Department of Mechanical, Materials and Manufacturing Engineering, The University of Nottingham Ningbo China, Ningbo 315100, China.
ARC Centre of Excellence in Exciton Science, School of Mathematics and Statistics, The University of Melbourne, Victoria 3010, Australia.
Phys Rev E. 2019 Nov;100(5-1):053317. doi: 10.1103/PhysRevE.100.053317.
Oscillatory noncontinuum gas flows at the micro and nanoscales are characterized by two dimensionless groups: a dimensionless molecular length scale, the Knudsen number Kn, and a dimensionless frequency θ, relating the oscillatory frequency to the molecular collision frequency. In a recent study [Shi et al., Phys. Rev. E 89, 033305 (2014)10.1103/PhysRevE.89.033305], the accuracy of the lattice Boltzmann (LB) method for simulating these flows at moderate-to-large Kn and θ 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.
在微观和纳米尺度上，非连续气体的振荡流动的特点是两个无量纲参数：无量纲分子长度尺度，即克努森数 Kn，以及无量纲频率θ，它将振荡频率与分子碰撞频率联系起来。在最近的一项研究中[Shi 等人，Phys. Rev. E 89, 033305 (2014)10.1103/PhysRevE.89.033305]，研究了格子玻尔兹曼（LB）方法在中等至较大 Kn 和 θ 下模拟这些流动的准确性。在这些情况下，LB 方法会出现虚假的数值振荡，无法通过使用来自更高阶高斯-赫尔米特求积的离散粒子速度来消除。在这里，我们确定了这些虚假效应的起源，并提出了一种最小化其存在的方法。该方法将线性化玻尔兹曼 Bhatnagar-Gross-Krook（BGK）方程分解为两个方程：（1）一个可以直接求解的均匀“无增益方程”，其中包含导致虚假振荡的项；（2）一个具有均匀边界条件（即静止边界）的非均匀“剩余方程”，使用传统的 LB 算法求解。该方法通过使用线性化玻尔兹曼 BGK 方程的出版高精度数值解进行验证，观察到非常好的一致性。
