Moment Equations for Polyatomic Gases

Pavić-Čolić, Milana; Simić, Srboljub

doi:10.1007/s10440-014-9928-6

Cited by 17 publications

(14 citation statements)

References 19 publications

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“…There will appear the main difference between our approach and the results of non-linear ET-our model is more flexible since it contains more free parameters in the source term, and their values may be adapted to fit into particular physical situation. Similar results were obtained in the case of 14 moments equations for polyatomic gases [21], where the presence of parameters admitted the matching with Prandtl number and temperature dependence of viscosity. As an illustration, the problem of shock structure will be analyzed and dependence of the shock profile upon the values of parameters will be discussed.…”

Section: Introductionsupporting

confidence: 83%

Polyatomic gases with dynamic pressure: Kinetic non-linear closure and the shock structure

Pavić-Čolić

Madjarević

Simić

2017

International Journal of Non-Linear Mechanics

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Section: Introductionsupporting

confidence: 83%

Polyatomic gases with dynamic pressure: Kinetic non-linear closure and the shock structure

Pavić-Čolić

Madjarević

Simić

2017

International Journal of Non-Linear Mechanics

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“…Locality The locality of RET is required from the outset and leads to the quasi-linear hyperbolic structure of equations. They are compatible with the moment equations of kinetic theory as well [44,47,48]. Then, the usual gradient terms in the constitutive equations emerge by the elimination of the higher moments [53].…”

Section: Comparison Of Concepts and Proceduresmentioning

confidence: 56%

“…Only the relaxation times (49) remain undetermined. However, their values may be estimated using more refined theories like the kinetic theory of gases (see [48]) or experimental data [49], since they are related to transport coefficients, i.e., viscosities and heat conductivity (see Eq. (5.62) in [28]).…”

Section: Constitutive Relations For Rarefied Gases Near Equilibriummentioning

confidence: 99%

Non-equilibrium theories of rarefied gases: internal variables and extended thermodynamics

Kovács

Madjarević

Simić

et al. 2020

Continuum Mech. Thermodyn.

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Limits of classical constitutive laws such as Fourier and Navier-Stokes equations are discovered since decades. However, the proper extensions-generalizations of these-are not unique. They differ in the underlying physical principles and in modeling capabilities. In this paper, two different theories are discussed and compared to each other, namely the kinetic theory-based rational extended thermodynamics (RET) and non-equilibrium thermodynamics with internal variables (NET-IV). First, the paper starts with the case of rigid heat conductors summarizing the result achieved so far. Then, a typical example of compressible bodies is shown by presenting the first generalization for rarefied gases, called Meixner's theory. It is further extended using generalized entropy current in the framework of NET-IV. It is shown how its structure is related to RET and how the compatibility between them can be acquired. Keywords Rarefied gases • Rational extended thermodynamics • Non-equilibrium thermodynamics • Internal variables 1 Motivation and preparation The simplest and most widely applied classical continuum theory is related to isotropic fluids. They are based upon conservation laws of mass, momentum and energy, adjoined by appropriate constitutive equations for Communicated by Andreas Öchsner.

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“…dσ dr dR dI * dv * dI dv, (30) where primed quantities as functions of non-primed ones are given in (8), and B w is from (29).…”

Section: 22mentioning

confidence: 99%

“…This research path starts with the fourteen moments model firstly introduced in [28], and improved in many ways afterwards [30,2,35]. Kinetic theory provides an insight by calculating the production terms that allows for explicit expressions of relaxation times, which are of phenomenological nature in the macroscopic theories.…”

mentioning

confidence: 99%

Polytropic gas modelling at kinetic and macroscopic levels

Djordjić¹,

Pavić-Čolić²,

Spasojević³

2021

KRM

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In this paper, we consider the kinetic model of continuous type describing a polyatomic gas in two different settings corresponding to a different choice of the functional space used to define macroscopic quantities. Such a model introduces a single continuous variable supposed to capture all the phenomena related to the more complex structure of a polyatomic molecule. In particular, we provide a direct comparison of these two settings, and show their equivalence after the distribution function is rescaled and the cross section is reformulated. We then focus on the kinetic model for which the rigorous existence and uniqueness result in the space homogeneous case is recently proven. Using the cross section proposed in that analysis together with the maximum entropy principle, we establish macroscopic models of six and fourteen fields. In the case of six moments, we calculate the exact, nonlinear, production term and prove its total agreement with extended thermodynamics. Moreover, for the fourteen moments model, we provide new expressions for relaxation times and transport coefficients in a linearized setting, that yield both matching with the experimental data for dependence of the shear viscosity upon temperature and a satisfactory agreement with the theoretical value of the Prandtl number.

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Moment Equations for Polyatomic Gases

Cited by 17 publications

References 19 publications

Polyatomic gases with dynamic pressure: Kinetic non-linear closure and the shock structure

Polyatomic gases with dynamic pressure: Kinetic non-linear closure and the shock structure

Non-equilibrium theories of rarefied gases: internal variables and extended thermodynamics

Polytropic gas modelling at kinetic and macroscopic levels

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