多相流系统的离散玻尔兹曼研究进展

许爱国; 陈杰; 宋家辉; 陈大伟; 陈志华

doi:10.7638/kqdlxxb-2021.0021

欢迎来到能源电力期刊网！

English Version 期刊登录

您当前的位置：

首页 >

文章列表页 >

多相流系统的离散玻尔兹曼研究进展

专栏——多相流研究进展及应用 | 更新时间：2026-05-28

- 多相流系统的离散玻尔兹曼研究进展
- Progress of discrete Boltzmann study on multiphase complex flows
- 空气动力学学报 2021年39卷第3期页码：138-169
- 作者机构：
  
  1. 北京应用物理与计算数学研究所,北京,100088
  2. 北京大学应用物理与技术研究中心和高能量密度物理数值模拟教育部重点实验室,北京,100871
  3. 北京理工大学爆炸科学与技术国家重点实验室,北京,100081
  4. 南京理工大学瞬态物理国家重点实验室,南京,210094
  5. 北京理工大学宇航学院,北京,100081
- 作者简介：
  
  许爱国*（1970-），男，山东人，研究员，研究方向：理论物理，物理力学.E-mail：Xu_Aiguo@iapcm.ac.cn
- 基金信息：
  
  国家自然科学基金（11772064，11702028）;中国工程物理研究院创新发展基金创新项目（CX2019033）;计算物理国防重点实验室稳定支持项目（W2018-05）;爆炸科学与技术国家重点实验室开放课题（KFJJ21-16M）
- DOI：10.7638/kqdlxxb-2021.0021
  中图分类号： O359;O411.3
- 纸质出版：2021
- 稿件说明：
移动端阅览
许爱国, 陈杰, 宋家辉, 等. 多相流系统的离散玻尔兹曼研究进展[J]. 空气动力学学报, 2021, 39(3): 138−169.

XU Aiguo, CHEN Jie, SONG Jiahui, et al. Progress of discrete Boltzmann study on multiphase complex flows[J]. 2021, 39(3): 138-169.
许爱国, 陈杰, 宋家辉, 等. 多相流系统的离散玻尔兹曼研究进展[J]. 空气动力学学报, 2021, 39(3): 138−169. DOI： 10.7638/kqdlxxb-2021.0021

XU Aiguo, CHEN Jie, SONG Jiahui, et al. Progress of discrete Boltzmann study on multiphase complex flows[J]. 2021, 39(3): 138-169. DOI： 10.7638/kqdlxxb-2021.0021.

摘要

针对多相复杂流体系统模拟研究，简要介绍从格子气模型到离散玻尔兹曼方法的发展历程。从统计物理学基本原理出发，通过粗粒化建模思路，给出玻尔兹曼方程；分析Chapman-Enskog多尺度展开方法所蕴含的测量逐步细化的物理图像，给出离散玻尔兹曼建模的基本原则和主要步骤。简要介绍离散玻尔兹曼在相分离、燃烧、流体不稳定性等系统中的应用。对于多相复杂流体系统的动理学建模，技术关键是分子间作用力和化学反应贡献的引入。不同颜色的示踪粒子的引入，使得在单流体理论框架下即可实现混合过程中物质粒子来源的确定；示踪粒子在其速度相空间的分布所形成的结构蕴含丰富的流场信息，为复杂流场研究张开一个全新的视角。在多介质情形，离散玻尔兹曼建模与动理学宏观建模的对应关系是一对多。随着系统非平衡程度加深，相对于动理学宏观建模与模拟思路，离散玻尔兹曼建模与模拟的复杂度上升速度较慢。作为系统行为粗粒化描述的一种物理模型构建方法，离散玻尔兹曼根据研究需求，选取一个视角，研究系统的一组动理学性质，因而要求描述这组性质的动理学矩在模型简化过程中保值；是动理学直接建模方法的一种，为连续介质建模失效或物理功能不足、而分子动力学方法因适用尺度受限而无能为力的介尺度情形提供了一条方便、有效的研究途径。

