Numerical modelling of microchannel gas flows in the transition flow   regime using the cascaded lattice Boltzmann method
  In the CLB method, a Bosanquet-type effective viscosity is employed to account for the rarefaction effect on the gas viscosity. To gain accurate simulations and to match the Bosanquet-type effective viscosity, the combined bounce-back/specular-reflection boundary scheme with a modified second-order slip boundary condition is adopted in the CLB method. The present method is applied to study gas flow in a microchannel with periodic boundary condition and gas flow in a long microchannel (the ratio of the length to the height L/H=100) with pressure boundary condition over a wide range of Knudsen numbers. The influence of the rarefaction effect on the velocity profile, the mass flow rate, and the non-linear pressure deviation distribution along the long microchannel are investigated. 
Qing Liu, Ya-Ling He
physics.comp-ph physics.flu-dyn