ИСТИНА

Hierarchy of gas dynamics. Probabilistic approach. Most of Oleg Mikhailovich's creative work was devoted to a computational experiment related to the Boltzmann equation, the substantiation of Monte Carlo methods. The probabilistic approach based on stochastic differential equations was developed by A.V. Skorokhod and, in relation to kinetic equations, by A.A. Arsen'ev with computational support by An. V. Lukshin. We will show how the simplest, but far from trivial, model of a gas from hard spheres leads to a micro-meso-macro hierarchy in descending order of the Knudsen number, due to the transitions of the description using random processes from discontinuous to diffusive in a six-dimensional phase space with reduction to three-dimensional. Such a chain allows us to refine the Boltzmann, Fokker-Planck-Kolmogorov and Navier-Stokes equations, and also allows us to build through algorithms within the framework of unified particle methods, stochastic and deterministic.