On the determination of the transfer coefficients in the heat and mass transfer equations, based on the Boltzmann equation

Abstract

At present, as a rule, the determination of the transfer characteristics of viscosity, diffusion, heat conduction and other characteristics in macro-equations of aerohydromechanics is carried out experimentally or on the basis of the kinetic theory of gases - the Boltzmann equation. The right “collisional” part of the Boltzmann equation contains multiple improper integrals with an oscillating integrand function, the values of which are used in determining transfer coefficients. This article proposes numerical algorithms suitable for calculating integrals of this type. They are based on the use of the Gauss - Christoffel quadrature formula that applies orthogonal polynomials. The oscillation nature of the integrand requires control of the quadrature error. In this case, the split nodes of the integration interval are distributed on the basis of minimizing the error of approximation of the integrand by orthogonal polynomials. Such an approach, in contrast to others, allows determining the values of integrals with oscillating integrand functions more qualitatively and efficiently and does not contain an “iterative” procedure for increasing the split nodes of the integration segment to achieve a given accuracy. This article is devoted to the problem of constructing quadrature formulas for calculating improper integrals, which are used in determining the transfer coefficients, based on the Boltzmann equation.