Low-variance deviational simulation Monte Carlo

We present and discuss a particle simulation method for solving the Boltzmann equation which incorporates the variance reduction ideas presented in L. L. Baker and N. G. Hadjiconstantinou [Physics of Fluids 17, 051703 (2005)]. The variance reduction, achieved by simulating only the deviation from equilibrium, results in a significant computational efficiency advantage for low speed flows compared to traditional particle methods such as the direct simulation Monte Carlo (DSMC). More specifically, the proposed method can efficiently simulate arbitrarily small deviations from equilibrium (e.g., low flow speed) at a computational cost that does not scale with the magnitude of the deviation from equilibrium, while maintaining the basic algorithmic structure of DSMC.