搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

燃烧系统的离散Boltzmann建模与模拟研究进展

许爱国 张广财 应阳君

引用本文:
Citation:

燃烧系统的离散Boltzmann建模与模拟研究进展

许爱国, 张广财, 应阳君

Progess of discrete Boltzmann modeling and simulation of combustion system

Xu Ai-Guo, Zhang Guang-Cai, Ying Yang-Jun
PDF
导出引用
  • 燃烧系统的诸多模拟依托于流体建模, 离散Boltzmann方法(discrete Boltzmann method, DBM) 是近年来发展起来的一种新的流体介观建模方法. 本文简要评述DBM发展的两个方向Navier-Stokes等偏微分方程的数值逼近解法和复杂系统的微介观动理学建模. 主要介绍在燃烧系统模拟方面DBM已有的工作、新近的思路、与传统流体建模的异同以及近期的研究成果. 本文重点传递的信息为: 作为复杂系统微介观动理学建模出现的DBM在模拟过程中同时给出流动及其相伴随的、关系最密切的那部分热动非平衡效应; 它为燃烧等复杂系统中各类非平衡行为的描述、非平衡信息的提取、非平衡程度的度量提供了一种简洁、有效的方法; 它所提供的热动非平衡测量量有两类: 一类是直接比较分布函数和平衡态分布函数的动理学矩关系得到的, 一类是来自于Chapman-Enskog多尺度分析给出的热传导和黏性项. 基于第二类DBM, 可以实现(燃烧等)一大类复杂流体系统的多尺度物理建模.
    Detonation is a kind of self-propagating supersonic combustion where the chemical reaction is rapid and violent under an extreme condition. The leading part of a detonation front is pre-shocked by a strong shock wave propagating into the explosive and triggering chemical reaction. The combustion system can be regarded as a kind of chemical reactive flow system. Therefore, the fluid modeling plays an important role in the studies on combustion and detonation phenomena. The discrete Boltzmann method (DBM) is a kind of new fluid modeling having quickly developed in recent thirty years. In this paper we review the progress of discrete Boltzmann modeling and simulation of combustion phenomena. Roughly speaking, the discrete Boltzmann models can be further classified into two categories. In the first category the DBM is regarded as a kind of new scheme to numerically solve partial differential equations, such as the Navier-Stokes equations, etc. In the second category the DBM works as a kind of novel mesoscopic and coarse-grained kinetic model for complex fluids. The second kind of DBM aims to probe the trans- and supercritical fluid behaviors or to study simultaneously the hydrodynamic non-equilibrium (HNE) and thermodynamic non-equilibrium (TNE) behaviors. It has brought significant new physical insights into the systems and promoted the development of new methods in the fields. For example, new observations on fine structures of shock and detonation waves have been obtained; The intensity of TNE has been used as a physical criterion to discriminate the two stages, spinodal decomposition and domain growth, in phase separation; Based on the feature of TNE, some new front-tracking schemes have been designed. Since the goals are different, the criteria used to formulate the two kinds of models are significantly different, even though there may be considerable overlaps between them. Correspondingly, works in discrete Boltzmann modeling and simulation of combustion systems can also be classified into two categories in terms of the two kinds of models. Up to now, most of existing works belong to the first category where the DBM is used as a kind of alternative numerical scheme. The first DBM for detonation [Yan, et al. 2013 Front. Phys. 8 94] appeared in 2013. It is also the first work aiming to investigate both the HNE and TNE in the combustion system via DBM. In this review we focus mainly on the development of the second kind of DBM for combustion, especially for detonation. A DBM for combustion in polar-coordinates [Lin, et al. 2014 Commun. Theor. Phys. 62 737] was designed in 2014. It aims to investigate the nonequilibrium behaviors in implosion and explosion processes. Recently, the multiple-relaxation-time version of DBM for combustion [Xu, et al. 2015 Phys. Rev. E 91 043306] was developed. As an initial application, various non-equilibrium behaviors around the detonation wave in one-dimensional detonation process were preliminarily probed. The following TNE behaviors, exchanges of internal kinetic energy between different displacement degrees of freedom and between displacement and internal degrees of freedom of molecules, have been observed. It was found that the system viscosity (or heat conductivity) decreases the local TNE, but increases the global TNE around the detonation wave. Even locally, the system viscosity (or heat conductivity) results in two competing trends, i.e. to increase and decrease the TNE effects. The physical reason is that the viscosity (or heat conductivity) takes part in both the thermodynamic and hydrodynamic responses to the corresponding driving forces. The ideas to formulate DBM with the smallest number of discrete velocities and DBM with flexible discrete velocity model are presented. As a kind of new modeling of combustion system, mathematically, the second kind of DBM is composed of the discrete Boltzmann equation(s) and a phenomenological reactive function; physically, it is equivalent to a hydrodynamic model supplemented by a coarse-grained model of the TNE behaviors. Being able to capture various non-equilibrium effects and being easy to parallelize are two features of the second kind of DBM. Some more realistic DBMs for combustion are in progress. Combustion process has an intrinsic multi-scale nature. Typical time scales cover a wide range from 10-13 to 10-3 second, and typical spatial scales cover a range from 10-10 to 1 meter. The hydrodynamic modeling and microscopic molecular dynamics have seen great achievements in combustion simulations. But for problems relevant to the mesoscopic scales, where the hydrodynamic modeling is not enough to capture the nonequilibrium behaviors and the molecular dynamics simulation is not affordable, the modeling and simulation are still keeping challenging. Roughly speaking, there are two research directions in accessing the mesoscopic behaviors. One direction is to start from the macroscopic scale to smaller ones, the other direction is to start from the microscopic scale to larger ones. The idea of second kind of DBM belongs to that of the first direction. It will contribute more to the studies on the nonequilibrium behaviors in combustion phenomena.
      通信作者: 许爱国, Xu_Aiguo@iapcm.ac.cn
    • 基金项目: 计算物理重点实验室基金、国家自然科学基金(批准号: 11475028, 11202003)、理论物理国家重点实验室(中国科学院理论物理研究所)开放课题(批准号: Y4KF151CJ1)和爆炸科学与技术国家重点实验室(北京理工大学)开放课题(批准号: KFJJ14-1M)资助的课题.
      Corresponding author: Xu Ai-Guo, Xu_Aiguo@iapcm.ac.cn
    • Funds: Project supported by the Science Foundations of National Laboratory for Science and Technology on Computational Physics, the National Natural Science Foundation of China (Grant Nos. 11475028, 11202003), the Open Project Program of State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences (Grant No. Y4KF151CJ1), and the Opening Project of State Key Laboratory of Explosion Science and Technology (Beijing Institute of Technology) (Grant No. KFJJ14-1M).
    [1]

