Mixed bounce-back boundary scheme of the general propagation lattice Boltzmann method for advection-diffusion equations

Xiuya Guo, Zhenhua Chai, Shengyong Pang, Yong Zhao, and Baochang Shi
Phys. Rev. E 99, 063316 – Published 27 June 2019

Abstract

In this work, a mixed bounce-back boundary scheme of general propagation lattice Boltzmann (GPLB) model is proposed for isotropic advection-diffusion equations (ADEs) with Robin boundary condition, and a detailed asymptotic analysis is also conducted to show that the present boundary scheme for the straight walls has a second-order accuracy in space. In addition, several numerical examples, including the Helmholtz equation in a square domain, the diffusion equation with sinusoidal concentration gradient, one-dimensional transient ADE with Robin boundary and an ADE with a source term, are also considered. The results indicate that the numerical solutions agree well with the analytical ones, and the convergence rate is close to 2.0. Furthermore, through adjusting the two parameters in the GPLB model properly, the present boundary scheme can be more accurate than some existing lattice Boltzmann boundary schemes.

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  • Received 30 September 2018
  • Revised 22 April 2019

DOI:https://doi.org/10.1103/PhysRevE.99.063316

©2019 American Physical Society

Physics Subject Headings (PhySH)

Fluid Dynamics

Authors & Affiliations

Xiuya Guo1, Zhenhua Chai1,2, Shengyong Pang3, Yong Zhao1, and Baochang Shi1,2,*

  • 1School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China
  • 2Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan 430074, China
  • 3State Key Laboratory of Material Processing and Die & Mould Technology, Huazhong University of Science and Technology, Wuhan 430074, China

  • *shibc@hust.edu.cn

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Issue

Vol. 99, Iss. 6 — June 2019

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