On Reduction of Computational Cost of Imitation Monte Carlo Algorithms for Modeling Rarefied Gas Flows

摘要

This article describes Monte Carlo methods and algorithms for the Boltzmann equation for rarefied gases problems in the case of large-scale flow areas. We consider imitation or continuous-time Monte Carlo methods where frequencies of interactions of pairs of particles depend on the difference of the coordinates of particles. The question about reduction of computational costs of algorithms is examined using the specificity of the problem. First, algorithms of an approximated method are con- structed, analyzed, and implemented. This method is obtained by using splitting (over groups of par- ticles) of the operator in master equations system. Second, we investigate the fictitious collisions tech- nique, where the upper bound for the number of interacting pairs is specified. The plane Poiseuille flow (in the field of external forces) problem, the heat transfer problem, and the temperature discon- tinuity propagation problem are numerically solved using the developed algorithms. Asymptotical estimates of the computational costs are confirmed with the data of the computational processes and the comparative properties of the later are fixed. The suggested algorithms of the method with splitting allow parallelization of a certain type.