Discrete-Velocity Vector-BGK Models Based Numerical Methods for the Incompressible Navier-Stokes Equations

Discrete-Velocity Vector-BGK Models Based Numerical Methods for the Incompressible Navier-Stokes Equations

Year:    2021

Author:    Jin Zhao

Communications in Computational Physics, Vol. 29 (2021), Iss. 2 : pp. 420–444

Abstract

In this paper, we propose a class of numerical methods based on discrete-velocity vector-BGK models for the incompressible Navier-Stokes equations. By analyzing a splitting method with Maxwell iteration, we show that the usual lattice Boltzmann discretization of the vector-BGK models provides a good numerical scheme. Moreover, we establish the stability of the numerical scheme. The stability and second-order accuracy of the scheme are validated through numerical simulations of the two-dimensional Taylor-Green vortex flows. Further numerical tests are conducted to exhibit some potential advantages of the vector-BGK models, which can be regarded as competitive alternatives of the scalar-BGK models.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2019-0192

Communications in Computational Physics, Vol. 29 (2021), Iss. 2 : pp. 420–444

Published online:    2021-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    25

Keywords:    Vector-BGK models incompressible Navier-Stokes equations Maxwell iteration weighted $L^2$-stability.

Author Details

Jin Zhao

  1. Lattice Boltzmann for linear elastodynamics: Periodic problems and Dirichlet boundary conditions

    Boolakee, Oliver | Geier, Martin | De Lorenzis, Laura

    Computer Methods in Applied Mechanics and Engineering, Vol. 433 (2025), Iss. P.117469

    https://doi.org/10.1016/j.cma.2024.117469 [Citations: 0]
  2. Frost Formation over an Inclined Plate Under Natural Convection with Lattice–Boltzmann Method

    Seddigh, Gholamreza | Tahavvor, Ali Reza

    Heat Transfer Engineering, Vol. (2024), Iss. P.1

    https://doi.org/10.1080/01457632.2024.2362541 [Citations: 0]
  3. A New Multi-Level Grid Multiple-Relaxation-Time Lattice Boltzmann Method with Spatial Interpolation

    Liu, Zhixiang | Li, Shengyong | Ruan, Jun | Zhang, Wenbo | Zhou, Liping | Huang, Dongmei | Xu, Jingxiang

    Mathematics, Vol. 11 (2023), Iss. 5 P.1089

    https://doi.org/10.3390/math11051089 [Citations: 7]
  4. A robust and efficient solver based on kinetic schemes for Magnetohydrodynamics (MHD) equations

    Baty, Hubert | Drui, Florence | Helluy, Philippe | Franck, Emmanuel | Klingenberg, Christian | Thanhäuser, Lukas

    Applied Mathematics and Computation, Vol. 440 (2023), Iss. P.127667

    https://doi.org/10.1016/j.amc.2022.127667 [Citations: 3]
  5. Family of parametric second-order boundary schemes for the vectorial finite-difference-based lattice Boltzmann method

    Zhang, Xi | Feng, Minfu | Zhao, Jin

    Physical Review E, Vol. 104 (2021), Iss. 5

    https://doi.org/10.1103/PhysRevE.104.055309 [Citations: 1]
  6. Vectorial finite-difference-based lattice Boltzmann method: Consistency, boundary schemes and stability analysis

    Zhao, Jin | Yong, Wen-An

    Journal of Computational and Applied Mathematics, Vol. 441 (2024), Iss. P.115677

    https://doi.org/10.1016/j.cam.2023.115677 [Citations: 0]
  7. Phase‐field‐based multiple‐distribution‐function lattice Boltzmann method for incompressible two‐phase flows

    Zhan, Chengjie | Chai, Zhenhua | Shi, Baochang

    International Journal for Numerical Methods in Fluids, Vol. 95 (2023), Iss. 5 P.683

    https://doi.org/10.1002/fld.5167 [Citations: 2]
  8. Multiple-distribution-function lattice Boltzmann method for convection-diffusion-system-based incompressible Navier-Stokes equations

    Chai, Zhenhua | Shi, Baochang | Zhan, Chengjie

    Physical Review E, Vol. 106 (2022), Iss. 5

    https://doi.org/10.1103/PhysRevE.106.055305 [Citations: 7]