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

Pavić-Čolić, Milana; Madjarević, Damir; Simić, Srboljub

doi:10.1016/j.ijnonlinmec.2017.04.008

Cited by 22 publications

(20 citation statements)

References 34 publications

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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 model is of particular interest, since it is one of the rare systems that admits a non-linear closure of the governing equations using the entropy principle [3,4,40]. It also admits the exact solution of the variational problem of maximum entropy principle, as shown in [33,6,29]. In particular, in [29] the dynamic pressure is not introduced a priori, but rather regarded as a measure of deviation of the system from an equilibrium state, through the analysis of pressure tensor trace.…”

mentioning

confidence: 99%

“…It also admits the exact solution of the variational problem of maximum entropy principle, as shown in [33,6,29]. In particular, in [29] the dynamic pressure is not introduced a priori, but rather regarded as a measure of deviation of the system from an equilibrium state, through the analysis of pressure tensor trace. The source term is calculated in [6] for the discrete energy model, and in [29] for the continuous model in the weighted setting which can be related to the source term of extended thermodynamics described in [3] for the cross section which it is not Galilean invariant, but yields the Galilean invariant production term.…”

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confidence: 99%

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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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“…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%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Polytropic gas modelling at kinetic and macroscopic levels

Djordjić¹,

Pavić-Čolić²,

Spasojević³

2021

KRM

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“…Another line of research will be related to a paradigmatic problem in non-equilibrium processes-the shock structure problem. It was studied in the framework of RET for 14 moments equations [49], for ET6 model [35,65] and from the point of view of the kinetic theory of gases [66]. There remains an open problem of the application of the NET-IV approach in this context, which will undoubtedly bring new insights.…”

Section: Second Lawmentioning

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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“…A shock-wave solution occurs when physical quantities undergo steep but continuous changes across a thin layer of a few mean free paths. The shock-wave problem for polyatomic gases has been studied in the literature also based on Extended Thermodynamics [32,33], or for different hydrodynamic closures [34], derived from kinetic models involving a discrete set of internal energy levels for molecules [35]. Profiles of different types appear, which become increasingly steep for increasing Mach number.…”

Section: Introductionmentioning

confidence: 99%

A Note on the Steady Navier–Stokes Equations Derived from an ES–BGK Model for a Polyatomic Gas

Aoki

Bisi

Groppi

et al. 2021

Fluids

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The two-temperature Navier–Stokes equations derived from an ellipsoidal Bhatnagar-Gross-Krook (ES-BGK) model for a polyatomic gas (Phys. Rev. E102, 023104 (2020)) are considered in regimes where bulk viscosity is much greater than the shear viscosity. Possible existence of a shock-wave solution for the steady version of these hydrodynamic equations is investigated resorting to the qualitative theory of dynamical systems. Stability properties of upstream and downstream equilibria are discussed for varying parameters.

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

Cited by 22 publications

References 34 publications

Polytropic gas modelling at kinetic and macroscopic levels

Polytropic gas modelling at kinetic and macroscopic levels

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

A Note on the Steady Navier–Stokes Equations Derived from an ES–BGK Model for a Polyatomic Gas

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