Calculation of the transport coefficients and slip velocities for molecules in the form of solid spheres

Abstract

A solution of the Boltzmann equation is carried out by the Monte Carlo method for problems of rarefied gasdynamics in a linear formulation. The problems are solved by calculating the transport coefficients and slip velocities on a solid wall for molecules in the form of solid spheres. The accuracy of the method due to various parameters of the computational scheme in the solution of the problem is investigated by calculating the transport coefficients for pseudo-Maxwellian molecules. The Boltzmann kinetic equation is a complex integro-differential equation which is very difficult to solve and analyze. Hence, the solution of even one-dimensional problems and for the linearized Boltzmann equation turns out to be quite difficult, and such problems are solved by approximate methods (the expansion in Knudsen numbers, the method of moments, the expansion in series, etc. [1]). A method of solving the linearized Boltzmann equation by the Monte Carlo method is proposed in [2]. An exact solution of a number of problems of rarefied gas dynamics has been obtained by this method [3, 4]. However, the method was applied for pseudo-Maxwellian molecules, for which the collision cross section is inversely proportional to the relative velocity of the colliding particles σ=σ0/g.