On the consequences of successively repeated collisions in no-time-counter collision scheme in DSMC

The current paper investigates the appropriateness and consequences of avoiding successively repeated collisions usually recommended in the Direct Simulation Monte Carlo (DSMC) solvers, which use the No Time Counter (NTC) collision technique. A sensitive test case, i.e., Fourier heat transfer problem at the early slip regime, is considered in the presence and absence of the successively repeated collisions. The effects of repeated collisions and avoiding them on different parameters such as heat flux, collision frequency, collision separation distance, accepted-to-selected collisions ratio, and probability distribution functions for the number of collisions and relative velocities of collision pairs are evaluated and discussed. The investigations are performed considering contributions of different computational parameters, i.e., cell sizes, time step, and number of particles. In addition to collision frequency and collision separation distance, which were reported previously as crucial parameters affecting the accuracy of the DSMC solution, we found that the level of repeated collisions also plays a pivotal role in the accuracy of the heat flux prediction in the Fourier problem. We show that direct avoiding of repeated collisions can lead to a distortion of collision probability distribution and consequently, to introduction of a systematic error in collision frequency and predicted heat flux. This error is negligible if one uses a large number of particles per cell, but it is of considerable importance if there are a few particles per cell.