Takashi Arima

National Institute of Technology, Tomakomai College · Department of Engineering for Innovation

A new expression is here proposed for the production term Q in the Boltzmann Equation. This new expression satisfies the H-Theorem (non approximated) and, in the transition to Ordinary Thermodynamics gives a result which is independent on the number N of the moments which are used both if the Maxwellian Iteration or the Eckart method are used.

A novel ES-BGK-based model of non-polytropic rarefied gases in the framework of kinetic theory is presented. Key features of this model are: an internal state density function depending only on the microscopic energy of internal modes (avoiding the dependence on temperature seen in previous reference studies); full compliance with the H-theorem; fe...

Flows of a rarefied polyatomic gas confined in a nozzle with simple geometry are numerically studied based on the rational extended thermodynamics theory with six independent fields (RET\(_6\)). Using the theory, we can focus on, in particular, the effect of the dynamic pressure (nonequilibrium part of the pressure) on nozzle gas-flows. Development...

We present a complete analysis of the dispersion relations for longitudinal and transverse waves in a rarefied polyatomic gas based on Rational Extended Thermodynamics (RET), which describes the evolution of a non-polytropic gas in nonequilibrium. Observability of the second mode of the longitudinal wave and the transverse wave is discussed althoug...

A relativistic version of the Kinetic Theory for polyatomic gas is considered and a new hierarchy of moments that takes into account the total energy composed by the rest energy and the energy of the molecular internal modes is presented. In the first part, we prove via classical limit that the truncated system of moments dictates a precise hierarc...

A relativistic version of the Kinetic Theory for polyatomic gas is considered and a new hierarchy of moments that takes into account the total energy composed by the rest energy and the energy of the molecular internal modes is presented. In the first part, we prove via classical limit that the truncated system of moments dictates a precise hierarc...

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 t...

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 t...

Motivated by a recent paper of Pennisi in the relativistic framework Pennisi (2021), we revisit the previous approach of two hierarchies of moments critically and propose a new natural physical hierarchy of moments to describe classical rarefied non-polytropic polyatomic gas in the framework of Molecular Rational Extended Thermodynamics. The differ...

Motivated by a recent paper of Pennisi (2021) in the relativistic framework, we revisit the previous approach of two hierarchies of moments critically and propose a new natural physical hierarchy of moments to describe classical rarefied non-polytropic polyatomic gas in the framework of Molecular Rational Extended Thermodynamics. The differential s...

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 equatio...

Recently, Pennisi and Ruggeri [J Stat Phys 179, 231-246 (2020)] consider the classical limit of the relativistic theory of moments associated with the Boltzmann-Chernikov equation truncated at a tensorial index $N+1$ and they proved that there exists a unique possible choice of the moments in the classical case for a given $N$ both for monatomic an...

We study the characteristic velocities of the extended thermodynamics of molecular rotational- and vibrational- relaxation processes for a van der Waals gas. The lower and upper bounds of the characteristic velocity are, respectively, estimated by the one of rarefied gases and the one evaluated on the spinodal curve. We also study the dispersion re...

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 vis...

We study theoretically the dispersion relation of a rarefied polyatomic gas with molecular rotational- and vibrational- relaxation processes basing on extended thermodynamics with 15 fields. We study, in particular, its temperature dependence in the cases where the rotational and vibrational modes may or may not be excited. It is shown that the cur...

The shock wave structure in rarefied polyatomic gases is analyzed based on extended thermodynamics (ET). In particular, the case with large relaxation time for the dynamic pressure, which corresponds to large bulk viscosity, is considered by adopting the simplest version of extended thermodynamics with only 6 independent fields (ET6); the mass dens...

In the framework of extended thermodynamics, we present three models of a dense polyatomic gases with 6 independent fields. The three models, respectively, represent the relaxation process due to the different molecular energy exchange among the translational, rotational and vibrational energies of a molecule. The characteristic velocities, the loc...

