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Volume 17, Issue 4
Thirteen-Velocity Three-Dimensional Multiple-Relaxation-Time Lattice Boltzmann Model for Incompressible Navier-Stokes Equations

Wenhuan Zhang, Shibo Kuang, Zhenhua Chai & Baochang Shi

DOI: 10.4208/aamm.OA-2023-0078

Adv. Appl. Math. Mech., 17 (2025), pp. 1037-1062.

Published online: 2025-05

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  • Abstract

This paper presents a three-dimensional thirteen-velocity (D3Q13) multiple-relaxation-time (MRT) lattice Boltzmann (LB) model for incompressible flows. The model can eliminate the second kind of compressibility error existing in previous D3Q13 MRT LB models. We simulate the three-dimensional steady Poiseuille flow, unsteady pulsatile flow, and lid-driven cavity flow to verify the validity of the current model. The excellent agreement between the numerical result and the analytical solution or the previous numerical result demonstrates the model’s effectiveness.

  • Keywords

Lattice Boltzmann method, multiple relaxation time, incompressible Navier-Stokes equations, compressibility error.

  • AMS Subject Headings

76M25, 76D05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-17-1037, author = {Zhang , WenhuanKuang , ShiboChai , Zhenhua and Shi , Baochang}, title = {Thirteen-Velocity Three-Dimensional Multiple-Relaxation-Time Lattice Boltzmann Model for Incompressible Navier-Stokes Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2025}, volume = {17}, number = {4}, pages = {1037--1062}, abstract = {

This paper presents a three-dimensional thirteen-velocity (D3Q13) multiple-relaxation-time (MRT) lattice Boltzmann (LB) model for incompressible flows. The model can eliminate the second kind of compressibility error existing in previous D3Q13 MRT LB models. We simulate the three-dimensional steady Poiseuille flow, unsteady pulsatile flow, and lid-driven cavity flow to verify the validity of the current model. The excellent agreement between the numerical result and the analytical solution or the previous numerical result demonstrates the model’s effectiveness.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2023-0078}, url = {http://global-sci.org/intro/article_detail/aamm/24053.html} }
TY - JOUR T1 - Thirteen-Velocity Three-Dimensional Multiple-Relaxation-Time Lattice Boltzmann Model for Incompressible Navier-Stokes Equations AU - Zhang , Wenhuan AU - Kuang , Shibo AU - Chai , Zhenhua AU - Shi , Baochang JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 1037 EP - 1062 PY - 2025 DA - 2025/05 SN - 17 DO - http://doi.org/10.4208/aamm.OA-2023-0078 UR - https://global-sci.org/intro/article_detail/aamm/24053.html KW - Lattice Boltzmann method, multiple relaxation time, incompressible Navier-Stokes equations, compressibility error. AB -

This paper presents a three-dimensional thirteen-velocity (D3Q13) multiple-relaxation-time (MRT) lattice Boltzmann (LB) model for incompressible flows. The model can eliminate the second kind of compressibility error existing in previous D3Q13 MRT LB models. We simulate the three-dimensional steady Poiseuille flow, unsteady pulsatile flow, and lid-driven cavity flow to verify the validity of the current model. The excellent agreement between the numerical result and the analytical solution or the previous numerical result demonstrates the model’s effectiveness.

Zhang , WenhuanKuang , ShiboChai , Zhenhua and Shi , Baochang. (2025). Thirteen-Velocity Three-Dimensional Multiple-Relaxation-Time Lattice Boltzmann Model for Incompressible Navier-Stokes Equations. Advances in Applied Mathematics and Mechanics. 17 (4). 1037-1062. doi:10.4208/aamm.OA-2023-0078
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