A new curved boundary treatment for LBM modeling of thermal gaseous microflow in the slip regime

Curved boundary conditions of the lattice Boltzmann method for simulating microgaseous flows in the slip flow regime

“…Furthermore, it has been exposed in the literature [22,23] that some discrete effects exist in the boundary schemes and should be corrected to realize the slip boundary condition. For a more accurate treatment of curved walls, it is common to include the distance ratio in the boundary condition to preserve the actual shape of curved geometries [26,27]. However, when these curved boundary schemes are implemented to realize the slip boundary condition at curved walls, the relaxation time in the LBE will depend on the distance ratio and thus varies with link directions at different boundary nodes [28][29][30].…”

“…Eq. ( 26), q = s , M=16 26) and (27). Empty shapes denote the results obtained under (a) r = 0.5 and τ q given by Eq.…”

“…The proposed boundary scheme is further applied to a microgaseous flow with more complex geometries, i.e., the microcylindrical Couette flow between two cylinders, to validate the theoretical analysis. This classical problem has been studied by many researchers as a benchmark case in fluid dynamics [27,28,32,43,44]. As shown in Fig.…”

“…In addition, the tangential velocity predicted with l = γ in Eqs. (26) and (27) are investigated as γ is artificially fixed to derive the uniform τ q . The simulated results are delineated in Fig.…”

“…But, the combination coefficient is still determined by that from the halfway bounce-back case. Based on the non-equilibrium extrapolation method for curved boundaries and the counter-extrapolation method for the velocity/temperature at curved surfaces, Liu et al [27] proposed a boundary condition involving the distance ratio for thermal gaseous microflows with curved slip walls.…”