Multi-block Local Mesh Refinement Method for LBM with Inversion of Distribution Function

doi:10.19596/j.cnki.1001-246x.8797

Abstract

Abstract:

In response to the complex coupling calculation of LBM (lattice Boltzmann method) local mesh refinement, a method of inverting macroscopic physical quantities to obtain particle distribution functions is proposed to avoid conversion of distribution functions. By rewriting the Boltzmann equation, the relationship (depends on Knudsen number) inside the distribution function is derived, and the inversion calculation equation of the distribution function is given. Based on this, a new multi-block mesh refinement algorithm is designed, and its performance is verified by applying the algorithm to an example. The results show that the algorithm can display the numerical characteristics of the flow field under different Reynolds numbers, and the streamline graph is continuous and complete. The position of the vortex center in the flow field obtained is consistent with literature data. This algorithm can be used for flow field simulations and provides guidance for the development of local mesh refinement.

Key words: lattice Boltzmann method, multi-block mesh, inversion of distribution function, local mesh refinement

CLC Number:

O351.3

Rupu WEI, Peng DING. Multi-block Local Mesh Refinement Method for LBM with Inversion of Distribution Function[J]. Chinese Journal of Computational Physics, 2024, 41(5): 643-650.

Figures/Tables 8

References 21

1	郭照立, 郑楚光. 格子Boltzmann方法的原理及应用[M]. 北京: 科学出版社, 2009.
2	LIN C L , LAI Y G . Lattice Boltzmann method on composite grids[J]. Physical Review E, 2000, 62 (2): 2219- 2225. DOI
3	赵玉龙, 刘香禺, 张烈辉, 等. 基于格子Boltzmann方法的非常规天然气微尺度流动基础模型[J]. 石油勘探与开发, 2021, 48 (1): 156- 165.
4	冯玲玲, 徐洪涛, 王迪, 等. 活性炭吸附甲醛的格子Boltzmann模拟[J]. 计算物理, 2021, 38 (1): 69- 78.
5	魏雪丹, 戴厚平, 李梦军, 等. 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.
6	张浏斌, 单彦广, 戎志成. 基于LBM的均匀电场池沸腾单气泡动力学模拟[J]. 计算物理, 2022, 39 (5): 537- 548.
7	杨子韬. 多层自适应网格的格子Boltzmann方法研究及其应用[D]. 上海: 上海大学, 2021.
8	BORAEY M A . An asymptotically adaptive successive equilibrium relaxation approach for the accelerated convergence of the lattice Boltzmann method[J]. Applied Mathematics and Computation, 2019, 353, 29- 41. DOI
9	FILIPPOVA O , HÄNEL D . Grid refinement for Lattice-BGK models[J]. Journal of Computational Physics, 1998, 147 (1): 219- 228. DOI
10	DUPUIS A , CHOPARD B . Theory and applications of an alternative lattice Boltzmann grid refinement algorithm[J]. Physical Review E, 2003, 67 (6 Pt 2): 066707.
11	王兴勇, 索丽生, 程永光, 等. 双重网格的Lattice Boltzmann方法[J]. 河海大学学报(自然科学版), 2003, 31 (1): 5- 10.
12	郭照立, 施保昌, 王能超. 基于区域分裂的非均匀Lattice Boltzmann方法[J]. 计算物理, 2001, 18 (2): 181- 184.
13	YU Dazhi , MEI Renwei , SHYY W . A multi-block lattice Boltzmann method for viscous fluid flows[J]. International Journal for Numerical Methods in Fluids, 2002, 39 (2): 99- 120. DOI
14	孙丽萍, 陆程, 王志凯, 等. 格子玻尔兹曼法多块网格的交界结构优化研究[J]. 计算力学学报, 2019, 36 (1): 13- 20.
15	LAGRAVA D , MALASPINAS O , LATT J , et al. Advances in multi-domain lattice Boltzmann grid refinement[J]. Journal of Computational Physics, 2012, 231 (14): 4808- 4822.
16	QIAN Y H , D'HUMIÈRES D , LALLEMAND P . Lattice BGK models for Navier-Stokes equation[J]. Europhysics Letters, 1992, 17 (6): 479.
17	何雅玲, 王勇, 李庆. 格子Boltzmann方法的理论及应用[M]. 北京: 科学出版社, 2009.
18	THORIMBERT Y , LAGRAVA D , MALASPINAS O , et al. Local mesh refinement sensor for the lattice Boltzmann method[J]. Journal of Computational Science, 2022, 64, 101864.
19	GHIA U , GHIA K N , SHIN C T . High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method[J]. Journal of Computational Physics, 1982, 48 (3): 387- 411.
20	VANKA S P . Block-implicit multigrid solution of Navier-Stokes equations in primitive variables[J]. Journal of Computational Physics, 1986, 65 (1): 138- 158.
21	HOU Shuling , ZOU Qisu , CHEN Shiyi , et al. Simulation of cavity flow by the lattice Boltzmann method[J]. Journal of Computational Physics, 1995, 118 (2): 329- 347.

