(untitled) (Advances in Applied Mathematics and Mechanics, 2021)
The widely used micro-flow wall-boundary conditions for lattice Boltzmann method (LBM) are evaluated in a force driven combined nanochannel flow. The flow field consists of a two-dimensional nanochannel (mother channel) of an infinite length having flat plates of a finite length inside. The flat plate is set above the bottom wall of the nanochannel with a narrow gap. The flow, thus, develops through this narrow gap (narrower channel) and the other side of the plate (wide gap). The Knudsen number based on the mother channel height is Kn=0.14 whereas the characteristic Knudsen number in the narrower channel is 1.1. To obtain the reference data, the molecular dynamics (MD) simulation is performed with a fully diffusive wall condition. The LBMs are based on the lattice BGK model and with the bounce-back/specular reflection (BSBC) and the diffuse scattering (DSBC) wall boundary conditions. The relaxation time is modified to include sensitivity to Kn. The DSBC shows generally satisfactory results in the test flow cases including fully developed force driven Poiseuille flows, where the BSBC performs worse at Kn>0.5 with a fixed bridge coefficient of b=0.7. This results in its overprediction of the flow rate in the narrower channel region since the characteristic Knudsen number there is 1.1. The MD simulation suggests that the flow develops gradually through the narrower channel region though all the LBM predictions show almost instant flow development. This fact suggests that the relaxation time model needs to have more sensitivity to the locally defined Kn. Further discussions of the BSBC with a different set of models suggest that the regularization process is required for predicting complex nanoscale flows.