The application of weighting schemes in the statistical modelling of flows of a multicomponent gas to the calculation of the structure of a shock

Abstract The method of statistical modelling is used to calculate the structure of a shock wave in binary and ternary gaseous mixtures in which the concentration of one or two of the components is small. Weighting algorithms are developed with a scheme of modelling the collisions by Bernoulli trials or with a ballot-box modelling scheme. It is shown that these algorithms lead to a kinetic equation which approximates the Boltzmann equation when there is molecular chaos with an accuracy up to the first order of smallness with respect to the time interval, Δt , into which the evolution of the model system is split and with respect to the characteristic size of a spatial cell. The concentration and temperature profiles, and the distribution functions of pairs of particles of different kinds with respect to their relative velocities, obtained in the calculations, are presented.