Kinetic models of polyatomic gas typically account for the internal degrees of freedom at the level of the two-particle distribution function. However, close to the hydrodynamic limit, the internal (rotational) degrees of freedom tend to be well represented just by rotational kinetic energy density. We account for the rotational energy by augmenting the Ellipsoidal-statistical BGK (ES-BGK) model, an extension of the Bhatnagar-Gross- Krook (BGK) model, at the level of the single-particle distribution function with an advection-diffusion-relaxation equation for the rotational energy. This reduced model respects the H theorem and recovers the compressible hydrodynamics for polyatomic gases as its macroscopic limit. As required for a polyatomic gas model, this extension of the ES-BGK model has not only correct specific heat ratio but also allows for three independent tunable transport coefficients: thermal conductivity, shear viscosity, and bulk viscosity. We illustrate the effectiveness of the model via a lattice Boltzmann method implementation.
A generalized kinetic model equation which takes into account the frequency depence of the thermal conductivity is used to analyze the problem of sound propagation in dilute polyatomic gases. By comparing the theoretical results with some available experimental data we infer that our model equation provides a precise transition between low and high-frequency limits.
In the classical irreversible thermodynamics (CIT) framework, the Navier Stokes Fourier (NSF) constitutive equations are obtained so as they satisfy the entropy inequality, by and large assuming that the entropy flux is equal to the heat flux over the temperature. This article is focused on the derivation of second-order constitutive equations for polyatomic gases; it takes the basis of CIT, but most importantly, allowing up to quadratic nonlinearities in the entropy flux.
In this article we deduce a mathematical model of Maxwell-Stefan type for a reactive mixture of polyatomic gases with a continuous structure of internal energy. The equations of the model are derived in the diffusive limit of a kinetic system of Boltzmann equations for the considered mixture, in the general non-isothermal setting. The asymptotic analysis of the kinetic system is performed under a reactive-diffusive scaling for which mechanical collisions are dominant with respect to chemical reactions. The resulting system couples the Maxwell-Stefan equations for the diffusive fluxes with the …
Simulating hypersonic flow around a space vehicle is challenging because of the multiscale and nonequilibrium nature inherent in these flows. To effectively deal with such flows, a novel particle particle hybrid scheme combining the stochastic particle Bhatnagar-Gross-Krook (BGK) method with Direct Simulation Monte Carlo (DSMC) was developed recently, but only for monatomic gases [Fei et. al., J. Comput. Phys. 2021]. Here this work is extended to the particle-particle hybrid method for polyatomic gases. In the near continuum regime, employing the Ellipsoidal Statistical BGK model proposed by Y…
This paper is concerned with the analysis of polyatomic gases within the framework of kinetic theory. Internal degrees of freedom are modeled using a single continuous variable corresponding to the molecular internal energy. Non-equilibrium velocity distribution function, compatible with macroscopic field variables, is constructed using the maximum entropy principle. A proper collision cross section is constructed which obeys the micro-reversibility requirement. The source term and entropy production rate are determined in the form which generalizes the results obtained within the framework of…
Semi-empirical procedure of obtaining the boundary conditions for strong evaporation of a polyatomic gas from a plane surface is proposed. The procedure is based on specifying the dependencies of specific momentum and enthalpy of the flow from the gas flow rate. The latter are derived from the analysis of the available data concerning the evaporation of polyatomic and monatomic gases. The procedure predicts the exactly sonic terminal velocity of the flow and leads to some corrections of existing boundary conditions in transonic region. Thus, for j = 2 and sonic flow the corrections for pressur…
Advanced kinetic theory with the Boltzmann-Curtiss equation provides a promising tool for polyatomic gas flows, especially for fluid flows containing inner structures, such as turbulence, polyatomic gas flows and others. Although a Hamiltonian-based distribution function was proposed for diatomic gas flow, a general distribution function for the generalized Boltzmann-Curtiss equations and polyatomic gas flow is still out of reach. With assistance from Boltzmann's entropy principle, a generalized Boltzmann-Curtiss distribution for polyatomic gas flow is introduced. The corresponding governing e…
We develop a tractable interaction model for a polyatomic gas, whose kinetic equation combines a Vlasov-type mean field forcing due to an intermolecular potential, and a Boltzmann-type collision integral due to rotational interactions. We construct a velocity moment hierarchy for the new kinetic equation, and find that, under the high Reynolds number condition, the pressure equation becomes decoupled from the angular momentum and stress. For the heat flux, we propose a novel closure by prescribing the specific heat capacity of the gas flow. Setting the specific heat capacity to that of a const…
