Oscillatory noncontinuum gas flows at the micro and nanoscales are characterized by two dimensionless groups: a dimensionless molecular length scale, the Knudsen number $\mathrm{Kn}$, and a dimensionless frequency $\theta$, relating the oscillatory frequency to the molecular collision frequency. In a recent study [Shi et al., Phys. Rev. E 89, 033305 (2014)], the accuracy of the lattice Boltzmann (LB) method for simulating these flows at moderate-to-large $\mathrm{Kn}$ and $\theta$ was examined. In these cases, the LB method exhibits spurious numerical oscillations that cannot be removed through the use of discrete particle velocities drawn from higher-order Gauss-Hermite quadrature. Here, we identify the origin of these spurious effects and formulate a method to minimize their presence. This proposed method splits the linearized Boltzmann Bhatnagar-Gross-Krook (BGK) equation into two equations: (1) a homogeneous “gain-free equation” that can be solved directly, containing terms responsible for the spurious oscillations; and (2) an inhomogeneous “remainder equation” with homogeneous boundary conditions (i.e., stationary boundaries) that is solved using the conventional LB algorithm. This proposed “splitting method” is validated using published high-accuracy numerical solutions to the linearized Boltzmann BGK equation where excellent agreement is observed.

• Received 23 May 2019

DOI:https://doi.org/10.1103/PhysRevE.100.053317