Lattice ellipsoidal statistical BGK model for thermal non-equilibrium flows
Lattice ellipsoidal statistical BGK model for thermal non-equilibrium flows
复制标题
DOI：
10.1017/jfm.2012.616
复制
发表时间：
2012-09
影响因子：
3.7
通讯作者：
J. Meng;Yonghao Zhang;N. Hadjiconstantinou;G. Radtke;X. Shan
中科院分区：
文献类型：
--
作者：
J. Meng;Yonghao Zhang;N. Hadjiconstantinou;G. Radtke;X. Shan
摘要基于椭球统计Bhatnagar-Gross-Krook（ES-BGK）碰撞算符，通过Hermite矩表象，构造了一个热格子Boltzmann模型。由此产生的晶格ES-BGK模型使用单个分布函数，并具有可调的普朗特数。数值模拟结果表明，使用一个适度的离散速度设置，该模型可以准确地恢复稳态和瞬态解的ES-BGK方程的滑流和早期过渡制度的小马赫数限制，这是典型的微尺度问题的实际利益。特别是在过渡区，ES-BGK模型的数值解，直接和低方差偏差蒙特卡罗模拟的克努森数的值高达约0美元的比较显示出良好的精度。五块钱。另一方面，以高马赫数为特征的高度非平衡现象，如粘性加热和大驱动力值下的力驱动的Poiffille流，在转捩区用考虑到计算效率而选择的离散化方法（如这里所用的方法）更难定量地捕捉，尽管随着离散速度数的增加，观察到精度有所提高。
Abstract A thermal lattice Boltzmann model is constructed on the basis of the ellipsoidal statistical Bhatnagar–Gross–Krook (ES-BGK) collision operator via the Hermite moment representation. The resulting lattice ES-BGK model uses a single distribution function and features an adjustable Prandtl number. Numerical simulations show that using a moderate discrete velocity set, this model can accurately recover steady and transient solutions of the ES-BGK equation in the slip-flow and early transition regimes in the small-Mach-number limit that is typical of microscale problems of practical interest. In the transition regime in particular, comparisons with numerical solutions of the ES-BGK model, direct and low-variance deviational Monte Carlo simulations show good accuracy for values of the Knudsen number up to approximately $0. 5$ . On the other hand, highly non-equilibrium phenomena characterized by high Mach numbers, such as viscous heating and force-driven Poiseuille flow for large values of the driving force, are more difficult to capture quantitatively in the transition regime using discretizations chosen with computational efficiency in mind such as the one used here, although improved accuracy is observed as the number of discrete velocities is increased.