Computational technologies for determining the collision term in Boltzmann equation

Abstract

For solution of applied tasks of mathematical modeling it is required to know the properties of the medium, which are difficult or impossible to determine experimentally or by semi-empirical formulas. In such cases it is important to be able to correctly evaluate capabilities of theoretical methods. Since the values of the transport characteristics of the medium are influenced by microprocesses, it is reasonable to use the approach of the molecular-kinetic theory of gases, the Boltzmann equation in particular. The right side “collision” part of this equation contains multiple improper integrals with singularities whose values are used in determining the transition coefficients. In this paper, we present computational technologies for determining the values of such integrals, which allows to reasonably determine the calculated values of the transfer coefficients in media based on the first principle of the molecular-kinetic theory of gases in mathematical modeling of problems of fluid and gas mechanics on the basis of macroequations of heat and mass transfer.