A Probabilistic Automatic Steady State Detection Method for the Direct Simulation Monte Carlo (Communications in Computational Physics, 2020)
The statistical error associated with sampling in the DSMC method can becategorized as type I and II, which are caused by the incorrect rejection and acceptanceof the null hypothesis, respectively. In this study, robust global and local automaticsteady state detection methods were developed based on an ingenious method basedpurely on the statistics and kinetics of particles. The key concept is built upon probabilisticautomatic reset sampling (PARS) to minimize the type II error caused by incorrectacceptance of the samples that do not belong to the steady state. The globalsteady state method is based on a relative standard variation of collisional invariants,while the local steady state method is based on local variations in the distributionfunction of particles at each cell. In order to verify the capability of the new methods,two benchmark cases – the one-dimensional shear-driven Couette flow and thetwo-dimensional high speed flow past a vertical wall – were extensively investigated.Owing to the combined effects of the automatic detection and local reset sampling, thelocal steady state detection method yielded a substantial gain of 30-36% in computationalcost for the problem studied. Moreover, the local reset feature outperformed theautomatic detection feature in overall computational savings.