Generalized modification in the lattice Bhatnagar-Gross-Krook model for incompressible Navier-Stokes equations and convection-diffusion equations.
Generalized modification in the lattice Bhatnagar-Gross-Krook model for incompressible Navier-Stokes equations and convection-diffusion equations.
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DOI：
10.1103/physreve.90.013309
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发表时间：
2014-07
期刊：
影响因子：
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通讯作者：
Xuguang Yang;B. Shi;Z. Chai
中科院分区：
文献类型：
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作者：
Xuguang Yang;B. Shi;Z. Chai
本文通过在发展方程中加入修正项，提出了求解不可压Navier-Stokes方程和对流扩散方程的两种修正格子Boltzmann-Bhatnagar-Gross-Krook（LBGK）模型。利用这种修正，可以使LBGK模型中的无量纲弛豫时间保持在适当的范围内，从而提高了LBGK模型的稳定性。虽然一些梯度算子被包括在校正项中，但它们可以使用局部计算方案有效地计算，使得本LBGK模型仍然保留晶格玻尔兹曼方法的固有并行特性。对定常Poillille流动和非定常Womersley流动的数值研究表明，改进的LBGK模型在空间上具有二阶收敛速度，并能消除普通LBGK模型中的可压缩性影响。此外，为了检验模型的稳定性，我们还对方腔内的自然对流进行了模拟，发现即使在很高的Rayleigh数（Ra = 10（12））下，模拟结果也与前人的研究结果吻合得很好。
In this paper, two modified lattice Boltzmann Bhatnagar-Gross-Krook (LBGK) models for incompressible Navier-Stokes equations and convection-diffusion equations are proposed via the addition of correction terms in the evolution equations. Utilizing this modification, the value of the dimensionless relaxation time in the LBGK model can be kept in a proper range, and thus the stability of the LBGK model can be improved. Although some gradient operators are included in the correction terms, they can be computed efficiently using local computational schemes such that the present LBGK models still retain the intrinsic parallelism characteristic of the lattice Boltzmann method. Numerical studies of the steady Poiseuille flow and unsteady Womersley flow show that the modified LBGK model has a second-order convergence rate in space, and the compressibility effect in the common LBGK model can be eliminated. In addition, to test the stability of the present models, we also performed some simulations of the natural convection in a square cavity, and we found that the results agree well with those reported in the previous work, even at a very high Rayleigh number (Ra = 10(12)).