Development and Comparative Studies of Three Non-free Parameter Lattice Boltzmann Models for Simulation of Compressible Flows
Development and Comparative Studies of Three Non-free Parameter Lattice Boltzmann Models for Simulation of Compressible Flows
复制标题
DOI：
10.1017/s2070073300001740
复制
发表时间：
2012-08
影响因子：
1.4
通讯作者：
L. M. Yang;C. Shu;Jie Wu
中科院分区：
文献类型：
--
作者：
L. M. Yang;C. Shu;Jie Wu
本文首先介绍了数值模拟含激波可压缩流动的有限体积格子Boltzmann方法（FV-LBM）。在FV-LBM中，单元界面处的法向对流通量采用一维可压缩格子Boltzmann模型计算，而切向通量则采用与传统Euler求解器相同的方法计算。然后，本文提出了一个平台来构建一维可压缩格子Boltzmann模型，用于FV-LBM。平台由力矩守恒形式构成。在该平台下，可以确定平衡分布函数和晶格速度，从而建立非自由参数模型。本文详细介绍了D1 Q3、D1 Q4和D1 Q5三种典型的非自由参数模型。本文对这三种模型的性能作了简要的分析，并将它们应用于求解一、二维的试验问题。结果表明，D1 Q3模型计算时间最短，D1 Q4和D1 Q5模型适用马赫数范围较宽。结果表明，D1 Q4模型是高超声速流场FV-LBM数值模拟的最佳选择。AMS科目分类：76 T10
This paper at first shows the details of finite volume-based lattice Boltz- mann method (FV-LBM) for simulation of compressible flows with shock waves. In the FV-LBM, the normal convective flux at the interface of a cell is evaluated by using one-dimensional compressible lattice Boltzmann model, while the tangential flux is calculated using the same way as used in the conventional Euler solvers. The paper then presents a platform to construct one-dimensional compressible lattice Boltzmann model for its use in FV-LBM. The platform is formed from the conser- vation forms of moments. Under the platform, both the equilibrium distribution functions and lattice velocities can be determined, and therefore, non-free parame- ter model can be developed. The paper particularly presents three typical non-free parameter models, D1Q3, D1Q4 and D1Q5. The performances of these three mod- els for simulation of compressible flows are investigated by a brief analysis and their application to solve some one-dimensional and two-dimensional test prob- lems. Numerical results showed that D1Q3 model costs the least computation time and D1Q4 and D1Q5 models have the wider application range of Mach number. From the results, it seems that D1Q4 model could be the best choice for the FV- LBM simulation of hypersonic flows. AMS subject classifications: 76T10