We present a new particle scheme for solving the Boltzmann equation; this scheme incorporates a recently developed variance reduction technique discussed in [L. L. Baker and N. G. Hadjiconstantinou, Physics of Fluids, vol. 17, art. no 051703, 2005] which exhibits a significant computational efficiency advantage for low speed flows, compared to traditional particle methods. This paper describes how this variance reduction approach, achieved by simulating only the deviation from equilibrium, can be implemented as a particle simulation method. The new scheme is validated using time dependent shear flow calculations.

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