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

Mengxin Zhang; Weifeng Zhao; Ping Lin

doi:10.1016/j.jcp.2019.03.045

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)

Mathematics

Research output: Contribution to journal › Article › peer-review

43 Citations (Scopus)

700 Downloads (Pure)

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 language	English
Pages (from-to)	147-163
Number of pages	17
Journal	Journal of Computational Physics
Volume	389
Early online date	5 Apr 2019
DOIs	https://doi.org/10.1016/j.jcp.2019.03.045
Publication status	Published - 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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10.1016/j.jcp.2019.03.045

Author Accepted ManuscriptAccepted author manuscript, 783 KBLicence: CC BY-NC-ND

Lin, Ping
- p.lindundee.acuk
- Mathematics - Professor
Person: Academic

Cite this

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title = "Lattice Boltzmann method for general convection-diffusion equations: MRT model and boundary schemes",

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.",

keywords = "nonlinear convection-diffusion equations, lattice Blotzmann model, anti-bounce-back scheme, single-node boundary schemes, second order accuracy",

author = "Mengxin Zhang and Weifeng Zhao and Ping Lin",

year = "2019",

month = jul,

day = "15",

doi = "10.1016/j.jcp.2019.03.045",

language = "English",

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journal = "Journal of Computational Physics",

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T1 - Lattice Boltzmann method for general convection-diffusion equations

T2 - MRT model and boundary schemes

AU - Zhang, Mengxin

AU - Zhao, Weifeng

AU - Lin, Ping

PY - 2019/7/15

Y1 - 2019/7/15

N2 - 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.

AB - 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.

KW - nonlinear convection-diffusion equations

KW - lattice Blotzmann model

KW - anti-bounce-back scheme

KW - single-node boundary schemes

KW - second order accuracy

U2 - 10.1016/j.jcp.2019.03.045

DO - 10.1016/j.jcp.2019.03.045

M3 - Article

SN - 0021-9991

VL - 389

SP - 147

EP - 163

JO - Journal of Computational Physics

JF - Journal of Computational Physics

ER -

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

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Keywords

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Lin, Ping

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