Abstract

The development of lattice gas model to discrete Boltzmann method is briefly introduced for modeling multiphase complex fluid systems. Based on the basic principles of statistical physics

the Boltzmann equation is given through the idea of coarse-grained modeling. The physical images of progressively refined measurements contained in the Chapman-Enskog multi-scale expansion method are analyzed

and the basic principles and main steps of Discrete Boltzmann Modeling (DBM) are given. The applications of discrete Boltzmann in phase separation

combustion and hydrodynamic instability systems are briefly reviewed. For the kinetic modeling of multiphase complex fluid systems

the key techniques are the introduction of intermolecular forces and the contribution of chemical reactions. The introduction of tracer particles of different colors makes it possible to determine the source of material particles in the mixing process under the framework of single-fluid theory. The structure formed by the distribution of tracer particles in their velocity space contains rich flow field information

which opens a new perspective for the study of complex flow field. In the case of multi-media

the correspondence between discrete Boltzmann modeling and Kinetic Macro Modeling (KMM) is one-to-several

where KMM means that to derive the macroscopic model equations from kinetic theory. As the degree of non-equilibrium of the system deepens

the complexity of discrete Boltzmann modeling and simulation increases more slowly than that of KMM and simulation. As a coarse-grained physical modeling method

discrete Boltzmann selects a perspective to study a set of kinetic properties of the system according to research requirements

so it is required that the kinetic moments describing this set of properties maintain their values in the process of model simplification. It provides a convenient and effective way to investigate the mesoscale situations where continuum modeling fails or physical functions are insufficient and molecular dynamics method is unable to do so due to the limited applicable scale.

关键词

Keywords

references

ALDER B J, WAINWRIGHT T E. Phase Transition for a Hard Sphere System[J]. Journal of Chemical Physics, 1957, 27(5): 1208-1209.

ALDER B J, WAINWRIGHT T E. Studies in Molecular Dynamics. I. General Method[J]. The Journal of Chemical Physics, 1959, 31(2): 459-466.

RAHMAN A. Correlations in the Motion of Atoms in Liquid Argon[J]. Physical Review, 1964, 136(2A): A405--A411.

RYCKAERT J P, CICCOTTI G, BERENDSEN H J C. Numerical integration of the cartesian equations of motion of a system with constraints: molecular dynamics of n-alkanes[J]. Journal of Computational. Physics, 1977, 23(3): 327-341.

ANDERSEN H C. Molecular dynamics simulations at constant pressure and/or temperature[J]. The Journal of Chemical Physics, 1980, 72(4): 2384-2393.

PARRINELLO M, RAHMAN A. Crystal Structure and Pair Potentials: A Molecular-Dynamics Study[J]. Physical review letters, 1980, 45(14): 1196-1199.

CAR R, PARRINELLO M. Unified Approach for Molecular Dynamics and Density-Functional Theory[J]. Physical Review Letters, 1985, 55(22): 2471.

CAGIN T, PETTITT B M. Grand Molecular Dynamics: A Method for Open Systems[J]. Molecular Simulation, 1991, 6(1-3): 5-26.

KARBALAEI A, KUMAR R, CHO H J. Thermocapillarity in Microfluidics—A Review[J]. Micromachines, 2016, 7(1): 13.

CRISTINI V, TAN Y C. Theory and numerical simulation of droplet dynamics in complex flows--a review[J]. Lab on A Chip, 2004, 4(4): 257-264.

TEZDUYAR T E. Interface-tracking and interface-capturing techniques for finite element computation of moving boundaries and interfaces[J]. Computer Methods in Applied Mechanics and Engineering, 2006, 195(23/24): 2983-3000.

SZEWC K, POZORSKI J, MINIER J P. Simulations of single bubbles rising through viscous liquids using Smoothed Particle Hydrodynamics[J]. International Journal of Multiphase Flow, 2013, 50(Complete): 98-105.

JACQMIN D. Calculation of Two-Phase Navier–Stokes Flows Using Phase-Field Modeling[J]. Journal of Computational Physics, 1999, 155(1): 96-127.

GUNSTENSEN A K, ROTHMAN D H, ZALESKI S, et al. Lattice Boltzmann model of immiscible fluids[J]. Physical Review A, 1991, 43(8): 4320-4327.

SHAN X W, CHEN H D. Lattice Boltzmann model for simulating flows with multiple phases and components[J]. Physical Review E, 1993, 47(3): 1815-1819.

