Saadat Mohammad Hossein, Dorschner Benedikt, Karlin Ilya
Department of Mechanical and Process Engineering, ETH Zurich, 8092 Zurich, Switzerland.
Entropy (Basel). 2021 Apr 17;23(4):475. doi: 10.3390/e23040475.
Conventional lattice Boltzmann models for the simulation of fluid dynamics are restricted by an error in the stress tensor that is negligible only for small flow velocity and at a singular value of the temperature. To that end, we propose a unified formulation that restores Galilean invariance and the isotropy of the stress tensor by introducing an extended equilibrium. This modification extends lattice Boltzmann models to simulations with higher values of the flow velocity and can be used at temperatures that are higher than the lattice reference temperature, which enhances computational efficiency by decreasing the number of required time steps. Furthermore, the extended model also remains valid for stretched lattices, which are useful when flow gradients are predominant in one direction. The model is validated by simulations of two- and three-dimensional benchmark problems, including the double shear layer flow, the decay of homogeneous isotropic turbulence, the laminar boundary layer over a flat plate and the turbulent channel flow.
用于流体动力学模拟的传统格子玻尔兹曼模型受到应力张量误差的限制，该误差仅在小流速和特定温度值时可忽略不计。为此，我们提出了一种统一的公式，通过引入扩展平衡来恢复伽利略不变性和应力张量的各向同性。这种修改将格子玻尔兹曼模型扩展到更高流速的模拟，并且可以在高于格子参考温度的温度下使用，通过减少所需的时间步数提高了计算效率。此外，扩展模型对于拉伸格子也仍然有效，当流动梯度在一个方向上占主导时，拉伸格子很有用。该模型通过二维和三维基准问题的模拟得到验证，包括双剪切层流动、均匀各向同性湍流的衰减、平板上的层流边界层和湍流通道流动。
