Lattice Boltzmann method for linear oscillatory noncontinuum flows

Shi, Yong; Yap, Ying Wan; Sader, John E.

Abstract

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.

Citation

Shi, Y., Yap, Y. W., & Sader, J. E. (2014). Lattice Boltzmann method for linear oscillatory noncontinuum flows. Physical Review E, 89(3), Article 033305. https://doi.org/10.1103/PhysRevE.89.033305

• Journal Article Type: Article
• Acceptance Date: Feb 1, 2014
• Publication Date: Mar 12, 2014
• Deposit Date: Oct 16, 2017
• Journal: Physical Review E
• Print ISSN: 2470-0045
• Electronic ISSN: 2470-0053
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 89
• Issue: 3
• Article Number: 033305
• DOI: https://doi.org/10.1103/PhysRevE.89.033305
• Public URL: https://nottingham-repository.worktribe.com/output/725167
• Publisher URL: https://doi.org/10.1103/PhysRevE.89.033305
• Additional Information: ©2014 American Physical Society