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Volume 21, Issue 2
An Alternative Lattice Boltzmann Model for Incompressible Flows and Its Stabilization

Liangqi Zhang, Zhong Zeng, Haiqiong Xie, Zhouhua Qiu, Liping Yao, Yongxiang Zhang & Yiyu Lu

DOI: 10.4208/cicp.091014.030515a

Commun. Comput. Phys., 21 (2017), pp. 443-465.

Published online: 2018-04

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  • Abstract

In this paper, an alternative lattice Boltzmann (LB) model for incompressible flows is proposed. By modifying directly the moments of the equilibrium distribution function (EDF), the continuous expression of the EDF in tensor Hermite polynomials is derived using the moment expansion and then discretized with the discrete velocity vectors of the D2Q9 lattice. The present model as well as its counterpart, the incompressible LB model proposed by Guo, reproduces the incompressible Navier-Stokes (N-S) equations for both steady and unsteady flows. Besides, an alternative pressure formula, which represents the pressure as the diagonal part of the stress tensor, is adopted in the present model. Furthermore, in order to enhance the stability of the present LB model, an additional relaxation time pertaining to the non-hydrodynamic mode is added to the BGK collision operator. The present LB model is validated by two benchmark tests: the cavity flow with different Reynolds number (Re) and the flow past an impulsively started cylinder at Re=40 and 550.

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@Article{CiCP-21-443, author = {Liangqi Zhang, Zhong Zeng, Haiqiong Xie, Zhouhua Qiu, Liping Yao, Yongxiang Zhang and Yiyu Lu}, title = {An Alternative Lattice Boltzmann Model for Incompressible Flows and Its Stabilization}, journal = {Communications in Computational Physics}, year = {2018}, volume = {21}, number = {2}, pages = {443--465}, abstract = {

In this paper, an alternative lattice Boltzmann (LB) model for incompressible flows is proposed. By modifying directly the moments of the equilibrium distribution function (EDF), the continuous expression of the EDF in tensor Hermite polynomials is derived using the moment expansion and then discretized with the discrete velocity vectors of the D2Q9 lattice. The present model as well as its counterpart, the incompressible LB model proposed by Guo, reproduces the incompressible Navier-Stokes (N-S) equations for both steady and unsteady flows. Besides, an alternative pressure formula, which represents the pressure as the diagonal part of the stress tensor, is adopted in the present model. Furthermore, in order to enhance the stability of the present LB model, an additional relaxation time pertaining to the non-hydrodynamic mode is added to the BGK collision operator. The present LB model is validated by two benchmark tests: the cavity flow with different Reynolds number (Re) and the flow past an impulsively started cylinder at Re=40 and 550.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.091014.030515a}, url = {http://global-sci.org/intro/article_detail/cicp/11245.html} }
TY - JOUR T1 - An Alternative Lattice Boltzmann Model for Incompressible Flows and Its Stabilization AU - Liangqi Zhang, Zhong Zeng, Haiqiong Xie, Zhouhua Qiu, Liping Yao, Yongxiang Zhang & Yiyu Lu JO - Communications in Computational Physics VL - 2 SP - 443 EP - 465 PY - 2018 DA - 2018/04 SN - 21 DO - http://doi.org/10.4208/cicp.091014.030515a UR - https://global-sci.org/intro/article_detail/cicp/11245.html KW - AB -

In this paper, an alternative lattice Boltzmann (LB) model for incompressible flows is proposed. By modifying directly the moments of the equilibrium distribution function (EDF), the continuous expression of the EDF in tensor Hermite polynomials is derived using the moment expansion and then discretized with the discrete velocity vectors of the D2Q9 lattice. The present model as well as its counterpart, the incompressible LB model proposed by Guo, reproduces the incompressible Navier-Stokes (N-S) equations for both steady and unsteady flows. Besides, an alternative pressure formula, which represents the pressure as the diagonal part of the stress tensor, is adopted in the present model. Furthermore, in order to enhance the stability of the present LB model, an additional relaxation time pertaining to the non-hydrodynamic mode is added to the BGK collision operator. The present LB model is validated by two benchmark tests: the cavity flow with different Reynolds number (Re) and the flow past an impulsively started cylinder at Re=40 and 550.

Liangqi Zhang, Zhong Zeng, Haiqiong Xie, Zhouhua Qiu, Liping Yao, Yongxiang Zhang and Yiyu Lu. (2018). An Alternative Lattice Boltzmann Model for Incompressible Flows and Its Stabilization. Communications in Computational Physics. 21 (2). 443-465. doi:10.4208/cicp.091014.030515a
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