    Ju Y 2014 Adv. Mech. 44 201402

    [2]

    Chu S, Majumdar A 2012 Nature 488 294

    [3]

    Jangsawang W, Fungtammasan B, Kerdsuwan S 2005 Energ. Convers. Manage. 46 3137

    [4]

    Schott G L 1965 Phys. Fluids 8 850

    [5]

    Bykovskii F A, Zhdan S A, Vedernikov E F 2006 Journal of Propulsion and Power 22 1204

    [6]

    Ju Y, Maruta K 2011 Progress in Energy and Combustion Science 37 669

    [7]

    Fernandez-Pello A C 2002 Proceedings of the Combustion Institute 29 883

    [8]

    Sabourin J L, Dabbs D M, Yetter R A, Dryer F L, Aksay I A 2009 ACS Nano 3 3945

    [9]

    Ohkura Y, Rao P M, Zheng X 2011 Combust. Flame 158 2544

    [10]

    Dec J E 2009 Proc. Combust. Inst. 32 2727

    [11]

    Starikovskiy A, Aleksandrov N 2012 Progress in Energy and Combustion Science 39 61

    [12]

    Uddi M, Jiang N, Mintusov E, Adamovich I V, Lempert W R 2009 Proceedings of the Combustion Institute 32 929

    [13]

