• Open Access

Three-dimensional cascaded lattice Boltzmann method: Improved implementation and consistent forcing scheme

Linlin Fei, Kai H. Luo, and Qing Li
Phys. Rev. E 97, 053309 – Published 25 May 2018
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Abstract

The cascaded or central-moment-based lattice Boltzmann method (CLBM) proposed in [Phys. Rev. E 73, 066705 (2006)] possesses very good numerical stability. However, two constraints exist in three-dimensional (3D) CLBM simulations. First, the conventional implementation for 3D CLBM involves cumbersome operations and requires much higher computational cost compared to the single-relaxation-time (SRT) LBM. Second, it is a challenge to accurately incorporate a general force field into the 3D CLBM. In this paper, we present an improved method to implement CLBM in 3D. The main strategy is to adopt a simplified central moment set and carry out the central-moment-based collision operator based on a general multi-relaxation-time (GMRT) framework. Next, the recently proposed consistent forcing scheme for CLBM [Fei and Luo, Phys. Rev. E 96, 053307 (2017)] is extended to incorporate a general force field into 3D CLBM. Compared with the recently developed nonorthogonal CLBM [Rosis, Phys. Rev. E 95, 013310 (2017)], our implementation is proved to reduce the computational cost significantly. The inconsistency of adopting the discrete equilibrium distribution functions in the nonorthogonal CLBM is analyzed and validated. The 3D CLBM developed here in conjunction with the consistent forcing scheme is verified through numerical simulations of several canonical force-driven flows, highlighting very good properties in terms of accuracy, convergence, and consistency with the nonslip rule. Finally, the techniques developed here for 3D CLBM can be applied to make the implementation and execution of 3D MRT-LBM more efficient.

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  • Received 22 January 2018

DOI:https://doi.org/10.1103/PhysRevE.97.053309

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Fluid Dynamics

Authors & Affiliations

Linlin Fei1, Kai H. Luo1,2,*, and Qing Li3,†

  • 1Center for Combustion Energy; Key laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, China
  • 2Department of Mechanical Engineering, University College London, Torrington Place, London WC1E 7JE, UK
  • 3School of Energy Science and Engineering, Central South University, Changsha 410083, China

  • *Corresponding author: K.Luo@ucl.ac.uk
  • Corresponding author: qingli@csu.edu.cn

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Vol. 97, Iss. 5 — May 2018

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