Simulation of Microchannel Flows Using Higher Order Lattice Boltzmann With an Effective Mean Free Path

Microscale flow simulation is considered in this paper for a microchannel flow geometry. Higher order Lattice Boltzmann Model was used as the numerical method for flow simulation, in which an effective mean free path was used in relaxation time appeared in LBM. To accurately describe rarefied gas dynamics beyond the Navier-Stokes level, high-order LB models have been used. One reason the standard lattice BGK model fails to capture the nonlinear constitutive behavior is that it only retains velocity terms up to second order in the Hermite expansion of the equilibrium distribution function. This is not sufficient to accurately describe stresses in isothermal flows. To capture nonequilibrium effects, we should retain up to fourth-order terms in the Hermite expansion. The effective mean free path makes it possible to investigate flow characteristics in slip flow regime, for which Knudsen number varies from 0.1 to 10 while does not change the computational efficiency of standard LBM. Results are obtained for pressure-driven and a shear flow configurations in microchannels. The nonlinear flow characteristics of the Knudsen layer were captured in shear flow regime.