    Sun W, Chen Z, Gou X, Ju Y 2010 Combust. Flame 157 1298

    [14]

    Won S H, Windom B, Jiang B, Ju Y 2014 Combust. Flame 161 475

    [15]

    Ombrello T, Qin X, Ju Y, Gutsol A, Fridman A, Carter C 2006 AIAA Journal 44 142

    [16]

    Sun W, Uddi M, Won S H, Ombrello T, Carter C, Ju Y 2012 Combust. Flame 159 221

    [17]

    Sun W, Ju Y 2013 J Plasma Fusion Res. 89 208

    [18]

    Chapman D L 1899 Philos. Mag. 47 90

    [19]

    Jouguet E J 1905 J. Math. Pures Appl. 1 347

    [20]

    Zeldovich Ya B 1940 J. Exp. Theor. Phys. 10 542

    [21]

    von Neumann J 1942 Theory of Detonation Waves (New York: Macmillan)

    [22]

    Doering W 1943 Ann. Phys. 43 421

    [23]

    Fickett W, Davis W C 2000 Detonation: Theory and Experiment (Mineola, New York: Dover Publications, INC.)

    [24]

    Chen Z 2009 Ph. D Dissertation (Princeton: Princeton University)

    [25]

    Dai P, Chen Z, Chen S, Ju Y 2015 Proc. Combust. Inst. 35 3045

    [26]

    Yu H, Han W, Santner J, Gou X, Sohn C H, Ju Y, Chen Z 2014 Combust. Flame 161 2815

    [27]

    Bai B, Chen Z, Zhang H, Chen S 2013 Combust. Flame 160 2810

    [28]

    Ren Z Y, Lu Z, Hou L Y, Lu L 2014 Sci. China: Phys. Mech. Astron. 57 1495

    [29]

    Huang X F, Li S J, Zhou D H, Zhao G J, Wang G Q, Xu J R 2014 Acta Phys. Sin. 63 178802(in Chinese) [黄雪峰, 李盛姬, 周东辉, 赵冠军, 王关晴, 徐江荣 2014 物理学报 63 178802]

    [30]

    Yang J C, Xia Z X, Hu J X 2013 Acta Phys. Sin. 62 074701(in Chinese) [杨晋朝, 夏智勋, 胡建新 2013 物理学报 62 074701]

    [31]

    Shi Y B, Ying Y J, Li J H 2007 Acta Phys. Sin. 56 6911(in Chinese) [施研博, 应阳君, 李金虹 2007 物理学报 56 6911]

    [32]

    Benzi R, Succi S, Vergassola M 1992 Phys. Reports 222 145

    [33]

    Succi S 2001 The Lattice Boltzmann Equation for Fluid Dynamics and Beyond (New York: Oxford University Press)

    [34]

    Succi S, Karlin I V, Chen H 2002 Rev. Mod. Phys. 74 1203

    [35]

    Chen H, Kandasamy S, Orszag S, Shock R, Succi S, Yakhot V 2003 Science 301 633

    [36]

    Xu A, Zhang G, Gan Y, Chen F, Yu X 2012 Front. Phys. 7 582

    [37]

    Xu A G, Zhang G C, Li Y J, Li H 2014 Prog. Phys. 34 136(in Chinese) [许爱国, 张广财, 李英骏, 李华 2014 物理学进展 34 136]

    [38]

    Guo Z, Shu C 2013 Lattice Boltzmann Method and Its Applications in Engineering (advances in computational fluid dynamics) (Sigapore: World Scientific Publishing Company)

    [39]

    Chen S 2010 Non-equilibrium Statistical Mechanics (Beijing: Scientific Press) (in Chinese) [陈式刚 编著 2010 非平衡统计力学(北京: 科学出版社)]

    [40]

    Shokhov E M 1968 Fluid Dyn. 3 95

    [41]

    Bhatnagar L, Gross E P, Krook M 1954 Phys. Rev. 94 511

    [42]

    Holway Jr L H 1966 Phys. Fluids (1958-1988) 9 1658

    [43]

    Rykov V A 1975 Fluid Dyn. 10 959

    [44]

