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Volume 29, Issue 2
Discrete-Velocity Vector-BGK Models Based Numerical Methods for the Incompressible Navier-Stokes Equations

Jin Zhao

DOI: 10.4208/cicp.OA-2019-0192

Commun. Comput. Phys., 29 (2021), pp. 420-444.

Published online: 2020-12

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  • 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.

  • Keywords

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

  • AMS Subject Headings

65M06, 65M12, 35Q30, 76P05

  • Copyright

COPYRIGHT: © Global Science Press

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  • BibTex
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@Article{CiCP-29-420, author = {Zhao , Jin}, title = {Discrete-Velocity Vector-BGK Models Based Numerical Methods for the Incompressible Navier-Stokes Equations}, journal = {Communications in Computational Physics}, year = {2020}, volume = {29}, number = {2}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2019-0192}, url = {http://global-sci.org/intro/article_detail/cicp/18473.html} }
TY - JOUR T1 - Discrete-Velocity Vector-BGK Models Based Numerical Methods for the Incompressible Navier-Stokes Equations AU - Zhao , Jin JO - Communications in Computational Physics VL - 2 SP - 420 EP - 444 PY - 2020 DA - 2020/12 SN - 29 DO - http://doi.org/10.4208/cicp.OA-2019-0192 UR - https://global-sci.org/intro/article_detail/cicp/18473.html KW - Vector-BGK models, incompressible Navier-Stokes equations, Maxwell iteration, weighted $L^2$-stability. AB -

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.

Jin Zhao. (2020). Discrete-Velocity Vector-BGK Models Based Numerical Methods for the Incompressible Navier-Stokes Equations. Communications in Computational Physics. 29 (2). 420-444. doi:10.4208/cicp.OA-2019-0192
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