document: Designers of microfluidic devices are in need of computational tools that can be used to analyse problems that involve rarefied gas flows in complex micro geometries. Numerical simulation of the gas flow through such geometries is, however, extremely challenging. Conventional continuum fluid dynamics (CFD) becomes invalid or inaccurate as the characteristic scale of the geometry (e.g. the channel height, h) approaches the molecular mean free path, λ [1,2]. When λ/h≳0.1, the error in solutions obtained from CFD may be significant, and we must consider the fluid for what it is: a collection of interacting particles. However, the computational expense of simulating the flow of a rarefied gas in high-aspect-ratio micro geometries (i.e. ones that are long, relative to their cross section) using a particle method, such as the direct simulation Monte Carlo (DSMC) method [2], can be prohibitively high [3,4]. The computational intensity of the particle method is greater still when simulating low-speed microfluidic devices where there are only small deviations from equilibrium, characterised by extremely low Mach numbers and weak temperature gradients.
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