    Liu G 1990 Phys. Fluids A: Fluid Dyn. (1989-1993) 2 277

    [45]

    Frisch U, Hasslacher B, Pomeau Y 1986 Phys. Rev. Lett. 56 1505

    [46]

    Koelman J 1991 EPL 15 603

    [47]

    Chen S, Chen H, Martinez D, Matthaeus W 1991 Phys. Rev. Lett. 67 3776

    [48]

    Qian Y, d’Humieres D, Lallemand P 1992 EPL 17 479

    [49]

    He X Y, Luo L S 1997 Phys. Rev. E 55 R6333

    [50]

    Nie X B 1988 M.S. Dissertation (Beijing: Graduate School, China Academy of Engineering Physics) (in Chinese) [聂小波 1988 硕士学位论文(北京: 中国工程物理研究院研究生部)]

    [51]

    MeNamara G R, Zanetti G 1988 Phys. Rev. Lett. 61 2332

    [52]

    Higuera F L, Jimenez J 1989 EPL 9 663

    [53]

    He Y L, Wang Y, Li Q 2009 Lattice Boltzmann Method: Theory and Applications (Beijing: Scientific Press) (in Chinese) [何雅玲, 王勇, 李庆 2009 格子Boltzmann 方法的理论及应用 (北京: 科学出版社)]

    [54]

    Yan B 2013 Ph. D. Dissertation (Changchun: Jilin University) (in Chinese) [闫铂 2013 博士学位论文(长春: 吉林大学)]

    [55]

    Gonnella G, Orlandini E, Yeomans J M 1997 Phys. Rev. Lett. 78 1695

    [56]

    Denniston C, Yeomans J M 2001 Phys. Rev. Lett. 87 275505

    [57]

    Toth G, Denniston C, Yeomans Y M 2002 Phys. Rev. Lett. 88 105504

    [58]

    Shan X, Chen H 1993 Phys. Rev. E 47 1815

    [59]

    Chen S, Doolen G D 1998 Annu. Rev. Fluid Mech. 30 329

    [60]

    Kang Q, Zhang D, Chen S, He X 2002 Phys. Rev. E 65 036318

    [61]

    Fang H, Wang Z, Lin Z, Liu M 2002 Phys. Rev. E 65 051925

    [62]

    Dawson S, Chen S, Doolen G D 1993 J. Chem. Phys. 98 1514

    [63]

    Weimar J R, Boon J P 1996 Physica A 224 207

    [64]

    Zhang R, Xu Y, Wen B, Sheng N, Fang H 2014 Sci. Reports 4 5738

    [65]

    Chen S, Martinez D, Mei R 1996 Phys. Fluids 8 2527

    [66]

    Lai H, Ma C 2011 Phys. Rev. E 84 046708

    [67]

    Xu A, Gonnella G, Lamura A 2006 Phys. Rev. E 74 011505

    [68]

    Xu A, Gonnella G, Lamura A, Amati G, Massaioli F 2005 EPL 71 651

    [69]

    Xu A, Gonnella G, Lamura A 2006 Physica A 362 42

    [70]

    Xu A, Gonnella G, Lamura A 2004 Physica A 344 750

    [71]

    Xu A, Gonnella G, Lamura A 2004 Physica A 331 10

    [72]

    Xu A, Gonnella G, Lamura A 2003 Phys. Rev. E 67 056105

    [73]

    Gan Y, Xu A, Zhang G, Li Y 2012 Front. Phys. 7 481

    [74]

    Gan Y, Xu A, Zhang G, Li Y 2012 Commun. Theore. Phys. 57 681

    [75]

    Gan Y, Xu A, Zhang G, Wang J, Yu X, Yang Y 2014 Int. J. Mod. Phys. C 25 1441002

    [76]

    Gan Y, Xu A, Zhang G, Li Y 2011 Phys. Rev. E 83 056704

    [77]

    Gan Y, Xu A, Zhang G, Zhang P, Li Y 2012 EPL 97 44002

    [78]

