Guo Xiuya, Chai Zhenhua, Pang Shengyong, Zhao Yong, Shi Baochang
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. 2019 Jun;99(6-1):063316. doi: 10.1103/PhysRevE.99.063316.
In this work, a mixed bounce-back boundary scheme of general propagation lattice Boltzmann (GPLB) model is proposed for isotropic advection-diffusion equations (ADEs) with Robin boundary condition, and a detailed asymptotic analysis is also conducted to show that the present boundary scheme for the straight walls has a second-order accuracy in space. In addition, several numerical examples, including the Helmholtz equation in a square domain, the diffusion equation with sinusoidal concentration gradient, one-dimensional transient ADE with Robin boundary and an ADE with a source term, are also considered. The results indicate that the numerical solutions agree well with the analytical ones, and the convergence rate is close to 2.0. Furthermore, through adjusting the two parameters in the GPLB model properly, the present boundary scheme can be more accurate than some existing lattice Boltzmann boundary schemes.
在这项工作中，针对具有罗宾边界条件的各向同性平流扩散方程（ADEs），提出了一种广义传播格子玻尔兹曼（GPLB）模型的混合反弹边界格式，并进行了详细的渐近分析，以表明所提出的直壁边界格式在空间上具有二阶精度。此外，还考虑了几个数值例子，包括方形域中的亥姆霍兹方程、具有正弦浓度梯度的扩散方程、具有罗宾边界的一维瞬态ADE以及具有源项的ADE。结果表明，数值解与解析解吻合良好，收敛速率接近2.0。此外，通过适当调整GPLB模型中的两个参数，所提出的边界格式可以比一些现有的格子玻尔兹曼边界格式更精确。
