Analysis of force treatment in the pseudopotential lattice Boltzmann equation method

Lin Zheng, Qinglan Zhai, and Song Zheng
Phys. Rev. E 95, 043301 – Published 3 April 2017

Abstract

In this paper, different force treatments are analyzed in detail for a pseudopotential lattice Boltzmann equation (LBE), and the contribution of third-order error terms to pressure tensor with a force scheme is analyzed by a higher-order Chapman-Enskog expansion technique. From the theoretical analysis, the performance of the original force treatment of Shan-Chen (SC), Ladd, Guo et al., and the exact difference method (EDM) are ɛLadd<ɛGuo<ɛEDMɛSC with the relaxation time τ1, while ɛLadd<ɛGuo<ɛSC<ɛEDM with τ<1; here ɛ is a parameter related to the mechanical stability and the subscripts are the corresponding force scheme. To be consistent with the thermodynamic theory, a force term is introduced to modify the coefficients in the pressure tensor. Some numerical simulations are conducted to show that the predictions of modified force treatment of the pseudopotential LBE are all in good agreement with the analytical solution and other predictions.

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  • Received 16 August 2016
  • Revised 3 January 2017

DOI:https://doi.org/10.1103/PhysRevE.95.043301

©2017 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
Fluid Dynamics

Authors & Affiliations

Lin Zheng1,*, Qinglan Zhai2, and Song Zheng3

  • 1MIIT Key Laboratory of Thermal Control of Electronic Equipment, School of Energy and Power Engineering, Nanjing University of Science and Technology, Nanjing 210094, P.R. China
  • 2School of Economics Management and Law, Chaohu University, Chaohu 238000, P.R. China
  • 3School of Mathematics and Statistics, Zhejiang University of Finance and Economics, Hangzhou, Zhejiang 310018, P.R. China

  • *Corresponding author: lz@njust.edu.cn

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Issue

Vol. 95, Iss. 4 — April 2017

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