    Gan Y, Xu A, Zhang G, Li Y, Li Y 2011 Phys. Rev. E 84 046715

    [79]

    Chen F, Xu A, Zhang G, Li Y 2011 Phys. Lett. A 375 2129

    [80]

    Pan X F, Xu A, Zhang G, Jiang S 2007 Int. J. Mod. Phys. C 18 1747

    [81]

    Yan B, Xu A, Zhang G, Ying Y, Li H 2013 Front. Phys. 8 94

    [82]

    Lin C, Xu A, Zhang G, Li Y 2014 Commun. Theor. Phys. 62 737

    [83]

    Xu A, Lin C, Zhang G, Li Y 2015 Phys. Rev. E 91 043306

    [84]

    Xu A, Zhang G, Gan Y 2014 arXiv:1403.3744

    [85]

    Gan Y, Xu A, Zhang G, Succi S 2015 Soft Matter 11 5336

    [86]

    Chen F, Xu A, Zhang G, Wang Y 2014 Front Phys. 9 246

    [87]

    Lin C, Xu A, Zhang G, Li Y, Succi S 2014 Phys. Rev. E 89 013307

    [88]

    Lai H 2015 Postdoctoral Research Report (Beijing: Institute of Applied Physics and Computational Mathematics) (in Chinese) [赖惠林 2015 博士后出站报告(北京: 应用物理与计算数学研究所)]

    [89]

    Lai H, Xu A, Zhang G, Gan Y, Ying Y, Succi S 2015 arXiv:1507.01107

    [90]

    Gan Y B, Xu A G, Zhang G C 2015 Guest Professor Research Report (Beijing: Institute of Applied Physics and Computational Mathematics) (in Chinese) [甘延标, 许爱国, 张广财 2015 Kelvin-Helmholtz不稳定性的离散Boltzmann建模、模拟与非平衡效应研究 (北京: 北京应用物理与计算数学研究所客座研究报告)]

    [91]

    Succi S, Bella G, Papetti F 1997 J. Sci. Comput. 12 395

    [92]

    Filippova O, Hanel D 1998 Int. J. Mod. Phys. C 9 1439

    [93]

    Filippova O, Hanel D 2000 J. Comput. Phys. 158 139

    [94]

    Filippova O, Hanel D 2000 Comput. Phys. Commun. 129 267

    [95]

    Yu H, Luo L, Girimaji S 2002 Int. J. Comput. Eng. Sci. 3 73

    [96]

    Yamamoto K, He X, Doolen G 2002 J. Stat. Phys. 107 367

    [97]

    Yamamoto K 2003 Int. J. Mod. Phys. B 17 197

    [98]

    Yamamoto K, Takada N, Misawa M 2005 Proc. Comb. Inst. 30 1509

    [99]

    Lee T, Lin C, Chen L 2006 J. Comput. Phys. 215 133

    [100]

    Chiavazzo E, Karlin I V, Gorban A N, Boulouchos K 2009 J. Stat. Mech.: Theory and Experiment P06013

    [101]

    Chiavazzo E, Karlin I V, Gorban A N, Boulouchos K 2010 Combust. Flame 157 1833

    [102]

    Chiavazzo E, Karlin IV, Gorban A N, Boulouchos K 2011 Int.J. Numerical Methods for Heat & Fluid Flow 21 494

    [103]

    Chen S, Liu Z, Zhang C, He Z, Tian Z, Shi B, Zheng C 2007 Appl. Math. Comput. 193 266

    [104]

    Chen S, Liu Z, Tian Z, Shi B, Zheng C 2008 Comput. Math. Appl. 55 1424

    [105]

    Chen S, Krafczyk M 2009 Int. J. Therm. Sci. 48 1978

    [106]

    Chen S 2010 Int. J. Hydrogen Energ. 35 1401

    [107]

    Chen S, Li J, Han H, Liu Z, Zheng C 2010 Int. J. Hydrogen Energ. 35 3891

    [108]

    Chen S, Han H, Liu Z, Li J, Zheng C 2010 Int. J. Hydrogen. Energ. 35 4736

    [109]

