This paper provides a convergence study of the DSMC method for the one dimensional Fourier heat-flow problem. The simulations are performed using the Simplified Bernoulli Trials (SBT) collision algorithm. The convergence metric is taken as the ratio of the DSMC-calculated bulk thermal conductivity, KDSMC to the infinite-approximation, Chapman-Enskog (CE) theoretical value, K. In general, three parameters are known to limit the numerical accuracy of the DSMC method: the number of simulators (particles) per cell, Nc; the time step, Δt; and the cell size, Δx. The dependency of these discretization errors have been investigated in comparison with the conventional collision algorithm, i.e., no time counter (NTC). These results provide a strong verification that SBT collision algorithm is accurate and efficient with small number of particles if fine grids and small time step were used. We also show that the DSMC-calculated velocity distribution function, as measured by the Sonine-polynomial coefficients ak, is in suitable agreement with CE theoretical predictions.

Keywords