Collision process, the most complicated evolution term in the Boltzmann or Kac stochastic equations, is treated statistically in the direct simulation Monte Carlo (DSMC) method. The treatment of collision pair selection is of crucial importance in DSMC. A subsequent of several collision algorithms called Bernoulli-trials family schemes have been put forward, which were mathematically based on the Kac stochastic equation. The purpose of this paper is to report an extensive evaluation of the most recent variant of the Bernoulli Trials schemes, i.e., Generalized Bernoulli-trial (GBT) in treating standard problems such as cavity flow and hypersonic flow around a cylinder. The key feature of the GBT collision algorithm is its adaption to any number of particle pairs (Nsel) and its lower computational costs compared to standard schemes. The results show that the GBT scheme, compared to the standard “No Time Counter (NTC)”, “Nearest neighbor (NN)” and “Simplified Bernoulli Trials (SBT)” schemes, successfully captures the collision frequency in the cavity flow, shock wave and wake structure in the cylinder flow and held the same level of accuracy as the other standard collision schemes using a wide range of desired Nsel. A comparison of two variants of the GBT scheme (Scheme 1 and Scheme 2) indicates that Scheme-1 performs the simulation with a lower computational cost. The results prove that using a variable particle per subcell (PPSC) control approach significantly improves the collision probability accuracy and performance of the GBT scheme, especially in regions with high requirements for accurate collision process calculation.

Keywords