Ryosuke Yano

Analytical and numerical study on the nonequilibrium relaxation by the simplified Fokker–Planck equation

Nonequilibrium relaxation by the simplified Fokker–Planck equation is studied by calculating the relaxation of Grad’s moments. From calculated relaxation of moments, we propose two simplified Fokker–Planck-type equations. For the quantitative validation of nonequilibrium relaxation by using the simplified Fokker–Planck-type equations, we solve a rarefied shock layer problem. To study the stronger diffusion of the distribution function than the simplified Fokker–Planck-type equation, we consider diffusion of the distribution function due to the gain term of the Boltzmann equation, because the Boltzmann equation can be described by a partial differential equation with higher-order terms than the simplified Fokker–Planck equation. The effect of the gain term of the Boltzmann equation is discussed based on comparisons with our proposed Bhatnagar–Gross–Krook equation with velocity-dependent collision frequency.

Formulation and numerical analysis of diatomic molecular dissociation using Boltzmann kinetic equation

The direct description of chemical reactions by the Boltzmann equation still involves some difficulties in the kinetic theory. In this paper, we describe diatomic molecular dissociation due to transitions of vibrational quantum states resulting from inelastic collisions. These can be described by the Wang Chang-Uhlenbeck (WCU) equation. To avoid direct evaluation of the strong nonlinear collision kernel of the WCU equation, we used a kinetic equation. For accurate description of the dissociation process, we describe improvements we made to the conventional inelastic collision model (the so-called Morse model). Combining this inelastic collision model with the gas mixture model by Oguchi, we formulated a model for representing diatomic molecular dissociations. We validated this model by simulating a hypersonic shock layer with diatomic molecular dissociation.

Opinion formation with upper and lower bounds

We investigate the opinion formation with upper and lower bounds. We formulate the binary exchange of opinions between two peoples under the second (or political) party using the relativistic inelastic-Boltzmann-Vlasov equation with randomly perturbed motion. In this paper, we discuss the relativistic effects on the opinion formation of peoples from the standpoint of the relativistic kinetic theory.

Numerical analysis of relativistic shock layer problem by using relativistic Boltzmann–kinetic equations

The relativistic shock layer problem was numerically analyzed by using two relativistic Boltzmannkinetic equations. One is Marle model, and the other is Anderson-Witting model. As with Marle model, the temperature of the gain term was determined from its relation with the dynamic pressure in the framework of 14-moments theory. From numerical results of the relativistic shock layer problem, behaviors of projected moments in the nonequilibrium region were clarified. Profiles of the heat flux given by Marle model and Anderson-Witting model were quite adverse to the profile of the heat flux approximated by Navier-Stokes-Fourier law. On the other hand, profiles of the heat flux given by Marle model and Anderson-Witting model were similar to the profile approximated by Navier-Stokes-Fourier law. Additionally we discuss the differences between Anderson-Witting model and Marle model by focusing on the fact that the relaxational rate of the distribution function depends on both flow velocity and molecular velocity for Anderson-Witting model, while it depends only on the molecular velocity for Marle model.

Formulation and numerical analysis of vibrationally coupled recombination of monatomic molecules using Boltzmann kinetic equation

Monatomic molecular recombination is formulated using the Boltzmann kinetic equation. The recombination is coupled to the diatomic molecular vibrational states using the truncated harmonic oscillator model. The obtained recombination rate is equal to the modified Arrhenius rate, which is independent of the dissociation (activation) energy, when the temperature defined in the gain term on the basis of the intermediate’s collisions is much lower than that of the dissociation. The formulated model is numerically analyzed by solving the hypersonic shock layer problem with dissociation-recombination reactions. The obtained numerical results indicate that dissociated monatomic molecules behind a shock wave recombine into diatomic molecules owing to the decrease in the temperature near the wall.

