Application of Gaussian Moment Closure Methods to Three-Dimensional Micro-Scale Flows

A parallel, block-based, three-dimensional, hexahedral finite-volume scheme with adaptive mesh refinement has been developed for the solution of the 10-moment Gaussian closure for the modelling of fully three-dimensional micro-scale, non-equilibrium flows. The Gaussian closure has been shown to be a more effective tool for modelling rarefied flows lying within the transition regime than the Navier-Stokes equations, which encounter mathematical difficulties approaching free-molecular flows, and is computationally less expensive than particle-based methods for flows approaching the continuum limit. The hyperbolic nature of the moment equations is computationally attractive and the generalized transport equations can be solved in an accurate and efficient manner using Godunov-type finite-volume schemes as considered here. Details are given of the Gaussian closure, along with extensions for diatomic gases and slip-flow boundaries. Numerical results for several canonical flows demonstrate the potential of these moment closures and the parallel solution scheme for accurately predicting fully three-dimensional non-equilibrium flow behaviour.