SWIFT M R, OSBORN W R, YEOMANS J M. Lattice Boltzmann Simulation of Non-Ideal Fluids[J]. Physical Review Letters, 1995, 75(5): 830-833.

HE X Y, CHEN S Y, ZHANG R Y. A Lattice Boltzmann Scheme for Incompressible Multiphase Flow and Its Application in Simulation of Rayleigh–Taylor Instability[J]. Journal of Computational Physics, 1999, 152(2): 642-663.

GONNELLA G, LAMURA A, SOFONEA V. Lattice Boltzmann simulation of thermal nonideal fluids[J]. Physical Review E, 2007, 76(3): 036703.

LI Q, LUO K H, KANG Q J, et al. Lattice Boltzmann methods for multiphase flow and phase-change heat transfer[J]. Progress in Energy and Combustion Science, 2016, 52: 62-105.

LI Q, LUO K H, GAO Y J, et al. Additional interfacial force in lattice Boltzmann models for incompressible multiphase flows[J]. Physical Review E, 2012, 85(2): 026704.

SUN D K, ZHU M F, WANG J, et al. Lattice Boltzmann modeling of bubble formation and dendritic growth in solidification of binary alloys[J]. International Journal of Heat and Mass Transfer, 2016, 94(MAR.): 474-487.

MILLER W, SUCCI S, MANSUTTI D. Lattice Boltzmann Model for Anisotropic Liquid-Solid Phase Transition[J]. Physical Review Letters, 2001, 86(16): 3578.

SUCCI S. The lattice Boltzmann equation for fluid dynamics and beyond[M]. Oxford: Oxford univeristy press, 2001.

HE Y L, WANG Y, LI Q. Lattice Boltzmann method: Theory and applications[M]. Beijing: Science Press, 2009(in Chinese).

GUO Z L, ZHENG C G. Theory and applications of lattice Boltzmann method[M]. Beijing: Science Press, 2009(in Chinese).

HUANG H B, SUKOP M C, LU X Y. Multiphase lattice Boltzmann methods: Theory and application[M], John Wiley Sons, Ltd, 2015.

XU A G, ZHANG G C, YING Y J. Progress of discrete Boltzmann modeling and simulation of combustion system[J]. Acta Physica Sinica, 2015, 64(18): 35-60.

XU A G, ZHANG G C, ZHANG Y D. Discrete Boltzmann modeling of compressible flows, Chapter 2[M]//KYZAS G Z, MITROPOULOS A C, edited. Kinetic Theory. Croatia: InTech, 2018.

XU A G, ZHANG G C, GAN Y B, et al. Lattice Boltzmann modeling and simulation of compressible flows[J]. Frontiers of Physics, 2012, 7(5): 582-600.

XU A G, LIN C D, ZHANG G C, et al. Multiple-relaxation-time lattice Boltzmann kinetic model for combustion[J]. Physical Review E, 2015, 91(4): 043306.

XU A G, ZHANG G C, YING Y J, et al. Complex fields in heterogeneous materials under shock: modeling, simulation and analysis[J]. Science China Physics, 2016, 59(5): 650501.

LIN C D, LUO K H. Discrete Boltzmann modeling of unsteady reactive flows with nonequilibrium effects[J]. Physical Review E, 2019, 99(1): 012142.

GAN Y B, XU A G, ZHANG G C, et al. Discrete Boltzmann trans-scale modeling of high-speed compressible flows[J]. Physical Review E, 2018, 97(5): 053312.

ZHANG Y D, XU A G, ZHANG G C, et al. Discrete Boltzmann method for non-equilibrium flows: Based on Shakhov model[J]. Computer Physics Communications, 2019, 238: 50-65.

LEE T D, YANG C N. Statistical Theory of Equations of State and Phase Transitions. II. Lattice Gas and Ising Model[J]. Physical Review, 1952, 87(3): 410--419.

NIE X B. A two-dimensional lattice gas model for compressible fluid simulation[D]. Bei Jing: Institute of Applied Physics and Computational Mathematics, 1988(in Chinese).

CHOPARD B, DROZ M. Cellular automata modeling of physical systems[M]. Cambridge: Cambridge University Press, 1998.

