Low-noise Monte Carlo simulation of the variable hard sphere gas

Abstract

We present an efficient particle simulation method for the Boltzmann transport equation based on the low-variance deviational simulation Monte Carlo approach to the variable-hard-sphere gas. The proposed method exhibits drastically reduced statistical uncertainty for low-signal problems compared to standard particle methods such as the direct simulation Monte Carlo method. We show that by enforcing mass conservation, accurate simulations can be performed in the transition regime requiring as few as ten particles per cell, enabling efficient simulation of multidimensional problems at arbitrarily small deviation from equilibrium.