For the achievement of low-cost computations of the fluid flow through micro-nano sized porous media such as catalyst layer of fuel cell, lattice Boltzmann method (LBM) has been improved for high Knudsen number flows by considering the diffuse scattering boundary condition, effective relaxation time related to Knudsen number and the regularization procedure. These treatments have been validated in simple geometries such as two-dimensional Couette flow and channel flow. In this paper, above micro-flow LBM is extended to three dimensional flow. A nano-mesh structure is presumed and its applicability is discussed in terms of discrete velocity (Q19 and Q39 models) by comparing to the molecular dynamics simulation. It is found that the resulted velocity profile by LBM agrees with that by molecular dynamics including the velocity slip at the porous wall. The Q19 model has enough accuracy compared to Q39 model, which suggests that the advantage of the simple model for the application. The less difference between Q19 and Q39 models implies that the third order term in Hermite polynomials becomes less effective for the complicated flow regime.
