一维空间Riesz分数阶对流扩散方程的格子Boltzmann方法

doi:10.19596/j.cnki.1001-246x.8318

摘要/Abstract

摘要：

建立格子Boltzmann方法（LBM）的D1Q3演化模型，研究一类Riesz空间分数阶对流扩散方程的数值求解问题。对分数阶微积分算子中的积分项离散化处理，得到逼近的标准对流扩散方程。结合Taylor展式和Chapman-Enskog多尺度展开技术得到模型的各个方向上的平衡态分布函数，通过D1Q3演化模型正确恢复所要求解的宏观方程。数值算例验证该方法的有效性。

关键词: Riesz空间分数阶对流扩散方程, 格子Boltzmann方法, Chapman-Enskog展开

Abstract:

A D1Q3 evolution model of lattice Boltzmann method (LBM) is established to numerically solve a class of spatial fractional convection-diffusion equation in Riesz sense. By discretizing the integral term of fractional order operator, the fractional convection-diffusion equation is transformed into a standard one with Riesz derivative. With Taylor expansion, Chapman-Enskog and multi-scales expansion, equilibrium distribution functions of the model are derived in all directions. Furthermore, the macroscopic equation to be solved is recovered correctly. Finally, numerical experiments are carried out to verify the model.

Key words: Riesz spatial fractional convection-diffusion equation, lattice Boltzmann method, Chapman-Enskog expansion

中图分类号:

O241.82

魏雪丹, 戴厚平, 李梦军, 郑洲顺. 一维空间Riesz分数阶对流扩散方程的格子Boltzmann方法[J]. 计算物理, 2021, 38(6): 683-692.

Xuedan WEI, Houping DAI, Mengjun LI, Zhoushun ZHENG. Lattice Boltzmann Method for One-dimensional Riesz Spatial Fractional Convection-Diffusion Equations[J]. Chinese Journal of Computational Physics, 2021, 38(6): 683-692.

图/表 15

参考文献 32

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T	GRE	CPU/s
0.1	8.360 8×10^-4	0.12
0.3	2.485 3×10^-3	0.18
0.5	4.089 1×10^-3	0.23
0.8	6.427 8×10^-3	0.31
1	7.948 4×10^-3	0.37

T	GRE	CPU/s
0.1	8.360 8×10^-4	0.12
0.3	2.485 3×10^-3	0.18
0.5	4.089 1×10^-3	0.23
0.8	6.427 8×10^-3	0.31
1	7.948 4×10^-3	0.37

β	GRE
0.1	8.663 6×10^-4
0.3	7.875 1×10^-4
0.5	7.128 5×10^-4
0.7	6.365 5×10^-4
0.9	5.634 8×10^-4

β	GRE
0.1	8.663 6×10^-4
0.3	7.875 1×10^-4
0.5	7.128 5×10^-4
0.7	6.365 5×10^-4
0.9	5.634 8×10^-4

T	GRE	MAE
0.1	7.335 1×10^-4	2.310 2×10^-6
0.2	2.097 0×10^-3	8.476 8×10^-6
0.4	4.735 2×10^-3	7.851 2×10^-5
0.8	9.664 9×10^-3	5.866 0×10^-4
1.6	1.912 3×10^-3	4.466 4×10^-3