Discrete effect on single-node boundary schemes of lattice Bhatnagar–Gross–Krook model for convection-diffusion equations

Liang Wang, Xuhui Meng (), Hao-Chi Wu (), Tian-Hu Wang and Gui Lu
Additional contact information
Liang Wang: Key Laboratory of Condition Monitoring and Control for Power Plant Equipment of Ministry of Eduction, North China Electric Power University, Beijing 102206, P. R. China†School of Energy Power and Mechanical Engineering, North China Electric Power University, Beijing 102206, P. R. China
Xuhui Meng: #x2021;Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
Hao-Chi Wu: #xA7;School of Control and Computer Engineering, North China Electric Power University, Beijing 102206, P. R. China
Tian-Hu Wang: Key Laboratory of Condition Monitoring and Control for Power Plant Equipment of Ministry of Eduction, North China Electric Power University, Beijing 102206, P. R. China†School of Energy Power and Mechanical Engineering, North China Electric Power University, Beijing 102206, P. R. China
Gui Lu: Key Laboratory of Condition Monitoring and Control for Power Plant Equipment of Ministry of Eduction, North China Electric Power University, Beijing 102206, P. R. China†School of Energy Power and Mechanical Engineering, North China Electric Power University, Beijing 102206, P. R. China

International Journal of Modern Physics C (IJMPC), 2020, vol. 31, issue 01, 1-22

Abstract: The discrete effect on the boundary condition has been a fundamental topic for the lattice Boltzmann method (LBM) in simulating heat and mass transfer problems. In previous works based on the anti-bounce-back (ABB) boundary condition for convection-diffusion equations (CDEs), it is indicated that the discrete effect cannot be commonly removed in the Bhatnagar–Gross–Krook (BGK) model except for a special value of relaxation time. Targeting this point in this paper, we still proceed within the framework of BGK model for two-dimensional CDEs, and analyze the discrete effect on a non-halfway single-node boundary condition which incorporates the effect of the distance ratio. By analyzing an unidirectional diffusion problem with a parabolic distribution, the theoretical derivations with three different discrete velocity models show that the numerical slip is a combined function of the relaxation time and the distance ratio. Different from previous works, we definitely find that the relaxation time can be freely adjusted by the distance ratio in a proper range to eliminate the numerical slip. Some numerical simulations are carried out to validate the theoretical derivations, and the numerical results for the cases of straight and curved boundaries confirm our theoretical analysis. Finally, it should be noted that the present analysis can be extended from the BGK model to other lattice Boltzmann (LB) collision models for CDEs, which can broaden the parameter range of the relaxation time to approach 0.5.

Keywords: Lattice Boltzmann method; Bhatnagar–Gross–Krook model; discrete effect; single-node boundary schemes; convection-diffusion equations (search for similar items in EconPapers)
Date: 2020
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0129183120500175
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:ijmpcx:v:31:y:2020:i:01:n:s0129183120500175

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0129183120500175

Access Statistics for this article

International Journal of Modern Physics C (IJMPC) is currently edited by H. J. Herrmann

More articles in International Journal of Modern Physics C (IJMPC) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().