We study the nonequilibrium pressure and temperatures within the framework of extended thermodynamics of gases with 6 independent fields. We derive thermodynamic relations for these quantities from the entropy principle. These relations indicate the usefulness of nonequilibrium thermodynamic potentials. We also introduce the nonequilibrium temperat...

After summarizing the present status of Rational Extended Thermodynamics (RET) of gases, which is an endeavor to generalize the Navier-Stokes and Fourier (NSF) theory of viscous heat-conducting fluids, we develop the molecular RET theory of rarefied polyatomic gases with 15 independent fields. The theory is justified, at mesoscopic level, by a gene...

We revisit the extended thermodynamic (ET) theory of dense polyatomic gases developed in the paper (Arima et al. in Phys Rev Fluids 2:013401, 2017) from the viewpoint of the energy exchange between two subsystems: the subsystem with the kinetic and potential energies and the subsystem of the internal modes such as molecular rotation and vibration....

After defining, in analogy with a mixture of continuous media, a system of balance laws of mixture type, we study the general properties obtained by imposing the Galilean invariance principle. For constitutive equations of local type we study also the entropy principle and we prove the compatibility between the two principles. These general results...

We present a more refined version of rational extended thermodynamics of rarefied polyatomic gases in which molecular rotational and vibrational relaxation processes are treated individually. In this case we need a triple hierarchy of the moment system and the system of balance equations is closed via the maximum entropy principle. Three different...

We present an extended thermodynamics (ET) theory of dissipative dense gases. In particular, we study the ET theory with six fields, where we neglect shear viscosity and heat conductivity. We postulate a simple principle of duality between rarefied and dense gases. This principle is based on the microscopic analysis of the energy exchange between d...

The difference in the theoretical structure between monatomic and polyatomic gases in highly nonequilibrium states is discussed from the viewpoint of molecular extended thermodynamics (MET) of rarefied gases, which is free from the local equilibrium assumption. The MET theories of these two types of gases are based on the moment balance equations w...

We review the recently developed theory of extended thermodynamics (ET) of real gases with six independent fields, i.e., the mass density, the velocity, the temperature and the dynamic pressure, without adopting near-equilibrium approximation. We discuss the polytropic and non-polytropic cases of rarefied polyatomic gases in detail, including the c...

Molecular extended thermodynamics is justified at the mesoscopic level by the moment equations associated with the Boltzmann equation. For polyatomic gases we have a binary hierarchy of moments in contrast with the usual single hierarchy for monatomic gases. In this paper, taking one-dimensional space variables for simplicity, we review the closure...

On the basis of the nonlinear extended thermodynamics theory discussed in Part I, the shock wave structure in a rarefied non-polytropic gas is analyzed. It is found that the effect of nonlinearity in the constitutive equation on the shock wave structure becomes significant only when the Mach number is large. The deviation from the exponential decay...

The shock wave structure in a rarefied polyatomic gas is analyzed on the basis of non-linear extended thermodynamics with 6 independent fields (ET6); the mass density, the velocity, the temperature and the dynamic pressure, which permits us to study the shock profile also for large Mach numbers. The first result of this paper is that the shock wave...

We establish extended thermodynamics (ET) of real gases with 6 independent fields, i.e., the mass density, the velocity, the temperature and the dynamic pressure, without adopting the near-equilibrium approximation. We prove its compatibility with the universal principles (the entropy principle, the Galilean invariance and the stability), and obtai...

We study the six-field model of fluids (ET6) derived from extended thermodynamics. The six fields are the mass density, the velocity, the temperature, and the dynamic pressure (nonequilibrium pressure). We present the basic system of field equations of ET6. And we elucidate its characteristic features through the studies of the singular limit from...

Extended thermodynamics of rarefied polyatomic gases is characterized by two hierarchies of equations for moments of a suitable distribution function in which the internal degrees of freedom of a particle is taken into account. To obtain the closed set of the field equations for the system with many moments and for an arbitrary entropy functional t...