FRISCH U, HASSLACHER B, POMEAU Y. Lattice-Gas Automata for the Navier-Stokes Equation[J]. Physical Review Letters, 1986, 56(14): 1505-1508.

BHATNAGAR P L, GROSS E P, KROOK M. A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems[J]. Physical Review, 1954, 94(3): 511--525.

HOLWAY, L H. New Statistical Models for Kinetic Theory: Methods of Construction[J]. Physics of Fluids, 1966, 9(9): 1658-1673.

SHAKHOV E M. Generalization of the Krook kinetic relaxation equation[J]. Fluid Dynamics, 1968, 3(5): 142-145.

LARINA I N, RYKOV V A. Kinetic model of the Boltzmann equation for a diatomic gas with rotational degrees of freedom[J]. Computational Mathematics and Mathematical Physics, 2010, 50(12): 2118-2130.

LIU G J. A method for constructing a model form for the Boltzmann equation[J]. Physics of Fluids A, 1990, 2(2): 277-280.

ZHANG Y D, XU A G, ZHANG G C, et al. Entropy production in thermal phase separation: a kinetic-theory approach[J]. Soft Matter, 2019, 15(10): 2245-2259.

ONUKI A. Phase transition dynamics[M]. Cambridge: Cambridge University Press, 2002.

张玉东. 非平衡流与多相流的建模与研究基于离散Boltzmann方法[D]. 南京: 南京理工大学, 2019.

KLIMONTOVICH Y L. Kinetic theory of nonideal gases nonideal plasmas[M]. Oxford: Pergamon, 1982.

CARNAHAN N F, STARLING K E. Equation of State of Non Attracting Rigid Spheres[J]. The Journal of Chemical Physics, 1969, 51(2): 635-636.

XU A G, ZHANG G C, LI Y J, et al. Modeling and Simulation of Nonequilibrium and Multiphase Complex Systems -Lattice Boltzmann kinetic Theory and Application[J]. Progress in Physics, 2014, 34(03): 136-167.

ZHANG D J, XU A G, ZHANG Y D, et al. Two-fluid discrete Boltzmann model for compressible flows: Based on ellipsoidal statistical Bhatnagar–Gross–Krook[J]. Physics of Fluids, 2020, 32(12): 126110.

ANDRIES P, AOKI K, PERTHAME B. A consistent BGK-type model for gas mixtures[J]. Journal of Statistical Physics, 2002, 106(5-6): 993-1018.

HAACK J R, HAUCK C D, MURILLO M S. A Conservative, Entropic Multispecies BGK Model[J]. Journal of Statistical Physics, 2017, 168(9): 1-31.

LAI H L, XU A G, ZHANG G C, et al. Non-equilibrium thermo-hydrodynamic effects on the Rayleigh-Taylor instability in compressible flows[J]. Physical Review E, 2016, 94(2): 023106.

LI D M, LAI H L, XU A G, et al. Discrete Boltzmann simulation of Rayleigh-Taylor instability in compressible flows[J]. Acta Physica Sinica, 2018, 067(008): 080501.

CHEN F, XU A G, ZHANG G C. Viscosity, heat conductivity, and Prandtl number effects in the Rayleigh-Taylor Instability[J]. Frontiers of Physics, 2016, 11(6): 114703.

GAN Y B, XU A G, ZHANG G C, et al. Nonequilibrium and morphological characterizations of Kelvin-Helmholtz instability in compressible flows[J]. Frontiers of Physics, 2019, 4(14): 83-99.

XU A G, ZHANG G C, PAN X F, et al. Morphological characterization of shocked porous material[J]. Journal of Physics D Applied Physics, 2009, 42(7): 075409.

GAN Y B, XU A G, ZHANG G C, et al. Phase separation in thermal systems: A lattice Boltzmann study and morphological characterization[J]. Physical Review E, 2011, 84(4): 046715.

GAN Y B, XU A G, ZHANG G C, et al. Lattice Boltzmann study on Kelvin-Helmholtz instability: the roles of velocity and density gradients[J]. Physical Review E, 2010, 83(2): 056704.

