Molecular extended thermodynamics of rarefied polyatomic gases and wave velocities for increasing number of moments

Arima, Takashi; Mentrelli, Andrea; Ruggeri, Tommaso

doi:10.1016/j.aop.2014.03.011

Cited by 70 publications

(75 citation statements)

References 48 publications

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“…In this way the number of the eqs. (1) 2 will be equal to that of (1) 1 decreased of an unity obtaining in this way the same set of equations of [5].…”

Section: Introductionmentioning

confidence: 99%

“…Now, always in [5], it is shown that in the context of the kinetic approach is necessary to choose N = M − 1 if we want characterisic velocities depending on the degrees of freedom of a molecule. This is not a problem because we can proceed in the following way: Let us consider the subsystem obtained by simply removing from (1) 1 the equation for n = N + 2; this can be done by simply putting equal to zero the corresponding Lagrange multiplier according to the technique outlined in [6].…”

Section: Introductionmentioning

confidence: 99%

“…(1) 2 goes from 0 to an arbitrary number M restricted by M ≤ N + 1 and the resulting model can be called the (N − 2, M )− Model as in [5] which belongs to the kinetic approach. But this apparently more general model can be obtained from the present one in the following way:…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The General Exact Solution for the Many Moments Macroscopic Approach to Extended Thermodynamics of Polyatomic Gases

Carrisi¹,

Tchame²,

Obounou³

et al. 2017

Int. J. of Pure and Appl. Math.

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A new model for Polyatomic and for Dense Gases has been proposed in literature in the last five years in the framework of Extended Thermodynamics. The case with an arbitrary but fixed number of moments has been recently studied, both with the kinetic approach than with the macroscopic approach; this last one is more general and includes the results of the kinetic approach only as a particular case.Scope of the "closure problem" is to find the expression of some arbitrary functions which appear in the balance equations. Up to now only a recurrence procedure has been published which outlines how to find the solution of this problem with the macroscopic approach; by using this procedure, a numberable set of solutions has been found and written explicitly, while we find here the most general exact solution. It is determined except for some arbirary terms and it is interesting that these terms appear also in the 24 moments model; so we find here that they are transmitted from the model with 24 moments to those with an arbitrary number of moments, without any further arbitrary term.

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“…In this way the number of the eqs. (1) 2 will be equal to that of (1) 1 decreased of an unity obtaining in this way the same set of equations of [5].…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The General Exact Solution for the Many Moments Macroscopic Approach to Extended Thermodynamics of Polyatomic Gases

Carrisi¹,

Tchame²,

Obounou³

et al. 2017

Int. J. of Pure and Appl. Math.

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“…• It is to verify Equation (32), because H * 0 given by Equation (41) becomes zero when calculated in λ i = 0.…”

Section: The Expression For ∆Hmentioning

confidence: 99%

“…A new approach has been proposed in [24] and other articles, such as [25][26][27][28][29][30][31][32][33][34][35][36][37][38], which overcomes this problem by considering two blocks of balance equations. In this framework, we have recently studied two different cases: one deals with rarefied polyatomic gases [37], even if the reduced set of applicability is not indicated in the title of that paper.…”

Section: Introductionmentioning

confidence: 99%

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

Carrisi

Tchame

Obounou

et al. 2015

Entropy

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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.

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Shock Waves in Hyperbolic Systems of Nonequilibrium Thermodynamics

Ruggeri

Taniguchi

2019

Mathematics of Planet Earth

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Molecular extended thermodynamics of rarefied polyatomic gases and wave velocities for increasing number of moments

Cited by 70 publications

References 48 publications

The General Exact Solution for the Many Moments Macroscopic Approach to Extended Thermodynamics of Polyatomic Gases

The General Exact Solution for the Many Moments Macroscopic Approach to Extended Thermodynamics of Polyatomic Gases

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

Shock Waves in Hyperbolic Systems of Nonequilibrium Thermodynamics

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