◽  
pp. 20190176 ◽  
Author(s):  
Takashi Arima ◽  
Tommaso Ruggeri ◽  
Masaru Sugiyama
Keyword(s):  
Bulk Viscosity ◽  
Rarefied Gas ◽  
Molecular Rotation ◽  
Extended Thermodynamics ◽  
Molecular Vibration ◽  
Duality Principle ◽  
Linear Wave ◽  
Polyatomic Gases ◽  
Dense Gases ◽  
Rational Extended Thermodynamics

The paper aims to construct a rational extended thermodynamics (RET) theory of dense polyatomic gases by taking into account the experimental evidence that the relaxation time of molecular rotation and that of molecular vibration are quite different from each other. For simplicity, we focus on gases with only one dissipative process due to bulk viscosity. In fact, in some polyatomic gases, the effect of bulk viscosity is much larger than that of shear viscosity and heat conductivity. The present theory includes the previous RET theory of dense gases with six fields as a particular case, and it also includes the RET theory of rarefied polyatomic gases with seven fields in the rarefied-gas limit. The closure is carried out by using the universal principles, that is, Galilean invariance and objectivity, entropy principle, and thermodynamic stability (convexity of entropy), where the duality principle connecting rarefied gases to dense gases also plays an important role. A detailed discussion is devoted to the expression of the production terms in the system of balance equations. As typical examples, we study a gas with virial equations of state and a van der Waals gas. Lastly the dispersion relation of a linear wave is derived, and its comparison with experimental data is made. This article is part of the theme issue ‘Fundamental aspects of nonequilibrium thermodynamics’.

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

2010 ◽  
Vol 466 (2118) ◽  
pp. 1645-1666 ◽  
Author(s):  
M. C. Carrisi ◽  
M. A. Mele ◽  
S. Pennisi
Keyword(s):  
Exact Solution ◽  
Thermodynamic Model ◽  
Conservation Law ◽  
Entropy Density ◽  
Extended Thermodynamics ◽  
Dense Gases ◽  
Galilean Relativity ◽  
Extended Thermodynamic ◽  
Entropy Principle ◽  
The Moment

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 Taylor's 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.

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.

scholarly journals Relativistic Extended Thermodynamics of Polyatomic Gases with Rotational and Vibrational Modes

2021 ◽  
Vol 2 (3) ◽  
pp. 187-201
Author(s):  
Sebastiano Pennisi
Keyword(s):  
Maximum Entropy Principle ◽  
Classical Case ◽  
Fixed Number ◽  
Vibrational Modes ◽  
Balance Equations ◽  
Relativistic Limit ◽  
Polyatomic Gases ◽  
Vectorial Function ◽  
Entropy Principle ◽  
Infinite Set

In a recent article an infinite set of balance equations has been proposed to modelize polyatomic gases with rotational and vibrational modes in the non-relativistic context. To obtain particular cases, it has been truncated to obtain a model with 7 or 15 moments. Here the following objectives are pursued: 1) to obtain the relativistic counterpart of this model which, at the non-relativistic limit, gives the same balance equations as in the known classical case; 2) to obtain the previous result for the model with an arbitrary but fixed number of moments, 3) to obtain the closure of the resulting relativistic model so that all the functions appearing in the balance equations are expressed in terms of the independent variables. To achieve these goals, the following methods are used: 1) The Entropy Principle is imposed. As a result is obtained that the closure is determined up to a single 4-vectorial function usually called 4-potential. 2) To determine this last function, a more restrictive principle is imposed, namely the Maximum Entropy Principle (MEP). 3) Since all the functions involved must be expressed in the covariant form, so as not to depend on the observer, the Representation Theorems are used. Findings of this article are exactly the goals outlined earlier. They are clearly novelty because they had never been achieved before. They can be considered also improvements because, if the aforementioned arbitrary number of moments is restricted to 16, the present work coincide with that already known in literature. Doi: 10.28991/HIJ-2021-02-03-04 Full Text: PDF

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