Characterizing fluid flow by the ratio of mean free path and a characteristic flow length (the Knudsen number
) we have two extremes: dense gases (
≪ 1) where modeling by Euler or Navier-Stokes equations is valid and rarefied gases (
≫ 1) for which modeling by the Boltzmann equation is necessary. Developing models for the intermediate transition regime is subject to active current research because despite the tremendously growing increase in computational and algorithmic computing performance, numerical simulation of flows in the transition regime remains a challenging problem. Thus there is a considerable gap in the ability to model flows where mean free path and characteristic flow lengths are comparable. However, efficient methods for simulating transition regime flows will be an important design tool for micro-scale machinery, where dense gas models become invalid.