  Rooted from the gas kinetics, the lattice Boltzmann method is a powerful tool
in modeling hydrodynamics. In the past decade, it has been extended to simulate
the rarefied gas flow beyond the Navier-Stokes level, either by using the
high-order Gauss-Hermite quadrature, or by introducing the relaxation time that
is a function of the gas-wall distance. While the former method, with a limited
number of discrete velocities (i.e. D2Q36), is accurate up to the early
transition flow regime, the latter method, with the same discrete velocities as
that used in simulating hydrodynamics (i.e. D2Q9), is accurate up to the
free-molecular flow regime in the Poiseuille flow between two parallel plates.
This is quite astonishing in the sense that more discrete velocities are less
accurate. In this paper, by solving the Bhatnagar-Gross-Krook kinetic equation
accurately via the discrete velocity method, we find that the accuracy of the
lattice Boltzmann method is reduced significantly in the simulation of rarefied
gas flows through the rough surface and porous media. Our simulation results
could serve as benchmarking cases for future development of the lattice
Boltzmann method for modeling and simulation of rarefied gas flows in complex
geometries.
