In this paper, the rarefied gas flow in a microchannel with backward facing step is simulated by Lattice Boltzmann method. A model with two relaxation times in slip and transient flow regimes is used. The slip velocity in the walls of the microchannel is improved by using the wall operation function, known as power-law analytical function. The advantage of this model in comparison with a single relaxation time model is the accuracy of the slip velocity and its advantage over a model with a multiple relaxation times is the low cost and running time along with simplicity of programing. The boundary conditions used in the inlet and outlet sections of this geometry are Zou-He condition and the bounce back and Specular Reflection boundary condition is considered on the walls. The profiles of Mach number, pressure, and mass flow rate are studied in the slip and transient flow regimes at Reynolds numbers of 6.43 and 0.052, respectively. The effects of Knudsen number on the velocity and vortex formation are also discussed. The results are also compared with the results obtained by the Direct Simulation Monte Carlo method and a good agreement between two results is observed, which shows the accuracy of the model.

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