Lin Yuxin, Hong Ning, Shi Baochang, Chai Zhenhua
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China.
School of General Education, Wuchang University of Technology, Wuhan 430223, China.
Phys Rev E. 2021 Jul;104(1-2):015312. doi: 10.1103/PhysRevE.104.015312.
In this paper, we first present a multiple-relaxation-time lattice Boltzmann (MRT-LB) model for one-dimensional diffusion equation where the D1Q3 (three discrete velocities in one-dimensional space) lattice structure is considered. Then through the theoretical analysis, we derive an explicit four-level finite-difference scheme from this MRT-LB model. The results show that the four-level finite-difference scheme is unconditionally stable, and through adjusting the weight coefficient ω_{0} and the relaxation parameters s_{1} and s_{2} corresponding to the first and second moments, it can also have a sixth-order accuracy in space. Finally, we also test the four-level finite-difference scheme through some numerical simulations and find that the numerical results are consistent with our theoretical analysis.
在本文中，我们首先针对一维扩散方程提出了一种多松弛时间格子玻尔兹曼（MRT-LB）模型，其中考虑了D1Q3（一维空间中的三个离散速度）格子结构。然后通过理论分析，我们从该MRT-LB模型推导出了一种显式四级有限差分格式。结果表明，该四级有限差分格式是无条件稳定的，并且通过调整与一阶和二阶矩对应的权重系数ω₀以及松弛参数s₁和s₂，它在空间上还可以具有六阶精度。最后，我们还通过一些数值模拟对该四级有限差分格式进行了测试，发现数值结果与我们的理论分析一致。
