Comparative study of the discrete velocity and lattice Boltzmann methods for rarefied gas flows through irregular channels

Abstract: 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.