On time counting procedures in the DSMC method for rarefied gases

The DSMC (direct simulation Monte Carlo) method for rarefied gas dynamics is studied. The behaviour of the underlying stochastic particle system is determined by three main components – the time step between subsequent collisions, the random mechanism for the choice of the collision partners, and the random mechanism for calculating the result of the collision. The purpose of this paper is to illustrate the interplay between these various components and to propose some new modifications of the DSMC method. Different time counting procedures are derived and their influence on the other parts of the algorithm is investigated. Various modifications of the DSMC method are compared with respect to different criteria such as efficiency, systematic error, and statistical fluctuations.