    Chen S, Zheng C 2011 Int. J. Hydrogen Energ. 36 15403

    [110]

    Chen S, Mi J, Liu H, Zheng C 2012 Int. J. Hydrogen. Energ. 37 5234

    [111]

    Sun J S, Zhu J S 1995 Theoretical Explosion Physics (Beijing: National Defense Industry Press) (in Chinese) [孙锦山, 朱建士 1995 理论爆轰物理(北京: 国防工业出版社)]

    [112]

    Cochran S G, Chan J 1979 Lawrence Livermore National Laboratory Report UCID-18024

    [113]

    Lee E L, Tarver C M 1980 Phys. Fluids 23 2362

    [114]

    Gou X, Sun W, Chen Z, Ju Y 2010 Combust. Flame 157 1111

    [115]

    Pan X, Xu A, Zhang G, Jiang S 2007 Int. J. Mod. Phys. C 18 1747

    [116]

    Gan Y, Xu A, Zhang G, Yu X, Li Y 2008 Physica A 387 1721

    [117]

    Chen F, Xu A, Zhang G, Li Y, Succi S 2010 EPL 90 54003

    [118]

    Chen F, Xu A, Zhang G, Li Y 2011 Commun. Theore. Phys. 55 325

    [119]

    Gan Y, Xu A, Zhang G, Yang Y 2013 EPL 103 24003

    [120]

    Chen F, Xu A, Zhang G, Li Y 2011 Commun. Theore. Phys. 56 333

    [121]

    Chen F, Xu A, Zhang G, Li Y 2011 Theore. & Appl. Mech. Lett. 1 052004

    [122]

    Gan Y, Xu A, Zhang G, Li Y 2011 Commun. Theore. Phys. 56 490

    [123]

    Chen F, Xu A, Zhang G, Li Y 2011 Commun. Theore. Phys. 55 325

    [124]

    Lin C, Xu A, Zhang G, Li Y 2014 arXiv:1405.5500

  • [1]

    Ju Y 2014 Adv. Mech. 44 201402

    [2]

    Chu S, Majumdar A 2012 Nature 488 294

    [3]

    Jangsawang W, Fungtammasan B, Kerdsuwan S 2005 Energ. Convers. Manage. 46 3137

    [4]

    Schott G L 1965 Phys. Fluids 8 850

    [5]

    Bykovskii F A, Zhdan S A, Vedernikov E F 2006 Journal of Propulsion and Power 22 1204

    [6]

    Ju Y, Maruta K 2011 Progress in Energy and Combustion Science 37 669

    [7]

    Fernandez-Pello A C 2002 Proceedings of the Combustion Institute 29 883

    [8]

    Sabourin J L, Dabbs D M, Yetter R A, Dryer F L, Aksay I A 2009 ACS Nano 3 3945

    [9]

    Ohkura Y, Rao P M, Zheng X 2011 Combust. Flame 158 2544

    [10]

    Dec J E 2009 Proc. Combust. Inst. 32 2727

    [11]

    Starikovskiy A, Aleksandrov N 2012 Progress in Energy and Combustion Science 39 61

    [12]

    Uddi M, Jiang N, Mintusov E, Adamovich I V, Lempert W R 2009 Proceedings of the Combustion Institute 32 929

    [13]

    Sun W, Chen Z, Gou X, Ju Y 2010 Combust. Flame 157 1298

    [14]

    Won S H, Windom B, Jiang B, Ju Y 2014 Combust. Flame 161 475

    [15]

    Ombrello T, Qin X, Ju Y, Gutsol A, Fridman A, Carter C 2006 AIAA Journal 44 142

    [16]

    Sun W, Uddi M, Won S H, Ombrello T, Carter C, Ju Y 2012 Combust. Flame 159 221

    [17]

    Sun W, Ju Y 2013 J Plasma Fusion Res. 89 208

    [18]

    Chapman D L 1899 Philos. Mag. 47 90

    [19]

    Jouguet E J 1905 J. Math. Pures Appl. 1 347

    [20]

    Zeldovich Ya B 1940 J. Exp. Theor. Phys. 10 542

    [21]

    von Neumann J 1942 Theory of Detonation Waves (New York: Macmillan)

    [22]

    Doering W 1943 Ann. Phys. 43 421

    [23]

    Fickett W, Davis W C 2000 Detonation: Theory and Experiment (Mineola, New York: Dover Publications, INC.)

