Exact Direct-Simulation-Scheme for the Boltzmann Equation/Correlation of Molecular Velocities Subject to Renewal Processes

概要

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The correlation of velocity between the molecules in a simulation cell is lessened by a renewal process such that new uncorrelated molecules come into the cell and some correlated ones go out of the cell. Moreover, if a portion of the cell boundary is a diffusely reflecting wall, the molecules are subject to another renewal process; each time a molecule is incident on the wall. its velocity is renewed. It is shown that the correlation coefficient between the velocities of the molecules subject to these renewal processes is O(N^<-1>) no matter how large the time may be, where N is the number of the molecules in the cell; by choosing a large N one can make the correlation coefficient as small as one desires. This fact assures that the exact direct-simulation method is applicable to the calculation of steady flows, which are obtained as the large time states of unsteady flows. Also, the expressions for correlation functions are obtained. These are necessary for the estimation of the sampling interval used in obtaining the time-averaged data of the steady flows.
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