The exact direct-simulation-scheme previously reported is summarized as a stochastic difference equation for a molecular velocity. By using this stochastic equation the correlation of velocity between a molecule and its collision partner is examined. It is shown that the correlation grows stronger as τ/N increases, where τ is the time made dimensionless by means of a time of the order of mean collision time and N is the number of simulated molecules. The assumption of molecular chaos requires a negligibly small correlation, so that the condition τ/N≪1 is necessary for solutions of the stochastic difference equation to agree with solutions of the Boltzmann equation. Also, the correlation functions for the velocities at two time points are obtained. Suppose that N≫1 and τ/N≪1. If these velocities belong to a single molecule, the function is exp(-θη)+O(N^<-1>), and if they belong to different molecules, the function is of O(N^<-1>), where θ is a number and η is the (dimensionless) interval between the time points.
ボルツマン方程式の厳密な直接シミュレーション法 : 閉系内分子の速度相関
SA0166534.pdf
(522.22KB)
