Выпуск: 1 , Том: 510 , Год издания: 2014

The talk examines a system of pairwise interaction particles, which models a rarefied gas in accordance with the nonlinear Boltzmann equation, the master equations of Markov evolution of this system and corresponding numerical Monte Carlo methods. Selection of some optimal method for simulation of rarefied gas dynamics depends on the spatial size of the gas ow domain. For problems with the Knudsen number Kn of order unity "imitation", or "continuous time", Monte Carlo methods ([2]) are quite adequate and competitive. However if Kn 0:1 (the large sizes), excessive punctuality, namely, the need to see all the pairs of particles in the latter, leads to a signicant increase in computational cost(complexity). We are interested in to construct the optimal methods for Boltzmann equation problems with large enough spatial sizes of the ow. Speaking of the optimal, we mean that we are talking about algorithms for parallel computation to be implemented on high-performance multi-processor computers. The characteristic property of large systems is the weak dependence of sub-parts of each other at a suciently small time intervals.