Micro-macro Fokker–Planck–Kolmogorov models for a gas of rigid spheres

Macroscopic system of gas dynamic equations, differing from Navier–Stokes and quasi gas dynamic ones, is derived from a stochastic microscopic model of a hard sphere gas in a phase space. The model is diffusive in velocity space and valid for moderate Knudsen numbers. The main pecularity of our derivation is more accurate velocity averaging due to analitical solving stochastic differential equations with respect to Wiener mesure which describe our original meso model. It is shown at an example of a shock wave front structure that our approach leads to larger than Navier–Stokes front widening that corresponds to reality. The numerical solution is performed by a well suited to super computer applications special «discontinious» particle method.