Shi Yong, Yap Ying Wan, Sader John E
Department of Mechanical, Materials and Manufacturing Engineering, The University of Nottingham Ningbo China, Ningbo 315100, People's Republic of China.
Department of Mathematics and Statistics, The University of Melbourne, Victoria 3010, Australia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Mar;89(3):033305. doi: 10.1103/PhysRevE.89.033305. Epub 2014 Mar 12.
Oscillatory gas flows are commonly generated by micro- and nanoelectromechanical systems. Due to their small size and high operating frequencies, these devices often produce noncontinuum gas flows. Theoretical analysis of such flows requires solution of the unsteady Boltzmann equation, which can present a formidable challenge. In this article, we explore the applicability of the lattice Boltzmann (LB) method to such linear oscillatory noncontinuum flows; this method is derived from the linearized Boltzmann Bhatnagar-Gross-Krook (BGK) equation. We formulate four linearized LB models in the frequency domain, based on Gaussian-Hermite quadratures of different algebraic precision (AP). The performance of each model is assessed by comparison to high-accuracy numerical solutions to the linearized Boltzmann-BGK equation for oscillatory Couette flow. The numerical results demonstrate that high even-order LB models provide superior performance over the greatest noncontinuum range. Our results also highlight intrinsic deficiencies in the current LB framework, which is incapable of capturing noncontinuum behavior at high oscillation frequencies, regardless of quadrature AP and the Knudsen number.
振荡气流通常由微机电系统和纳机电系统产生。由于其尺寸小和工作频率高，这些设备常常产生非连续气流。对此类气流的理论分析需要求解非稳态玻尔兹曼方程，这可能是一项艰巨的挑战。在本文中，我们探讨格子玻尔兹曼（LB）方法对此类线性振荡非连续气流的适用性；该方法源自线性化的玻尔兹曼 Bhatnagar-Gross-Krook（BGK）方程。我们基于不同代数精度（AP）的高斯-埃尔米特求积法，在频域中构建了四个线性化LB模型。通过与振荡库埃特流的线性化玻尔兹曼-BGK方程的高精度数值解进行比较，评估了每个模型的性能。数值结果表明，高阶LB模型在最大非连续范围内具有卓越的性能。我们的结果还突出了当前LB框架的内在缺陷，即无论求积AP和克努森数如何，它都无法在高振荡频率下捕捉非连续行为。
