Maxwellian iteration of a causal relativistic model of polyatomic gases and evaluation of bulk, shear viscosity and heat conductivity

Carrisi, Maria Cristina; Pennisi, Sebastiano; Ruggeri, Tommaso

doi:10.1016/j.aop.2021.168447

Cited by 12 publications

(21 citation statements)

References 19 publications

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“…This is because

is related to

by ( 64 ), and it affects the balance laws corresponding to

in RET

. In fact, from ( 66 ) and ( 67 ), we can obtain the closed field equations for

, and then, through the Maxwellian iteration, as has been done in [ 9 ], we obtain the bulk viscosity for RET

as follows:

We remark that the heat conductivity and the shear viscosity is the same between RET

and RET

.…”

Section: Maxwellian Iteration and Phenomenological Coefficientsmentioning

confidence: 99%

“…Let us compare the phenomenological coefficients with the ones for the monatomic case obtained in [ 9 ]. In Figure 1 , we plot the dependence of the dimensionless heat conductivity and shear viscosity on

for both diatomic and monatomic cases.…”

Section: Maxwellian Iteration and Phenomenological Coefficientsmentioning

confidence: 99%

“…Recently, Pennisi and Ruggeri first constructed a relativistic RET theory for polyatomic gases with ( 2 ) in the case of

[ 7 ] (see also [ 8 , 9 ]) whose moments are given by

where the distribution function

depends on the extra variable

, similar to the classical one (see [ 2 ] and references therein), that has the physical meaning of the molecular internal energy of internal modes in order to take into account the exchange of energy due to the rotation and vibration of a molecule, and

is the state density of the internal mode.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Arima

Carrisi

Pennisi

et al. 2021

Entropy

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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.

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“…This is because

is related to

by ( 64 ), and it affects the balance laws corresponding to

in RET

. In fact, from ( 66 ) and ( 67 ), we can obtain the closed field equations for

, and then, through the Maxwellian iteration, as has been done in [ 9 ], we obtain the bulk viscosity for RET

as follows:

We remark that the heat conductivity and the shear viscosity is the same between RET

and RET

.…”

Section: Maxwellian Iteration and Phenomenological Coefficientsmentioning

confidence: 99%

for both diatomic and monatomic cases.…”

Section: Maxwellian Iteration and Phenomenological Coefficientsmentioning

confidence: 99%

“…Recently, Pennisi and Ruggeri first constructed a relativistic RET theory for polyatomic gases with ( 2 ) in the case of

[ 7 ] (see also [ 8 , 9 ]) whose moments are given by

where the distribution function

depends on the extra variable

is the state density of the internal mode.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Arima

Carrisi

Pennisi

et al. 2021

Entropy

Self Cite

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show abstract

“…In any case, the equations for the classical case can be easily obtained from the relativistic ones jut making their limit for c which tends to infinity. For this reason, articles on polyatomic gases in the context of relativity have already been published, such as [6], [8], [9], [10], [11].…”

Section: Introductionmentioning

confidence: 99%

Consistent Order Approximations in Extended Thermodynamics of Polyatomic Gases

Pennisi¹

2021

JANSET

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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.

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“…Recently, Pennisi and Ruggeri first constructed a relativistic ET theory for polyatomic gases with (2) in the case of N = 2 [7] (see also [8,9]) whose moments are given by…”

Section: Introductionmentioning

confidence: 99%

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

Arima

Ruggeri

2021

Fluids

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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.

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Maxwellian iteration of a causal relativistic model of polyatomic gases and evaluation of bulk, shear viscosity and heat conductivity

Cited by 12 publications

References 19 publications

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

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

Consistent Order Approximations in Extended Thermodynamics of Polyatomic Gases

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

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