Re		左下涡		右下涡
Re		x	y	x	y
100	Ref.[19]	0.031 3	0.039 1	0.945 3	0.062 5
	Ref.[20]	0.037 5	0.031 3	0.937 5	0.056 3
	Ref.[21]	0.039 2	0.035 3	0.945 1	0.062 7
	局部加密算法	0.033 7	0.033 6	0.941 9	0.061 6
1 000	Ref.[19]	0.085 9	0.078 1	0.859 4	0.109 4
	Ref.[20]	0.075 0	0.081 3	0.862 5	0.106 3
	Ref.[21]	0.090 2	0.078 4	0.866 7	0.113 7
	局部加密算法	0.084 3	0.076 0	0.874 4	0.110 4
5 000	Ref.[19]	0.070 3	0.136 7	0.808 6	0.074 2
	Ref.[20]	0.062 5	0.156 3	0.850 0	0.081 3
	Ref.[21]	0.078 4	0.137 3	0.807 8	0.074 5
	局部加密算法	0.072 7	0.138 5	0.828 0	0.075 1

Re		左下涡		右下涡
Re		x	y	x	y
100	Ref.[19]	0.031 3	0.039 1	0.945 3	0.062 5
	Ref.[20]	0.037 5	0.031 3	0.937 5	0.056 3
	Ref.[21]	0.039 2	0.035 3	0.945 1	0.062 7
	局部加密算法	0.033 7	0.033 6	0.941 9	0.061 6
1 000	Ref.[19]	0.085 9	0.078 1	0.859 4	0.109 4
	Ref.[20]	0.075 0	0.081 3	0.862 5	0.106 3
	Ref.[21]	0.090 2	0.078 4	0.866 7	0.113 7
	局部加密算法	0.084 3	0.076 0	0.874 4	0.110 4
5 000	Ref.[19]	0.070 3	0.136 7	0.808 6	0.074 2
	Ref.[20]	0.062 5	0.156 3	0.850 0	0.081 3
	Ref.[21]	0.078 4	0.137 3	0.807 8	0.074 5
	局部加密算法	0.072 7	0.138 5	0.828 0	0.075 1

数据传递次数	迭代误差值
数据传递次数	数据传递前	数据传递后
1	3.285 338×10^-4	1.434 647×10^-3
2	1.549 239×10^-4	1.167 056×10^-3
3	1.152 190×10^-4	1.054 449×10^-3
4	9.959 176×10^-5	1.010 602×10^-3

数据传递次数	迭代误差值
数据传递次数	数据传递前	数据传递后
1	3.285 338×10^-4	1.434 647×10^-3
2	1.549 239×10^-4	1.167 056×10^-3
3	1.152 190×10^-4	1.054 449×10^-3
4	9.959 176×10^-5	1.010 602×10^-3

