Low Variance Particle Simulations of the Boltzmann Transport Equation for the Variable Hard Sphere Collision Model

We present and validate a variance reduced deviational particle method for simulating the Boltzmann transport equation for the variable hard sphere (VHS) collision operator. In comparison with the direct simulation Monte Carlo (DSMC) method, the proposed method is more suitable for simulating transport in regimes where the departure from equilibrium is small, such as dilute gas flows in small-scale devices (MEMS, NEMS). In fact, the proposed method has a constant signalto-noise ratio in the limit of small departure from equilibrium, and is thus able to simulate arbitrarily small deviations from equilibrium. The approach developed herein combines the variable hard sphere collision algorithm developed by Wagner [1] with an efficient advection routine based on Ref. [2]. The resulting method is stable and highly efficient, and results in dramatically reduced statistical noise in regimes typical of transport in small-scale devices.