Abstract
The focus of the present study is the simulations of micro-channel flow at different Knudsen numbers using lattice Boltzmann method. There are two issues to be addressed, which are the influences of the boundary implementations and wall models. In order to capture the Knudsen layer near the wall, three different wall models are adopted here, i.e. Stop wall function(SWF), Lockerby wall function(LWF), and Guo wall function(GWF). As for the boundary condition implementation, this is achieved by the combinations of the bounce-back rule and diffusive-scattering boundary condition. The weighting of the boundary conditions combined with different wall models is obtained by optimizations with the fully developed channel flow results from linearized Boltzmann equations at Knudsen number ranging from 0.1 to 10. The adopted lattice models are D2Q9, D2Q13, D2Q17 and D2Q21. Among the wall models, Stop's wall model outperforms the other two. Using the Stop wall model, all the lattice models can be optimized to produce correct linearized Boltzmann solutions. The model results also compares favorably with the DSMC results for Knudsen number from 0.1 to 10. The capability of the models to predict developing channel flow are further examined. Due to the difficulty in implementing inlet and outlet boundary conditions for D2Q13, D2Q17 and D2Q21, only D2Q9 is adopted. Results show that simulations with Stop wall model can produce correctly the pressure variations in response the change of the Knudsen number and reproduce the results from DSMC simulations.