We establish Extended Thermodynamics (ET) of rarefied polyatomic gases with six independent fields, i.e., the mass density, the velocity, the temperature and the dynamic pressure, without adopting the near-equilibrium approximation. The closure is accomplished by the Maximum Entropy Principle (MEP) adopting a distribution function that takes into account the internal degrees of freedom of a molecule. The distribution function is not necessarily near equilibrium. The result is in perfect agreement with the phenomenological ET theory. To my knowledge, this is the first example of molecular exten…
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 system of the previous approach is proved to be a \emph{principal subsystem} of the present one. The main idea is that at the molecular level, the total energy is the kinetic energy plus the energy of internal mode due to the rotation and vibration, a…
We reconsider some fundamental aspects of the fluid mechanics model, and the derivation of continuum flow equations from gas kinetic theory. Two topologies for fluid representation are presented, and a set of macroscopic equations are derived through a modified version of the classical Boltzmann kinetic equation for monatomic gases. The free volumes around the gaseous molecules are introduced into the set of kinetic microscopic parameters. Our new description comprises four, rather than three, conservation equations; the classical continuity equation, which conflates actual mass-density and nu…
The Hilbert-Chapman-Enskog expansion of the kinetic equations in mean flight times is believed to be asymptotic rather than convergent. It is therefore inadvisable to use lower order results to simplify the current approximation as is done in the traditional Chapman-Enskog procedure, since that is an iterative method. By avoiding such recycling of lower order results, one obtains macroscopic equations that are asymptotically equivalent to the ones found in the Chapman-Enskog approach. The new equations contain higher order terms that are discarded in the Chapman-Enskog method. These make a sig…
A new form of the model collision operator for a Boltzmann gas of hard spheres and Coulomb plasma is derived. One-component and many-component systems are considered. The collision operator proposed takes properly into account the relaxation of the first 13 hydrodynamic moments. An expression for the intensity of the Langevin source in the model kinetic equation is obtained in the same approximation. A technique for reconstruction of the model collision integral based on a known expression for the model linearized operator is proposed. It is shown that, within our model, the collision integral…
The Kramers problem for quantum Bose-gases with specular-diffuse boundary conditions of the kinetic theory is considered. On an example of Kramers' problem the new generalized method of a source of the decision of the boundary problems from the kinetic theory is developed. The method allows to receive the decision with any degree of accuracy. At the basis of a method lays the idea of representation of a boundary condition on distribution function in the form of a source in the kinetic equation. By means of integrals Fourier the kinetic equation with a source is reduced to the integral equation…
Soliton hydrodynamics is an appealing tool to describe strong turbulence in low-dimensional systems. Strong turbulence in quasi-one dimensional spuerfluids, such as Bose-Einstein condensates, involves the dynamics of dark solitons and, therefore, the description of a statistical ensemble of dark-solitons, i.e. soliton gases, is necessary. In this work, we propose a phase-space (kinetic) description of dark-soliton gases, introducing a kinetic equation that is formally similar to the Vlasov equation in plasma physics. We show that the proposed kinetic theory can capture the dynamical features o…
Loosely speaking, the Mpemba effect appears when hotter systems cool sooner or, in a more abstract way, when systems further from equilibrium relax faster. In this paper, we investigate the Mpemba effect in a molecular gas with nonlinear drag, both analytically (by employing the tools of kinetic theory) and numerically (direct simulation Monte Carlo of the kinetic equation and event-driven molecular dynamics). The analysis is carried out via two alternative routes, recently considered in the literature: first, the kinetic or thermal route, in which the Mpemba effect is characterized by the cro…
The adiabatic piston problem is solved at the mesoscale using a Kinetic Theory approach. The problem is to determine the evolution towards equilibrium of two gases separated by a wall with only one degree of freedom (the adiabatic piston). A closed system of equations for the distribution functions of the gases conditioned to a position of the piston and the distribution function of the piston is derived from the Liouville equation, under the assumption of a generalized molecular chaos. It is shown that the resulting kinetic description has the canonical equilibrium as a steady-state solution.…
