Graeme Bird developed the Direct Simulation of Monte Carlo (DSMC) in the 1960s, and nowadays this method has gained popularity in simulation of rarefied gas dynamics and micro gas flow problems. In addition to the requirement of employing multidimensional computational mesh, the DSMC method uses a finite set of particles or simulators, denoted by their positions and velocities, to model the advection and collision terms of the Boltzmann equation. The requirement of these large computational resources have been a prohibitive barrier in the DSMC analysis of massive computational two- and three-dimensional problems in rarefied gas dynamics. This work is dedicated to review some recent advancements in reducing the DSMC computational requirements by using Kac model -based collision schemes in the Direct Simulation of Monte Carlo. In general, two major concepts exist for obtaining collision schemes, and here we focus our attention to the one based on the Kac stochastic model. The common advantage of these schemes is that their algorithms avoid the repeat collisions, and can be used to reduce the number of particles as a portion of computational resources. The paper reviews this conception since Yanitiskiy first introduced the Bernoulli Trials collision scheme (BT), to the introduction of Simplified Bernoulli Trials (SBT), proposed by Stefanov. We also present a new intelligent variant of the SBT collision scheme, entitled ISBT, which enters some semi-deterministic elements in the SBT scheme, that ensure selection of closer placed collision pairs.

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