Near-wall effects in rarefied gas micro-flows: some modern hydrodynamic approaches

Methods for simulating the critical near-wall region in hydrodynamic models of gas micro-flows are discussed. Two important non-equilibrium flow features – velocity slip at solid walls, and the Knudsen layer (which extends one or two molecular mean free paths into the gas from a surface) – are investigated using different modelling approaches. In addition to a discussion of Maxwell’s slip boundary condition, a newly implemented ‘wall-function’ model that has been developed to improve hydrodynamic simulations of the Knudsen layer is described. Phenomenological methods are compared to physical modelling and it is shown that, while both simulation types have merit, and both can quantitatively improve results in most cases, there are drawbacks associated with each approach. Phenomenological techniques, for example, may not be sufficiently general, whilst issues with applicability and stability are known to exist in some physical models.It is concluded that, at present, neither approach is unambiguously preferable to the other, and that both physical and phenomenological modelling should be the subject of future work.