[1]	Xiwen WANG, Xuemin YE, Dan LI, Chunxi LI. Three-dimensional Lattice Boltzmann Method Simulation of A Large Droplet Impacting A Small Sphere with Different Wettability [J]. Chinese Journal of Computational Physics, 2024, 41(2): 172-181.
[2]	Ming GAO, Lu CHEN, Jia LIANG, Dongmin WANG, Yugang ZHAO, Lixin ZHANG, Quan SUN, Haojie LI. LBM Simulation of Two Droplets Merging and Bouncing at the Top of an Inclined Plane with a Wetting Gradient [J]. Chinese Journal of Computational Physics, 2023, 40(3): 333-342.
[3]	Shuting FENG, Houping DAI, Tongzheng SONG. Lattice Boltzmann Method for Two-dimensional Fractional Reaction-Diffusion Equations [J]. Chinese Journal of Computational Physics, 2022, 39(6): 666-676.
[4]	Liubin ZHANG, Yanguang SHAN, Zhicheng RONG. Single Bubble Dynamics in Pool Boiling Under Uniform Electric Field: LBM Simulation [J]. Chinese Journal of Computational Physics, 2022, 39(5): 537-548.
[5]	Jiaxin LIU, Lin ZHENG, Beihao ZHANG. Entropy Generation in Double-diffusive Natural Convection in a Square Porous Enclosure: Lattice Boltzmann Method [J]. Chinese Journal of Computational Physics, 2022, 39(5): 549-563.
[6]	Pin-liang LIN, Huan-huan FENG, Yu-hong DONG. Analysis of Flow Field Around a Cylinder with Porous Media Layer [J]. Chinese Journal of Computational Physics, 2022, 39(4): 418-426.
[7]	Qiao-ling ZHANG, He-fang JING. Flow Patterns in Three-dimensional Lid-driven Cavities with Curved Boundary: MRT-LBM Study [J]. Chinese Journal of Computational Physics, 2022, 39(4): 427-439.
[8]	Lu CHEN, Ming GAO, Jia LIANG, Dongmin WANG, Yugang ZHAO, Lixin ZHANG. Droplet Upward Movement on an Inclined Surface Under Wetting Gradient: Lattice Boltzmann Simulation [J]. Chinese Journal of Computational Physics, 2021, 38(6): 672-682.
[9]	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.
[10]	Jiangtao ZHENG, Ninghong JIA, Huifang HU, Yong YANG, Yang JU, Moran WANG. Study on Liquid-Liquid Spontaneous Imbibition Dynamics in Bifurcated Channels [J]. Chinese Journal of Computational Physics, 2021, 38(5): 543-554.
[11]	Qin LOU, Sheng TANG, Haoyuan WANG. Numerical Simulation of Bubble Dynamics in Porous Media with a Lattice Boltzmann Large Density Ratio Model [J]. Chinese Journal of Computational Physics, 2021, 38(3): 289-300.
[12]	Jia LIANG, Ming GAO, Lu CHEN, Dongmin WANG, Lixin ZHANG. Lattice Boltzmann Study of a Droplet Impinging on a Stationary Droplet on a Fixed Wall Surface with Different Wettability [J]. Chinese Journal of Computational Physics, 2021, 38(3): 313-323.
[13]	YUAN Junjie, YE Xin, SHAN Yanguang. Natural Convection in Triangular Cavity Filled with Nanofluid: Lattice Boltzmann Simulation [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2021, 38(1): 57-68.
[14]	ZHAO Ming, WANG Ke, YU Duanmin. Ruelle-Takens Chaotic Natural Convection in a Horizontal Annulus with an Internally Slotted Circle [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2020, 37(6): 667-676.
[15]	WANG Jianyi, PAN Zhenhai, WU Huiying. Numerical Study of Inertial Focusing Behavior of Ellipsoidal Particles in a Microchannel [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2020, 37(6): 677-686.