标题： 14速度和18速度多松弛时间格子玻尔兹曼模型用于三维不可压缩流体 显示英文标题

标题： 14-velocity and 18-velocity multiple-relaxation-time lattice Boltzmann models for three-dimensional incompressible flows

摘要： 本文提出了用于三维不可压缩流的14速度和18速度多松弛时间（MRT）格子玻尔兹曼（LB）模型。 这两个模型是基于He等人提出的不可压缩LBGK模型（Chin. Phys., 2004, 13: 40-46）和d'Humières等人提出的MRT LB模型（Philos. Trans. R. Soc., A, 2002, 360: 437-451）构建的，分别在计算效率和稳定性方面具有优势。 通过Chapman-Enskog分析，这些模型可以在低马赫数极限下恢复到三维不可压缩纳维-斯托克斯方程。 为了验证所提出的模型，模拟了三维稳态泊肃叶流、非稳态脉动流和驱动腔流。 模拟结果与解析解或现有的数值结果吻合良好。 此外，发现所提出的模型比d'Humières等人模型具有更高的精度，比He等人模型具有更好的稳定性。 显示英文摘要

摘要： In this paper, 14-velocity and 18-velocity multiple-relaxation-time (MRT) lattice Boltzmann (LB) models are proposed for three-dimensional incompressible flows. These two models are constructed based on the incompressible LBGK model proposed by He et al. (Chin. Phys., 2004, 13: 40-46) and the MRT LB model proposed by d'Humi\`{e}res et al. (Philos. Trans. R. Soc., A, 2002, 360: 437-451), which have advantages in the computational efficiency and stability, respectively. Through the Chapman-Enskog analysis, the models can recover to three-dimensional incompressible Navier-Stokes equations in the low Mach number limit. To verify the present models, the steady Poiseuille flow, unsteady pulsatile flow and lid-driven cavity flow in three dimensions are simulated. The simulation results agree well with the analytical solutions or the existing numerical results. Moreover, it is found that the present models show higher accuracy than d'Humi\`{e}res et al. model and better stability than He et al. model.