Chai Zhenhua, Shi Baochang, Zhan Chengjie
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China.
Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan 430074, China.
Phys Rev E. 2022 Nov;106(5-2):055305. doi: 10.1103/PhysRevE.106.055305.
In this paper, a multiple-distribution-function lattice Boltzmann method (MDF-LBM) with a multiple-relaxation-time model is proposed for incompressible Navier-Stokes equations which are considered as coupled convection-diffusion equations. Through direct Taylor expansion analysis, we show that the Navier-Stokes equations can be recovered correctly from the present MDF-LBM, and additionally, it is also found that the velocity and pressure can be directly computed through the zero and first-order moments of the distribution function. Then in the framework of the present MDF-LBM, we develop a locally computational scheme for the velocity gradient in which the first-order moment of the nonequilibrium distribution is used; this scheme is also extended to calculate the velocity divergence, strain rate tensor, shear stress, and vorticity. Finally, we also conduct some simulations to test the MDF-LBM and find that the numerical results not only agree with some available analytical and numerical solutions but also have a second-order convergence rate in space.
本文针对被视为耦合对流扩散方程的不可压缩纳维-斯托克斯方程，提出了一种具有多松弛时间模型的多分布函数格子玻尔兹曼方法（MDF-LBM）。通过直接泰勒展开分析，我们表明当前的MDF-LBM能够正确恢复纳维-斯托克斯方程，此外，还发现速度和压力可通过分布函数的零阶和一阶矩直接计算。然后在当前MDF-LBM的框架下，我们开发了一种用于速度梯度的局部计算方案，其中使用了非平衡分布的一阶矩；该方案还被扩展用于计算速度散度、应变率张量、剪应力和涡度。最后，我们还进行了一些模拟来测试MDF-LBM，发现数值结果不仅与一些现有的解析解和数值解一致，而且在空间上具有二阶收敛率。
