Место издания:European Community on Computational Methods in Applied Sciences (ECCOMAS) Crete Island, Greece Institute of Structural Analysis and Antiseismic Research School of Civil Engineering National Technical University of Athens (NTUA) Greece
Аннотация:Keywords: Boltzmann equation, Kolmogorov – Fokker – Planck equation, Navier – Stokes
equation; random processes, stochastic differential equations with respect to Poisson andWiener
measures, discontinuous particle method.
Abstract. 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 peculiarity of our derivation is more accurate velocity averaging due to analytical
solving stochastic differential equations with respect to Wiener measure 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 high performance computer applications)
special ”discontinuous” particle method.