  The lattice Boltzmann method (LBM) has shown its promising capability in
simulating microscale gas flows. However, the suitable boundary condition is
still one of the critical issues for the LBM to model microgaseous flows
involving curved geometries. In this paper, a local boundary condition of the
LBM is proposed to treat curved solid walls of microgaseous flows. The
developed boundary treatment combines the Maxwellian diffuse reflection scheme
and a single-node boundary scheme which contains a free parameter as well as
the distance ratio. The curved boundary condition is analyzed within the
multiple-relaxation-time (MRT) model for a unidirectional microflow. It is
shown that the derived slip velocity depends on the free parameter as well as
the distance ratio and relaxation times. By virtue of the free parameter, the
combination parameter and the uniform relaxation time are theoretically
determined to realize the accurate slip boundary condition. In addition, it is
found that besides the halfway diffuse-bounce-back (DBB) scheme, previous
curved boundary schemes only containing the distance ratio cannot ensure
uniform relaxation times to realize the slip boundary condition. Some numerical
examples with planar and curved boundaries are carried out to validate the
present curved boundary scheme. The good and robust consistency of numerical
predictions with analytical solutions demonstrates our theoretical analysis.
