Curved boundary condition for lattice Boltzmann modeling of binary gaseous micro-scale flows in the slip regime

Abstract Lattice Boltzmann method (LBM) is believed to be a promising method for simulating gaseous micro-scale flows. However, it is still a great challenge for the LBM to simulate micro-scale flows of gas mixtures, especially involving curved boundaries. In this work, we proposed a curved boundary condition for lattice Boltzmann (LB) model of binary gaseous micro-scale flows. The proposed boundary condition is a combination of the Maxwellian diffusive boundary condition and bounce-back boundary condition, where the combination parameters of the species are related to the distance between the boundary node and wall surface. The LB model associating with the proposed boundary condition is employed to simulate some typical micro-scale flows of binary mixture, such as Kramer problem, Couette flow, and micro cylindrical Couette flow. It is shown that the numerical results are in good agreement with the analytical results. Therefore, the LB model with the proposed boundary condition can serve as a potential approach for simulating binary gaseous micro-scale flows with curved boundaries.