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A rarefied gas flow induced around a flat plate with a uniformly heated single side in a closed vessel, which is also known as the radiometric flow, is considered. Its steady behavior is investigated on the basis of the Bhatnagar-Gross-Krook (BGK) model of the Boltzmann equation and the diffuse reflection boundary condition for a wide range of the Knudsen number, by means of an accurate finite-difference method which gives a correct description of the discontinuity contained in the velocity distribution function. It is found that a thermal edge flow is induced along the plate on both heated and unheated sides near the edge, that drives the overall circulating flow in the vessel. The detailed flow structure near the edge as well as along the plate is clarified. [ABSTRACT FROM AUTHOR]

The Taylor-Couette problem for a rarefied gas is studied numerically by the direct simulation Monte Carlo method. The gas is supposed to be contained in an annular domain, bounded by two coaxial rotating cylinders and top and bottom (specularly reflecting) boundaries, and the flow is assumed to be steady and axisymmetric. Special attention is focused on the effect of rotation of the outer cylinder on the type of the induced Taylor-vortex flow. It is shown that different types of flow can coexist stably in a wide range of speeds of rotation of the inner and outer cylinders unless the outer cylinder is rotating fast in the opposite direction to the inner. © 2005 American Institute of Physics [ABSTRACT FROM AUTHOR]

A binary mixture of rarefied gases between two parallel plates is considered. The Poiseuille flow, the thermal transpiration, and a flow caused by a concentration gradient of a component gas along the plates are investigated on the basis of the linearized Boltzmann equation for hard-sphere gases with the diffuse reflection boundary condition. Accurate numerical analyses are performed by means of a finite-difference method, in which the complicated collision integrals are computed efficiently by the numerical kernel method. As a result, the behavior of the mixture is clarified at the level of the velocity distribution functions as well as the macroscopic quantities for a wide range of the Knudsen number. © 2005 American Institute of Physics [ABSTRACT FROM AUTHOR]

A steady state of a binary mixture of hard-sphere gases in the near continuum regime, where the Knudsen number is small, is considered in the case where the density and temperature variations are large, but the Mach number of the flow is as small as the Knudsen number. Thus, the flow vanishes in the continuum limit where the Knudsen number goes to zero. The set of fluid-dynamic-type equations in this case was derived by Takata and Aoki [Transp. Theor. Stat. Phys. 30, 205 (2001)] by means of a systematic asymptotic analysis of the Boltzmann equation. This set gives the correct behavior of the mixture in the continuum limit, i.e., it describes the ghost effect discovered by Sone et al. for a single-component gas [Phys. Fluids 8, 628 (1996)]. The set contains various transport coefficients that depend on the local properties of the gas. In particular, their dependence on the local concentration of one of the components cannot be obtained explicitly. In this paper, this unknown dependence is established numerically by a direct numerical analysis of the basic integral equations, and a database that provides the numerical values of the transport coefficients immediately for an arbitrarily specified local state of the mixture is constructed. The database makes the fluid-dynamic-type equations applicable to practical problems. [ABSTRACT FROM AUTHOR]

The problem of heat transfer and temperature distribution in a binary mixture of rarefied gases between two parallel plates with different temperatures is investigated on the basis of kinetic theory. Under the assumption that the gas molecules are hard spheres and undergo diffuse reflection on the plates, the Boltzmann equation is analyzed numerically by means of an accurate finite-difference method, in which the complicated nonlinear collision integrals are computed efficiently by the deterministic numerical kernel method. As a result, the overall quantities (the heat flow in the mixture, etc.) as well as the profiles of the macroscopic quantities (the molecular number densities of the individual components, the temperature of the total mixture, etc.) are obtained accurately for a wide range of the Knudsen number. At the same time, the behavior of the velocity distribution function is clarified with high accuracy. [ABSTRACT FROM AUTHOR]

The structure of an infinitely strong shock wave (i.e., a shock wave with infinitely large upstream Mach number) is investigated on the basis of the Boltzmann equation. The velocity distribution function is expressed as a sum of a multiple of the Dirac delta function, centered at the upstream bulk velocity, and a remainder. Strong evidence that the remainder has a singularity in the molecular velocity space was provided by a previous Monte Carlo simulation for a hard-sphere gas [Cercignani et al., Phys. Fluids 11, 2757 (1999)]. Then, the singularity was confirmed and clarified with sufficient accuracy by a precise numerical analysis by means of a finite-difference method. More specifically, the equation for the remainder, which contains the linear collision term linearized around the delta function and the nonlinear collision term, is solved numerically for a hard-sphere gas after the nonlinear collision term is replaced by the BGK collision model. The present paper reports on the main result of this analysis. [ABSTRACT FROM AUTHOR]