Consideration of the vibrationally linked molecular dissociation model based on the kinetic theory

In recent year, the remarkable development of high performance computing gradually makes it possible to simulate hyper‐dimensional distribution function, which constitutes of Boltzmann equation or other model equations. Our interests exist in formulation of molecular dissociation process with distribution function including molecular quantum states, which needs higher dimensions in accordance with the number of quantum mode. In this paper, Boltzmann model equation is used and discussed primarily. For assurance of properties of Boltzmann model equation, various models are analyzed numerically. Additionally the mixture gaseous model by Oguti and inelastic collision model by Morse‐Holway is combined with and extended into the molecular dissociation formulation.

On the kinetic formulation of vibrationally coupled diatomic dissociation and monatomic recombination

In this paper, we formulate the diatomic dissociation-recombination by the kinetic theory. The collision term of the Wang-Chang-Uhlenbeck equation is replaced by the extended Morse model. The diatomic molecular dissociation is formulated by using the truncated model of the vibration mode. The recombination reaction is formulated by defining the distribution function of the intermediate. On the basis of formulated kinetic model, the catalysis on the wall is investigated using two kinetic models. Finally the ablation on the wall is formulated using the finite catalytic wall. The formulated kinetic models are numerically investigated by solving shock layer problem around a circular cylinder with the finite catalytic wall or ablation.

Transport coefficients of the inelastic variable hard sphere

The transport coefficients of the inelastic variable hard sphere are calculated using infinite Maxwellian iterations of Grad’s 14 moment equations and dimensional analysis on the basis of the Chapman‐Enskog expansion. The viscositycoefficient(μ)obtainedusinginfiniteMaxwellianiterationscoincides with that obtained using dimensional analysis on the basis of the Chapman‐ Enskogexpansion.Twotransportcoefficients(κ and η)calculatedusinginfinite Maxwellianiterations,whichdefinetheheatflux,coincidewiththosecalculated using dimensional analysis on the basis of the Chapman‐Enskog expansion, only when κ and η obtained using infinite Maxwellian iterations converge. Divergences of κ and η occur whenever the dissipating rate of the heat flux, via the inelastic collisional term, is equal to or smaller than the characteristic increasingordecreasingrateoftheheatfluxviathedecreaseinthetemperature.

Kinetic description of finite-wall catalysis for monatomic molecular recombination

In our previous study on hypothetical diatomic molecular dissociation and monatomic molecular recombination, A2 + M ↔ A + A + M [Yano et al., Phys. Fluids 21, 127101 (2009)], the interaction between the wall and A2* intermediates was not formulated. In this paper, we consider the effect of finite-wall catalysis on recombination of a monatomic molecule A via the interaction between the wall and A2*. According to the proposed Boltzmann model equation, the catalytic recombination rate depends on two quantities; the vibrational temperature and the translational temperature of A2* intermediates that are emitted from the wall. In particular, the translational temperature of A2* is related to its lifetime. In this paper, we investigate the change in the catalytic recombination rate of A upon changing the vibrational temperature of A2* intermediates that are emitted from the wall. As an object of analysis, the rarefied hypersonic flow around a cylinder with a finite wall-catalysis is considered using the proposed...

Kinetic analyses of thermally relativistic nonequilibrium flows

In this paper, we consider on the thermally relativistic nonequilibrium flows in the flat or curved spacetime. In the flat spacetime, the supersonic thermally relativistic flow around the prism is numerically analyzed using the Anderson‐Witting model. Obtained numerical results show that the flowfield is remarkably different from that obtained by the Bhatnagar‐Gross‐Krook equation, which is the nonrelativistic limit of the Anderson‐Witting model. Additionally, the sign of the dynamic pressure is opposite to that obtained by the Navier‐Stokes‐Fourier law on the basis of the Eckart decomposition. Finally, the thermally relativistic flow in the curved spacetime is numerically analyzed by solving the general relativistic Anderson‐Witting model and the Einstein’s equation simultaneously. In curved spacetime, nongravitational flow is induced owing to the local dependency of the equilibrium function on the local metric of curved spacetime. Such a flow is confirmed by the nongravitational initial cluster inside t...