Kim Seung Hyun, Pitsch Heinz, Boyd Iain D
Department of Mechanical Engineering, Stanford University, California 94305-3035, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Feb;77(2 Pt 2):026704. doi: 10.1103/PhysRevE.77.026704. Epub 2008 Feb 13.
We present mesoscopic fluid-wall interaction models for lattice Boltzmann (LB) model simulations of microscale flows. The exact solution of the slip velocity for the LB equation with the Bhatnagar-Gross-Krook collision operator is obtained for Poiseuille flow at finite Knudsen numbers. With a consistent definition of the Knudsen number, the slip coefficients of the LB equation with the standard D2Q9 scheme are found to be slightly larger than those of the Boltzmann equation with the same boundary condition, which makes the standard LB method remain quantitatively accurate only for small Knudsen numbers. By modifying the nonequilibrium energy flux or introducing the effective relaxation time, the LB method is analytically shown to reproduce the slip phenomena up to second order in the Knudsen number. For the standard LB method, the Knudsen layer is captured only with modification of the relaxation dynamics such as in the effective relaxation time model.
我们提出了用于微观尺度流动的格子玻尔兹曼（LB）模型模拟的介观流体-壁面相互作用模型。对于有限克努森数下的泊肃叶流，获得了具有 Bhatnagar-Gross-Krook 碰撞算子的 LB 方程滑移速度的精确解。通过对克努森数的一致定义，发现采用标准 D2Q9 格式的 LB 方程的滑移系数比具有相同边界条件的玻尔兹曼方程的滑移系数略大，这使得标准 LB 方法仅在小克努森数时保持定量准确。通过修改非平衡能量通量或引入有效弛豫时间，分析表明 LB 方法能够在克努森数的二阶范围内再现滑移现象。对于标准 LB 方法，只有通过修改弛豫动力学（如在有效弛豫时间模型中）才能捕捉到克努森层。
