时间步长对格子玻尔兹曼法模拟室内气流精度的影响

Effect of Time Steps on Accuracy of Indoor Airflow Simulation Using Lattice Boltzmann Method

摘要:

基于格子玻尔兹曼法的大涡模拟（LBM-LES）是湍流模拟的新方法，但不恰当的时间步长δt可能会影响其计算精度。首先理论总结了δt可能对LBM-LES湍流模拟造成的影响，阐明过大的δt会导致速度场产生压缩性误差，而过小的δt会导致超松弛碰撞产生速度场的数值振荡。其次，通过对等温室内气流案例进行LBM-LES模拟，定量讨论了δt引起的压缩性误差和数值振荡问题。结果表明，δt较大时流场密度变化剧烈，且格子玻尔兹曼单位的马赫数（M）超过0.3的区域中速度场产生了明显的压缩性误差。同时，过小的δt导致平均及脉动风速均产生了数值振荡，这在网格分辨率较高时尤为明显。建议模拟时在确保δt足够小以满足最大风速区域的M<0.3的基础上，尽量增大δt以防止产生数值振荡。

Abstract:

Lattice Boltzmann method-based large-eddy simulation （LBM-LES） is a new method to solve turbulence problems in recent decades. However， improper time step settings may affect the simulation accuracy of LBM-LES. This paper first analyzed and summarized the impact of time step δt on the results of LBM-LES，theoretically. An oversized δt will cause compressibility error in the velocity field， while a too small δt can lead to the over-relaxation colliding mode， causing the numerical oscillation of velocity field. Subsequently， LBM-LES simulations of an isothermal indoor airflow case were conducted to discuss these errors quantitatively. The results show that a large δt leads to a sharp density change， and the velocity field in the regions where the Mach number （M） in the lattice Boltzmann unit exceeds 0.3 showing that there are obvious compressibility errors. Meanwhile， a too-small δt causes apparent numerical oscillations of both time-averaged and fluctuating velocities. This phenomenon is more significant when the grid resolution is higher. Therefore，it is suggested that δt should be small enough to ensure M<0.3 in the maximum velocity regions， based on which， a larger δt should be utilized to prevent numerical oscillations.