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Linearized lattice Boltzmann method for micro- and nanoscale flow and heat transfer

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


Yong Shi

Ying Wan Yap

John E. Sader


Ability to characterize the heat transfer in flowing gases is important for a wide range of applications involving micro- and nanoscale devices. Gas flows away from the continuum limit can be captured using the Boltzmann equation, whose analytical solution poses a formidable challenge. An efficient and accurate numerical simulation of the Boltzmann equation is thus highly desirable. In this article, the linearized Boltzmann Bhatnagar-Gross-Krook equation is used to develop a hierarchy of thermal lattice Boltzmann (LB) models based on half-space Gaussian-Hermite (GH) quadrature ranging from low to high algebraic precision, using double distribution functions. Simplified versions of the LB models in the continuum limit are also derived, and are shown to be consistent with existing thermal LB models for noncontinuum heat transfer reported in the literature. Accuracy of the proposed LB hierarchy is assessed by simulating thermal Couette flows for a wide range of Knudsen numbers. Effects of the underlying quadrature schemes (half-space GH vs full-space GH) and continuum-limit simplifications on computational accuracy are also elaborated. The numerical findings in this article provide direct evidence of improved computational capability of the proposed LB models for modeling noncontinuum flows and heat transfer at small length scales.


Shi, Y., Yap, Y. W., & Sader, J. E. (2015). Linearized lattice Boltzmann method for micro- and nanoscale flow and heat transfer. Physical Review E, 92(1), doi:10.1103/PhysRevE.92.013307

Journal Article Type Article
Acceptance Date Jan 21, 2015
Publication Date Jul 21, 2015
Deposit Date Oct 16, 2017
Journal Physical Review E
Print ISSN 2470-0045
Electronic ISSN 1550-2376
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 92
Issue 1
Article Number 013307
Public URL
Publisher URL
Copyright Statement Copyright information regarding this work can be found at the following address:
Additional Information ©2015 American Physical Society

This file is under embargo due to copyright reasons.

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