A multiple-relaxation-time lattice Boltzmann method with Beam-Warming scheme for a coupled chemotaxis-fluid model
A multiple-relaxation-time lattice Boltzmann method with Beam-Warming scheme for a coupled chemotaxis-fluid model
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DOI：
10.3934/era.2020066
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发表时间：
2020
影响因子：
0.8
通讯作者：
Zhonghua Qiao;Xuguang Yang
中科院分区：
文献类型：
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作者：
Zhonghua Qiao;Xuguang Yang
在这项工作中，多重弛豫时间（MRT）格子玻尔兹曼方法（LBM）提出了解决耦合趋化性流体模型。在LBM的演化方程中，采用了束温（B-W）格式以提高数值稳定性。在数值试验中，首先通过模拟Keller-Segel（K-S）模型的爆破现象，对经典LBM和目前的B-W格式LBM进行了比较。数值结果表明，采用B-W格式的LBM的稳定性优于经典的LBM。然后，通过对N-S耦合K-S模型的数值研究，验证了所提出的B-W格式的二阶收敛速度。最后，通过求解趋化性-流体耦合模型，数值研究了降落细菌羽流的形成。数值结果与文献中已有的结果吻合良好。
In this work, a multiple-relaxation-time (MRT) lattice Boltzmann method (LBM) is proposed to solve a coupled chemotaxis-fluid model. In the evolution equation of the proposed LBM, Beam-Warming (B-W) scheme is used to enhance the numerical stability. In numerical experiments, at first, the comparison between the classical LBM and the present LBM with B-W scheme is carried out by simulating blow up phenomenon of the Keller-Segel (K-S) model. Numerical results show that the stability of the present LBM with B-W scheme is better than the classical one. Then, the second order convergence rate of the proposed B-W scheme is verified in the numerical study of the coupled Navier-Stokes (N-S) K-S model. Finally, through solving the coupled chemotaxis-fluid model, the formation of falling bacterial plumes is numerically investigated. Numerical results agree well with existing ones in the literature.