Boundary condition for lattice Boltzmann modeling of microscale gas flows with curved walls in the slip regime.

The lattice Boltzmann method (LBM) has been widely used to simulate microgaseous flows in recent years. However, it is still a challenging task for LBM to model that kind of microscale flow involving complex geometries, owing to the use of uniform Cartesian lattices in space. In this work, a boundary condition for microflows in the slip regime is developed for LBM in which the shape of a solid wall is well considered. The proposed treatment is a combination of the Maxwellian diffuse reflection scheme and the simple bounce-back method. A portion of each part is determined by the relative position between the boundary node and curved walls, which is the key point that distinguishes this method from some previous schemes where the smooth curved surface was assumed to be zigzag lines. The present curved boundary condition is implemented with the multiple-relaxation-times model and verified for several established cases, including the plane microchannel flow (aligned and inclined), microcylindrical Couette flow, and the flow over an inclined microscale airfoil. The numerical results agree well with those predicted by the direct simulation Monte Carlo method.