    [24]

    Chen Z 2009 Ph. D Dissertation (Princeton: Princeton University)

    [25]

    Dai P, Chen Z, Chen S, Ju Y 2015 Proc. Combust. Inst. 35 3045

    [26]

    Yu H, Han W, Santner J, Gou X, Sohn C H, Ju Y, Chen Z 2014 Combust. Flame 161 2815

    [27]

    Bai B, Chen Z, Zhang H, Chen S 2013 Combust. Flame 160 2810

    [28]

    Ren Z Y, Lu Z, Hou L Y, Lu L 2014 Sci. China: Phys. Mech. Astron. 57 1495

    [29]

    Huang X F, Li S J, Zhou D H, Zhao G J, Wang G Q, Xu J R 2014 Acta Phys. Sin. 63 178802(in Chinese) [黄雪峰, 李盛姬, 周东辉, 赵冠军, 王关晴, 徐江荣 2014 物理学报 63 178802]

    [30]

    Yang J C, Xia Z X, Hu J X 2013 Acta Phys. Sin. 62 074701(in Chinese) [杨晋朝, 夏智勋, 胡建新 2013 物理学报 62 074701]

    [31]

    Shi Y B, Ying Y J, Li J H 2007 Acta Phys. Sin. 56 6911(in Chinese) [施研博, 应阳君, 李金虹 2007 物理学报 56 6911]

    [32]

    Benzi R, Succi S, Vergassola M 1992 Phys. Reports 222 145

    [33]

    Succi S 2001 The Lattice Boltzmann Equation for Fluid Dynamics and Beyond (New York: Oxford University Press)

    [34]

    Succi S, Karlin I V, Chen H 2002 Rev. Mod. Phys. 74 1203

    [35]

    Chen H, Kandasamy S, Orszag S, Shock R, Succi S, Yakhot V 2003 Science 301 633

    [36]

    Xu A, Zhang G, Gan Y, Chen F, Yu X 2012 Front. Phys. 7 582

    [37]

    Xu A G, Zhang G C, Li Y J, Li H 2014 Prog. Phys. 34 136(in Chinese) [许爱国, 张广财, 李英骏, 李华 2014 物理学进展 34 136]

    [38]

    Guo Z, Shu C 2013 Lattice Boltzmann Method and Its Applications in Engineering (advances in computational fluid dynamics) (Sigapore: World Scientific Publishing Company)

    [39]

    Chen S 2010 Non-equilibrium Statistical Mechanics (Beijing: Scientific Press) (in Chinese) [陈式刚 编著 2010 非平衡统计力学(北京: 科学出版社)]

    [40]

    Shokhov E M 1968 Fluid Dyn. 3 95

    [41]

    Bhatnagar L, Gross E P, Krook M 1954 Phys. Rev. 94 511

    [42]

    Holway Jr L H 1966 Phys. Fluids (1958-1988) 9 1658

    [43]

    Rykov V A 1975 Fluid Dyn. 10 959

    [44]

    Liu G 1990 Phys. Fluids A: Fluid Dyn. (1989-1993) 2 277

    [45]

    Frisch U, Hasslacher B, Pomeau Y 1986 Phys. Rev. Lett. 56 1505

    [46]

    Koelman J 1991 EPL 15 603

    [47]

    Chen S, Chen H, Martinez D, Matthaeus W 1991 Phys. Rev. Lett. 67 3776

    [48]

    Qian Y, d’Humieres D, Lallemand P 1992 EPL 17 479

    [49]

    He X Y, Luo L S 1997 Phys. Rev. E 55 R6333

    [50]

    Nie X B 1988 M.S. Dissertation (Beijing: Graduate School, China Academy of Engineering Physics) (in Chinese) [聂小波 1988 硕士学位论文(北京: 中国工程物理研究院研究生部)]

