[1]张鸿雁,姜继鼎,朱洪宇,等.基于能量均分原理的微颗粒布朗运动LBM模拟[J].西安建筑科技大学学报(自然科学版),2017,49(04):561-564,584.[doi:10.15986/j.1006-7930.2017.04.016]
　ZHANG Hongyan,JIANG Jiding,ZHU Hongyu,et al.LBM simulation of microparticle brownian motion based on the energy equipartition principle[J].J. Xi’an Univ. of Arch. & Tech.(Natural Science Edition),2017,49(04):561-564,584.[doi:10.15986/j.1006-7930.2017.04.016]
点击复制

基于能量均分原理的微颗粒布朗运动LBM模拟()
分享到：

西安建筑科技大学学报（自然科学版）[ISSN:1006-7930/CN:61-1295/TU]

卷:
49
期数:
2017年04期
页码:
561-564,584
栏目:
出版日期:
2017-09-10

文章信息/Info

Title:
LBM simulation of microparticle brownian motion based on the energy equipartition principle
文章编号:
1006-7930(2017)04-0561-04
作者:
张鸿雁; 姜继鼎; 朱洪宇; 崔海航; 陈力
(西安建筑科技大学 环境与市政工程学院,陕西 西安 710055)
Author(s):
ZHANG Hongyan;  JIANG Jiding;  ZHU Hongyu;  CUI Haihang;  CHEN Li
(School of Environment and Municipal Engineering, Xian Univ. of Arch . & Tech ., Xian 710055, China)
关键词:
布朗运动; 格子Boltzmann方法; Ghost Fluid; 郎之万方程
Keywords:
Brownian motion;  lattice Boltzmann method;  Ghost Fluid;  Langevin equation
分类号:
O359
DOI:
10.15986/j.1006-7930.2017.04.016
文献标志码:
A
摘要:
基于格子Boltzmann方法（LBM）结合Ghost Fluid边界格式和格线反弹格式建立了模拟微颗粒布朗运动的动力学模型，在不添加能量方程的情况下，利用能量均分原理对郎之万方程中的布朗力直接执行修正，相对于涨落LBM模型大幅降低了计算量，降低了LBM的人工压缩性和等温假设带来的误差，提高了计算精度.本文模拟了二维圆型颗粒和三维球型颗粒的布朗运动，结果表明，采用该方法模拟所得颗粒运动的平动温度与转动温度均可以达到稳定的热平衡，且与周围流体的温度基本一致，颗粒运动的均方位移与观察时间间隔符合实验结果和理论解，验证了该方法的可行性与准确性
Abstract:
This paper built a dynamic model for the simulation of micro -particles Brownian motion, which combined the lattice Boltzmann method(LBM) and a Ghost Fluid / Link-bounce-back boundary scheme. Without the addition of the energy equation, the Brownian force in the Langevin equation was directly corrected by the energy equipartition principle . With the premise of ensuring the accuracy and reducing the compressibility of error, this means greatly reduced the price of computation relative to fluctuation LB method . The article simulated a Brownian motion of two -dimensional circular particle and three-dimensional spherical particles. The results showed that the translational temperature and rotational temperature of micro -particle motion using the method could satisfy stable thermal equilibrium, and agree with the temperature of surrounding fluid eventually. The mean square displacement of the particle motion and the observation time interval satisfied the Einstein relation . The method was proved to be reasonable and practicable

参考文献/References:

References

[1]HIDA T. Brownian motion [J]. Applications of Mathematics, 1980, 11: 44 -113.

[2]ZHANG J, KWOK D Y. Lattice boltzmann method (LBM) [M]. New York:Springer, 2015.

[3]LADD A J C. Short -time motion of colloidal particles: Numerical simulation via a fluctuating lattice-Boltzmann equation[J]. Physical Review Letters, 1993, 70(9): 1339 -1342.

[4]聂德明. 颗粒沉降及其在流场中做布朗运动的研究[D]. 杭州: 浙江大学, 2011.

NIE D M. Research on the particles sedimentation and Brownian motion [D]. Hangzhou:Zhejiang University,2011 .

[5]TIWARI A, VANKA S P. A ghost fluid Lattice Boltzmann method for complex geometries [J]. International Journal for Numerical Methods in Fluids, 2011, 69(2):481 -498.

[6]QIAN Y H, HUMIERES D, LALLEMAND P. Lattice BGK models for Navier-Stokes equation[J]. Euro physics Letters, 1992, 17(6): 479 -484.

[7]LADD A J. Numerical simulations of particulate suspensions via a discretized Boltzmann equation.Part 1 . Theoretical foundation [J]. Journal of Fluid Mechanics, 1994, 271(1):285 -309，83

[8]TSENG Y H, FERZIGER J H. A ghost -cell immersed boundary method for flow in complex geometry[J]. Journal of Computational Physics, 2003, 192(2): 593 -623.

[9]EINSTEIN A. Investigations on the theory of the Brownian movement [M]. Mineola, New York: Dover Publications, 1956: 19 -34.

备注/Memo

备注/Memo:
收稿日期:2016-04-08修改稿日期:2017-07-15
基金项目:国家自然科学基金应急管理项目理论物理专款(11447133)；国家自然科学基金青年基金(11602187)；陕西省教育厅专项科研计划(15JK1385)；陕西省自然科学基础研究计划青年人才项目(2016JQ1008)
第一作者:张鸿雁(1961-)，女，博士，教授，主要从事环境流体力学方面的研究， E -mail: zhanghongyan@xauat.edu.cn
通讯作者:陈力(1985-)，男，博士，讲师，主要从事环境流体力学方面的研究．E-mail: jasonchencl@163.com
更新日期/Last Update: 2017-09-11