DSMC Convergence Behavior for Fourier Flow

The convergence behavior of Bird’s Direct Simulation Monte Carlo (DSMC) method is explored for nearcontinuum, one-dimensional Fourier flow. An argon-like, hard-sphere gas is confined between two parallel, fully accommodating, motionless walls of unequal temperature. The simulations are performed using a one-dimensional code based on Bird’s DSMC prescription. The convergence metric is taken as the ratio of the DSMC-calculated bulk thermal conductivity to the infinite-approximation, Chapman-Enskog (CE) theoretical value. The convergence rate is monitored with respect to three parameters: time step, cell size, and number of computational molecules per cell. For a sufficiently large number of computational molecules, the DSMC discretization error is observed to decrease quadratically with time step and cell size, in good agreement with previous predictions based on Green-Kubo theory. When all three parameters are finite, the observed convergence behavior is complex. As numerical errors are systematically reduced, the DSMCcalculated conductivity is shown to approach the theoretical CE value to within 0.02%, showing that the present implementation of Bird’s DSMC algorithm provides an excellent representation of continuum, CE heat conduction.