Analysis of discretization in the direct simulation Monte Carlo

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Abstract
We propose a continuous-time formulation of the direct simulation Monte Carlo that allows the evaluation of the transport coefficient dependence on the time step through the use of the Green–Kubo theory. Our results indicate that the error exhibits quadratic dependence on the time step, and that for time steps of the order of one mean free time the error is of the order of 5%. Our predictions for the transport coefficients are in good agreement with numerical experiments. The calculation of the cell size dependence, first obtained by Alexander et al. [Phys. Fluids 10, 1540 (1998)], is reviewed and a correction is pointed out.