强迫均匀各向同性湍流的单松弛时间与多重修正矩阵格子Boltzmann模拟
Single Relaxation Time and Multiple Revised Matrix Lattice Boltzmann Simulations of Forced Isotropic Turbulence
AI总结：
本文在128^3和256^3三维强迫各向同性湍流中比较SRT与RM/MRT格子Boltzmann模型，结合Guo强迫和CFL稳定处理，评估湍流统计量与不可压缩性。
摘要：
本文在分辨率分别为128^3和256^3的三维强迫各向同性湍流模拟中，对单松弛时间（SRT）模型和修正矩阵（RM）格子Boltzmann模型进行了比较。两种模型均采用Guo等人（2002）提出的强迫技术，并使用相同的参数和条件。研究证实了一些新的方面和结果，例如MRT模型在模拟强迫湍流方面的优越性，以及利用Courant-Friedrichs-Lewy条件（CFL）（Courant等，1967），通过将速度输入乘以系数CFL<1.0来克服稳定性问题，并将输出速度数据除以同一CFL。初始速度场取为u(x;0)=0，所有算例均在低波数处注入强迫，且固定强迫振幅为10^-4。在所有SRT模拟中，单松弛时间设为0.503。结果表明，所得湍流速度场呈现出以往理论、实验和数值研究所证实的普适特征。模拟得到的Taylor雷诺数为：128^3情形下SRT的R=62、MRT的R=65；256^3情形下SRT的R=107、MRT的R=82。为检验SRT模型相对于MRT模型较弱的不可压缩性，文中绘制了密度概率分布函数（PDF），并发现在MRT情形下所有时间步的ρ几乎均为1，而SRT情形则可观察到围绕1的明显扰动。
英文摘要：
The single relaxation time (SRT) and the revised matrix (RM) lattice Boltzmann models are compared for simulations of three dimensional forced isotropic turbulence with resolutions of 128^3 and 256^3, respectively. The forcing technique by Guo et al. (2002) is applied with the two models using the same parameters and conditions. Some new aspects and results have been confirmed such as the superiority of the MRT model to simulate forced turbulence and using the Courant-Friedichs-Lewy condition (CFL) (Courant et al., 1967) by multiplying the velocity input with the coefficient CFL < 1.0 to overcome the stability problem and divide the output velocity data by the same CFL. The initial velocity field is chosen as u(x; 0) = 0 and the force is injected at low wave-numbers with a fixed forcing amplitude to 10^-4 for all cases. The single relaxation time is set to 0.503 in all SRT simulations. Results show that the obtained turbulent velocity fields yield universal characteristics as proven in previous theoretical, experimental and numerical studies. The Taylor Reynolds number for the simulations are found as SRT: R = 62 and MRT : R = 65 for 1283 and SRT: R= 107 and MRT: R = 82 for the case of 2563, respectively. To test the weak incompressibility for the SRT model in comparison to the MRT model, the density probability distribution function (PDF) is depicted and it is found that ? is almost unity at all timesteps for the MRT case, while a clear disturbance about unity is observed for the SRT case.
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