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The lattice Boltzmann method (LBM) has shown its promising capability insimulating microscale gas flows. However, the suitable boundary condition isstill one of the critical issues for the LBM to model microgaseous flowsinvolving curved geometries. In this paper, a local boundary condition of theLBM is proposed to treat curved solid walls of microgaseous flows. Thedeveloped boundary treatment combines the Maxwellian diffuse reflection schemeand a single-node boundary scheme which contains a free parameter as well asthe distance ratio. The curved boundary condition is analyzed within themultiple-relaxation-time (MRT) model for a unidirectional microflow. It isshown that the derived slip velocity depends on the free parameter as well asthe distance ratio and relaxation times. By virtue of the free parameter, thecombination parameter and the uniform relaxation time are theoreticallydetermined to realize the accurate slip boundary condition. In addition, it isfound that besides the halfway diffuse-bounce-back (DBB) scheme, previouscurved boundary schemes only containing the distance ratio cannot ensureuniform relaxation times to realize the slip boundary condition. Some numericalexamples with planar and curved boundaries are carried out to validate thepresent curved boundary scheme. The good and robust consistency of numericalpredictions with analytical solutions demonstrates our theoretical analysis.

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