DSMC Convergence Behavior for Fourier Flow
SANDIA NATIONAL LABS ALBUQUERQUE NM
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The convergence behavior of Birds Direct Simulation Monte Carlo DSMC method is explored for near-continuum, 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 Birds 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 DSMC-calculated conductivity is shown to approach the theoretical CE value to within 0.02, showing that the present implementation of Birds DSMC algorithm provides an excellent representation of continuum, CE heat conduction.
- Fluid Mechanics
- Statistics and Probability