Directo Simulation Scheme Derived from the Boltzmann Equation. IV. Correlation of Velocity
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The collision process described in the first paper of this series is written in theform of the stochastic difference equation for a molecular velocity. By using thisstoctxastic ectuation the correlation of velocitv between a molecule and its collisionpartner is examined. It is shown that the correlation grows stronger as c/Nincreases, where r is the time and N is the number of simulated molecules. Theassumption of molecular chaos requires a negligibly small correlation, so that thecondition c/N<<1 is necessary for solutions of the stochastic difference equation toagree with solutions of the Boltzmann equation.Also, the correlation coefficients of the velocities at two time points are obtained.Suppose that ./V>>1 and r/N<<1. Ifthese velocities belong to a single molecule, thecoefficient is exp ( -Q7)80(7V-'), and if they belong to different molecules, the"- coefficient is of 0(N-"), where 0 is a constant and r7 is the interval between thetime points.
- 社団法人日本物理学会の論文
- 1981-09-15
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