Lattice Boltzmann Flow Simulation in a Combined Nanochannel (Advances in Applied Mathematics and Mechanics, 2021)
The widely used micro-flow wall-boundary conditions for latticeBoltzmann method (LBM) are evaluated in a force driven combinednanochannel flow. The flow field consists of a two-dimensionalnanochannel (mother channel) of an infinite length having flatplates of a finite length inside. The flat plate is set above thebottom wall of the nanochannel with a narrow gap. The flow, thus,develops through this narrow gap (narrower channel) and the otherside of the plate (wide gap). The Knudsen number based on the motherchannel height is Kn=0.14 whereas the characteristic Knudsennumber in the narrower channel is 1.1. To obtain the referencedata, the molecular dynamics (MD) simulation is performed with afully diffusive wall condition. The LBMs are based on the latticeBGK model and with the bounce-back/specular reflection (BSBC) andthe diffuse scattering (DSBC) wall boundary conditions. Therelaxation time is modified to include sensitivity to Kn. The DSBCshows generally satisfactory results in the test flow casesincluding fully developed force driven Poiseuille flows, where theBSBC performs worse at Kn>0.5 with a fixed bridge coefficient of $b=0.7$. This results in its overprediction of the flow rate inthe narrower channel region since the characteristic Knudsen numberthere is 1.1. The MD simulation suggests that the flow developsgradually through the narrower channel region though all the LBMpredictions show almost instant flow development. This fact suggeststhat the relaxation time model needs to have more sensitivity to thelocally defined Kn. Further discussions of the BSBC with a differentset of models suggest that the regularization process is requiredfor predicting complex nanoscale flows.