Second-order curved boundary treatments of the lattice Boltzmann method for convection-diffusion equations

作者：Huang, Juntao; Hu, Zexi; Yong, Wen-An^*

来源：Journal of Computational Physics, 2016, 310: 26-44.

DOI：10.1016/j.jcp.2016.01.008

• Lattice Boltzmann method
• Convection-diffusion equations
• Curved boundaries
• Nonlinear Robin boundary conditions
• Approximate boundary conditions
• Second-order accuracy

In this paper, we present a kind of second-order curved boundary treatments for the lattice Boltzmann method solving two-dimensional convection-diffusion equations with general nonlinear Robin boundary conditions. The key idea is to derive approximate boundary values or normal derivatives on computational boundaries, with second-order accuracy, by using the prescribed boundary condition. Once the approximate information isknown, the second-order bounce-back schemes can be perfectly adopted. Our boundary treatments are validated with a number of numerical examples. The results show the utility of our boundary treatments and very well support our theoretical predications on the second-order accuracy thereof. The idea is quite universal. It can be directly generalized to 3-dimensional problems, multiple-relaxation-time models, and the Navier-Stokes equations.

• 出版日期2016-4-1
• 单位清华大学