Lattice Boltzmann method for general convection-diffusion equations: MRT model and boundary schemes

Mengxin Zhang, Weifeng Zhao (Lead / Corresponding author), Ping Lin (Lead / Corresponding author)

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Abstract

This paper is concerned with the lattice Boltzmann method for general convectiondiffusion equations. For such equations, we develop a multiple-relaxation-time lattice Boltzmann model and show its consistency under the diffusive scaling. The secondorder accuracy of the half-way anti-bounce-back scheme accompanying the present MRT model is justified based on an elegant relation of the collision matrix. Using the half-way anti-bounce-back scheme as a central step, we further construct some parameterized single-node second order schemes for curved boundaries. The accuracy of the proposed model and boundary schemes are numerically validated with several nonlinear convection-diffusion equations.
Original languageEnglish
Pages (from-to)147-163
Number of pages17
JournalJournal of Computational Physics
Volume389
Early online date5 Apr 2019
DOIs
Publication statusPublished - 15 Jul 2019

Keywords

  • nonlinear convection-diffusion equations
  • lattice Blotzmann model
  • anti-bounce-back scheme
  • single-node boundary schemes
  • second order accuracy

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