In the direct simulation Monte Carlo (DSMC) method for simulating rarefied gas flows, the velocities of simulator particles that cross a simulation boundary and enter the simulation space are typically generated using the acceptance-rejection method that samples the velocities from the theoretical velocity distribution. This paper analyses an alternative technique, where the velocities of entering particles are obtained by extending the simulation procedures to a region adjacent to the simulation space, and considering the movement of particles generated within that region during the simulation time step. The alternative method may be considered as a form of acceptance-rejection technique. The number flux obtained using the alternative method is slightly lower than the theoretical number flux, due to a depleted population of high velocities. Methods of obtaining the correct number flux are presented. The alternative method allows acceptance of all possible velocities, and represents an improvement over the acceptance-rejection method where some velocities are excluded to improve computational efficiency. For upstream boundaries in high speed flows, the alternative method is more computationally efficient than the acceptance-rejection method. However, for downstream boundaries, the alternative method is extremely inefficient. The alternative method, with the correct theoretical number flux, should therefore be used in favour of the acceptance-rejection method only for upstream boundaries in DSMC computations
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