On a Criterion for the Significance of Statistical Fluctuations in Rarefied Flows

Near the slip regime, the microscopic behavior within a gas becomes increasingly significant. As the characteristic length nears the mean free path, the flow shows great deviations from its equilibrium distribution and molecular-kinetic methods are employed. For rarefied gases, deterministic approaches are often limited by the required sample size to obtain accurate averages. We describe the influence of statistical fluctuations on models in the slip regime. Using numerical simulations, we demonstrate a relation between fluctuations in macroscopic flow properties and the number of simulated particles. The intersection between statistical fluctuations and the continuum limit is discussed and its implications on current algorithms are assessed. In particular, the break-down of statistical stability prior to reaching the continuum assumption is highlighted. We propose a criterion to predict the onset of statistical fluctuations in a dilute gas. Our derivations are supported by particle-based simulations, such as Direct Simulation Monte Carlo and molecular dynamics.