ИСТИНА

The accuracy of gas dynamic calculations can be increased by implementation of hierarchical algorithms based on micro – macro representations. Usually one starts from the Boltzmann equation with a nondimensionalization parameter Kn, depending on the space variable x. In the regions, where Kn is small, one can use the equation of Kolmogorov – Fokker – Planck type (a meso model for moderate Kn) or stochastic based quasi – gas dynamic equations (for very small Kn) The described micro – macro bridge is reached by the help of the theory of random processes. The stochastic processes are governed by stochastic differential equations and generate measures, the densities of which satisfied the above deterministic equations. The coefficients depend on collision model. That approach can be used to construct optimal hierarchical self-shock-capturing algorithms for gas dynamic simulation based on both stochastic and deterministic particle methods: the well known Monte – Carlo method for solving Boltzmann equation is equal to numerical realization of a stochastic (Poisson) particle method; the meso model can be solved both by stochastic (Wiener) particle method or by deterministic entropy – consistent particle method for the Kolmogorov – Fokker – Planck equation; to solve the system by deterministic particle method, to our opinion, is more efficient than the usual difference or FE methods especially for discontinuous 3D cases. Kn.