LIN C D, XU A G, ZHANG G C, et al. Discrete Boltzmann modeling of Rayleigh-Taylor instability in two-component compressible flows[J]. Physical Review E, 2017, 96(5): 053305.

CHEN F, XU A G, ZHANG G C. Collaboration and Competition Between Richtmyer-Meshkov instability and Rayleigh-Taylor instability[J]. Physics of Fluids, 2018, 30(10): 102105.

CHEN F, XU A G, ZHANG Y D, et al. Morphological and non-equilibrium analysis of coupled Rayleigh–Taylor–Kelvin–Helmholtz instability[J]. Physics of Fluids, 2020, 32(10): 104111.

GAN Y B, XU A G, ZHANG G C, et al. Lattice Boltzmann study of thermal phase separation: Effects of heat conduction, viscosity and Prandtl number[J]. EPL, 2012, 97(4): 44002.

GAN Y B, XU A G, ZHANG G C, et al. Discrete Boltzmann modeling of multiphase flows: hydrodynamic and thermodynamic non-equilibrium effects[J]. Soft Matter, 2015, 11: 5336-5345.

XU A G, ZHANG G C, GAN Y B. Progress in studies on discrete Boltzmann modeling of phase separation process[J]. Mechanics in engineering, 2016, 38(4): 361-374.

YAN B, XU A G, ZHANG G C, et al. Lattice Boltzmann model for combustion and detonation[J]. Frontiers of Physics, 2013, 8(1): 94-110.

LIN C D, XU A G, ZHANG G C, et al. Polar Coordinate Lattice Boltzmann Kinetic Modeling of Detonation Phenomena[J]. Communications in Theoretical Physics, 2014, 62(5): 737-748.

LIN C D, XU A G, ZHANG G C, et al. Double-distribution-function discrete Boltzmann model for combustion[J]. Combustion and Flame, 2016, 164: 137-151.

ZHANG Y D, XU A G, ZHANG G C, et al. Kinetic modeling of detonation and effects of negative temperature coefficient[J]. Combustion and Flame, 2016, 173: 483-492.

LIN C D, LUO K H, FEI L, et al. A multi-component discrete Boltzmann model for nonequilibrium reactive flows[J]. Scientific Reports, 2017, 7(1): 14580.

LIN C D, LUO K H. MRT discrete Boltzmann method for compressible exothermic reactive flows[J]. Computers and Fluids, 2018, 166: 176-183.

LIN C D, LUO K H. Mesoscopic Simulation of Nonequilibrium Detonation With Discrete Boltzmann Method[J]. Combustion and Flame, 2018, 198: 356-362.

ZHANG Y D, XU A G, ZHANG G C, et al. A One-Dimensional Discrete Boltzmann Model for Detonation and an Abnormal Detonation Phenomenon[J]. Communications in Theoretical Physics, 2019, 71: 117-126.

LIN C D, LUO K H. Kinetic Simulation of Unsteady Detonation with Thermodynamic Nonequilibrium Effects[J]. Combustion Explosion and Shock Waves, 2020, 56(4): 435-443.

LIU H, KANG W, ZHANG Q, et al. Molecular dynamics simulations of microscopic structure of ultra strong shock waves in dense helium[J]. Frontiers of Physics, 2016, 11(6): 1-11. DOI:10.1007/s11467-016-0590-5

LIU H, ZHANG Y, KANG W, et al. Molecular dynamics simulation of strong shock waves propagating in dense deuterium, taking into consideration effects of excited electrons[J]. Physical Review E, 2017, 95(2-1): 023201. DOI:10.1103/PhysRevE.95.023201

LIU H, KANG W, DUAN H L, et al. Recent progresses on numerical investigations of microscopic structure of strong shock waves in fluid[J]. Scientia Sinica (Physica,Mechanica Astronomica), 2017, 47(7): 19-27.(in Chinese)

浏览量

下载量

CSCD

文章被引用时，请邮件提醒。

提交

工具集

关联资源

多模态瑞利-泰勒不稳定性的离散玻尔兹曼数值研究

旋翼跨介质飞行气动特性与机理仿真分析

广义守恒相场简化多相流格子Boltzmann方法

风吹雪多相流运动及其在寒区雪水文中的应用

分子气体稀薄效应的动理学建模