We study the dispersion relation for sound in rarefied polyatomic gases basing on the recently developed theory of extended thermodynamics (ET) for both dense and rarefied polyatomic gases. For hydrogen and deuterium gases in a wide temperature range where the rotational and vibrational modes in a molecule play a role, we compare the dispersion rel...

A theory of the shock wave structure in a rarefied polyatomic gas is developed on the basis of the recent new approach to extended thermodynamics. We summarize the following points (i) and (ii) based on the previous study on this subject and also show the new point (iii): (i) The theory can explain the change of types of the shock wave structure ob...

The effect of the dynamic pressure (non-equilibrium pressure) on stationary heat conduction in a rarefied polyatomic gas at rest is elucidated by the theory of extended thermodynamics. It is shown that this effect is observable in a non-polytropic gas. Numerical studies are presented for a para-hydrogen gas as a typical example.

Molecular extended thermodynamics of rarefied polyatomic gases is characterized by two hierarchies of equations for moments of a suitable distribution function in which the internal degrees of freedom of a molecule is taken into account. On the basis of physical relevance the truncation orders of the two hierarchies are proven to be not independent...

The structure of a shock wave in a rarefied polyatomic gas is studied on the basis of the theory of extended thermodynamics. Three types of the shock wave structure observed in experiments, that is, the nearly symmetric shock wave structure (type A, small Mach number), the asymmetric structure (type B, moderate Mach number), and the structure compo...

We study the shock wave structure in a rarefied polyatomic gas based on a simplified model of extended thermodynamics in which the dissipation is due only to the dynamic pressure. In this case the differential system is very simple because it is a variant of Euler system with a new scalar equation for the dynamic pressure [T. Arima, S. Taniguchi, T...

We study the dispersion relation for sound in rarefied polyatomic gases (hydrogen, deuterium and hydrogen deuteride gases) basing on the recently developed theory of extended thermodynamics (ET) of dense gases. We compare the relation with those obtained in experiments and by the classical Navier–Stokes Fourier (NSF) theory. The applicable frequenc...

We show that, in the theory of extended thermodynamics, rarefied monatomic gases can be identified as a singular limit of rarefied polyatomic gases. Under naturally conditioned initial data we prove that the system of 14 field equations for polyatomic gases in the limit has the same solutions as those of the system of 13 field equations for monatom...

A recently-developed theory of extended thermodynamics of dense gases is reviewed and its characteristic features are discussed. The discussion is made in the following four cases separately: (i) Rarefied monatomic gases, (ii) rarefied polyatomic gases, (iii) dense monatomic gases, and (iv) dense polyatomic gases. In particular, for rarefied polyat...

We study extended thermodynamics of dense gases by adopting the system of field equations with a different hierarchy structure to that adopted in the previous works. It is the theory of 14 fields of mass density, velocity, temperature, viscous stress, dynamic pressure, and heat flux. As a result, most of the constitutive equations can be determined...

Basing on the recent theory of extended thermodynamics of dense gases, we study a thermodynamic theory of gases with the energy transfer from molecular translational mode to internal modes as an extension of Meixnerʼs theory. We focus our attention on the simplest case with only one dissipative process due to the dynamic pressure. The dispersion re...

We summarize the recent theory of fluctuating hydrodynamics based on extended thermodynamics, which is developed through the study of the 13-variable theory for a monatomic rarefied gas as a representative case. The relationship between the present theory and the Landau-Lifshitz theory is shown, and the hierarchy structure of the hydrodynamic fluct...

We develop a theory of fluctuating hydrodynamics based on extended thermodynamics through studying the 13-variable theory for a monatomic rarefied gas as a representative case. After analyzing the relationship between the present theory and the Landau–Lifshitz theory, we discuss the hierarchy structure of the hydrodynamic fluctuations.