Features of the rarefied gas description in terms of a distribution function

Abstract

The aim of the paper is to determine the relationship of the classical model for describing a rarefied gas using the distribution function and its discrete representation. Here we study the role of discreteness in the description of a medium in the kinetic theory and the interrelation between interaction of the discreteness and the “continuity” of a media. The question of the relationship between the discreteness of a medium and its description with the help of continuum mechanics is important both when processing experimental data and when going from a continuum model to discrete one in mechanics and physics. There are many studies devoted to the influence of the transition from a continuous to discrete medium in computational mathematics, but there is no study of inverse processes. The work related to the formulation of conservation laws as conditions of the equilibrium of forces and moments of forces, as well as the action of additional flows on the sides of an elementary volume, was carried out earlier. After refinement, non -symmetric stress tensor was obtained. The method for calculating this tensor was proposed. The equations for a gas were found from the modified Boltzmann equation and from the phenomenological theory. Inaccuracy leading to the symmetry of the stress tensor arises when calculating the Lagrange function of particles as the sum of pairwise interacting particles and the unchanged position of the inertia system center.