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The behavior of radionuclides (Kr and Xe) and process gases (CO) in the vacuum-cesium channel of a thermionic converter reactor is modeled by solving Boltzmann’s equation numerically. Modeling techniques and a software system were developed in the course of this work. Series of calculations were performed for the variation of the initial flux of radionuclides, the dependence of the radionuclide flux at the egress on the flux at the ingress was obtained, the dependence of the carbon monoxide pressure in the opening of the connecting channel on the size of the opening was obtained, and the overgrowth time of the opening due to the condensation of cesium carbonate was estimated.

Flows of a simple rarefied gas and gas mixtures are computed on the basis of the Boltzmann kinetic equation, which is solved by applying various versions of the conservative projection method, namely, a two-point method for a simple gas and gas mixtures with a small difference between the molecular masses and a multipoint method in the case of a large mass difference. Examples of steady and unsteady flows are computed in a wide range of Mach and Knudsen numbers.

The paper presents some results of computing of a gas mixture flows in Knudsen pumps. The simulations are carried out by numerically solving the Boltzmann kinetic equation by the conservative projection method. Interactions of gas molecule are modeled by Lennard-Jones and the newest ab initio potentials. The values of the pumping rate, gas mixture separation, and the graphics of gas flow parameters inside the pumps are given. The results obtained with different molecular models are compared and the influence of the molecular potentials on macroscopic flow parameters is shown. The simulations are performed in plane and 3D geometries.

The conservative method of calculating the Boltzmann collision integral for simple gases, gas mixtures and gases with rotational degrees of freedom of molecules is presented. In all cases the common approach based on the projection technique of summing up the contributions in the collision integral is used. The method is applied for solving the Boltzmann kinetic equation for two fundamental rarefied gas flow problems: the heat transfer problem and the problem of shock wave structure. A comparison with experimental and numerical data of other authors is reported. It is shown that the considered numerical method allows one to solve the Boltzmann equation for real gases with high accuracy.

The structure of a shock wave in a monatomic one-component gas was computed by solving the Boltzmann kinetic equation with accuracy controlled with respect to computational parameters. The hard-sphere molecular model and molecules with the Lennard-Jones potential were considered. The computations were performed in a wide range of Mach numbers with the accuracy no less than 3% for the shock front width and 1% for local values of density and temperature. The shock wave structure was studied in terms of macroscopic gas characteristics and in terms of the molecular velocity distribution function.

One considers a phenomenon that has been observed in some experimental works [1, 2], confirmed by an analysis based on the assumption of a bimodal shape of the distribution functions inside the SW [1] and by computations using the Monte Carlo simulation method [3–5]. The phenomenon consists of an excess of high-energy molecular collisions inside the SW in a gas mixture compared to the value behind the wave. It was found that the excess of such collisions is most expressed for gas mixtures with high difference of concentrations and molecular masses of the components.

The paper presents some results of computing gas mixture flows in Knudsen and Holweck pumps. Transient flow development processes and attainment of the steady state are considered. The calculations were performed using a problem solving environment developed by the authors. A conservative projection method of solving the Boltzmann kinetic equation upon which the problem solving environment is based is described. The paper is aimed to demonstrate the capabilities of the software at the actual stage of its development.

The paper describes the methodology of computing gas flows in narrow micro- and nanoscale channels on the basis of finite-difference solution of the Boltzmann kinetic equation using the conservative projection method of collision integral calculation. Mathematical framework of the method is considered and the problem solving environment for calculation of the above mentioned flows is described. Examples of the flow calculations in the plane and 3D geometry are given.

Gas separation in thermal creep based micro devices is studied by solving the Boltzmann kinetic equation by the finite difference discrete ordinates method. The collision integral is evaluated by two alternative versions of the conservative projection method developed for gas mixtures. The advection operator of the equation is approximated by flux-preserving schemes at rectangular or unstructured grids. The influence of a molecular potential on a gas separation rate is demonstrated.

A new projection method for computing the Boltzmann collision integral at a discrete momentum grid that is conservative by mass, momentum, and energy, and annul the integral from the Maxwellian distribution function is proposed. The method is applied for computing gas mixtures with large difference of molecular masses where it is computationally more efficient compared to the previously proposed projection method.

The main purpose of the work is optimization of the solver for rarefied gas flow modeling based on the Boltzmann equation. Optimization method is based on SIMD extensions for ×86 processors. Computational code is profiled and manually optimized with SSE instructions. Heat flow, shock waves and Knudsen pump are modeled with optimized solver. Dependencies of computational time from mesh sizes and CPU capabilities are provided.

In his study of thermal creep phenomena in 1910, M. Knudsen build a construction that was composed of 10 pairs of cylindrical tubes of different diameters heated at its junctions. He observed that at some conditions the construction worked as a gas compressor and he was able to obtain the pressure ratio at the ends of the device up to 10. The aim of the present work was to model the experiment using the power of modern computers and the efficient method for solving the Boltzmann kinetic equation. The computations were made for the same set of temperatures, gas pressures and geometrical parameters of the installation as in the experiment, and for molecular hydrogen with real Lenard-Jones potential and realistic rotational energy relaxation time. The Boltzmann equation was solved by the conservative projection method. The computations were carried out with the use of specially developed by the authors program-solving environment for modeling of rarefied gas flows with arbitrary geometry and real gas parameters. The obtained results are in reasonable good agreement with the experimental data.