Abstract
Non-equilibrium gas flows represent a fundamental modelling challenge and exist in many industrial applications and scientific research facilities, including mass spectrometry, low-pressure environments, vacuum pumps, micro-electromechanical systems (MEMS), high-altitude vehicles, and porous media. The extent of the non-equilibrium state is usually measured by the Knudsen number, Kn, which is the ratio of the gas molecular mean free path to the characteristic macroscopic length scale of the flow. In the early transition regime, (0.1 < Kn < 1), the Navier-Stokes-Fourier (NSF) equations are no longer able to predict the flow field with any degree of accuracy. Kinetic theory approaches, such as the Boltzmann equation or direct simulation Monte Carlo (DSMC), can be used in this regime. For the Boltzmann equation, the complexity of the collision term makes it difficult to use in all but simple problems. In the case of DSMC, the computational cost is prohibitive. The moment method offers the best approach for capturing rarefied phenomena. More physics is embedded in the moment equations than in the NSF equations, with only a modest increase in computational cost.
The development of the moment method in the well-established open-source software, Code_Saturne, is presented. Detailed computed results for Poiseuille flow, lid-driven cavity flow, thermally induced flow, and flow past a square cylinder are given to validate the implementation.