    [51]

    MeNamara G R, Zanetti G 1988 Phys. Rev. Lett. 61 2332

    [52]

    Higuera F L, Jimenez J 1989 EPL 9 663

    [53]

    He Y L, Wang Y, Li Q 2009 Lattice Boltzmann Method: Theory and Applications (Beijing: Scientific Press) (in Chinese) [何雅玲, 王勇, 李庆 2009 格子Boltzmann 方法的理论及应用 (北京: 科学出版社)]

    [54]

    Yan B 2013 Ph. D. Dissertation (Changchun: Jilin University) (in Chinese) [闫铂 2013 博士学位论文(长春: 吉林大学)]

    [55]

    Gonnella G, Orlandini E, Yeomans J M 1997 Phys. Rev. Lett. 78 1695

    [56]

    Denniston C, Yeomans J M 2001 Phys. Rev. Lett. 87 275505

    [57]

    Toth G, Denniston C, Yeomans Y M 2002 Phys. Rev. Lett. 88 105504

    [58]

    Shan X, Chen H 1993 Phys. Rev. E 47 1815

    [59]

    Chen S, Doolen G D 1998 Annu. Rev. Fluid Mech. 30 329

    [60]

    Kang Q, Zhang D, Chen S, He X 2002 Phys. Rev. E 65 036318

    [61]

    Fang H, Wang Z, Lin Z, Liu M 2002 Phys. Rev. E 65 051925

    [62]

    Dawson S, Chen S, Doolen G D 1993 J. Chem. Phys. 98 1514

    [63]

    Weimar J R, Boon J P 1996 Physica A 224 207

    [64]

    Zhang R, Xu Y, Wen B, Sheng N, Fang H 2014 Sci. Reports 4 5738

    [65]

    Chen S, Martinez D, Mei R 1996 Phys. Fluids 8 2527

    [66]

    Lai H, Ma C 2011 Phys. Rev. E 84 046708

    [67]

    Xu A, Gonnella G, Lamura A 2006 Phys. Rev. E 74 011505

    [68]

    Xu A, Gonnella G, Lamura A, Amati G, Massaioli F 2005 EPL 71 651

    [69]

    Xu A, Gonnella G, Lamura A 2006 Physica A 362 42

    [70]

    Xu A, Gonnella G, Lamura A 2004 Physica A 344 750

    [71]

    Xu A, Gonnella G, Lamura A 2004 Physica A 331 10

    [72]

    Xu A, Gonnella G, Lamura A 2003 Phys. Rev. E 67 056105

    [73]

    Gan Y, Xu A, Zhang G, Li Y 2012 Front. Phys. 7 481

    [74]

    Gan Y, Xu A, Zhang G, Li Y 2012 Commun. Theore. Phys. 57 681

    [75]

    Gan Y, Xu A, Zhang G, Wang J, Yu X, Yang Y 2014 Int. J. Mod. Phys. C 25 1441002

    [76]

    Gan Y, Xu A, Zhang G, Li Y 2011 Phys. Rev. E 83 056704

    [77]

    Gan Y, Xu A, Zhang G, Zhang P, Li Y 2012 EPL 97 44002

    [78]

    Gan Y, Xu A, Zhang G, Li Y, Li Y 2011 Phys. Rev. E 84 046715

    [79]

    Chen F, Xu A, Zhang G, Li Y 2011 Phys. Lett. A 375 2129

    [80]

    Pan X F, Xu A, Zhang G, Jiang S 2007 Int. J. Mod. Phys. C 18 1747

    [81]

    Yan B, Xu A, Zhang G, Ying Y, Li H 2013 Front. Phys. 8 94

    [82]

    Lin C, Xu A, Zhang G, Li Y 2014 Commun. Theor. Phys. 62 737

    [83]

    Xu A, Lin C, Zhang G, Li Y 2015 Phys. Rev. E 91 043306

    [84]

    Xu A, Zhang G, Gan Y 2014 arXiv:1403.3744

    [85]

    Gan Y, Xu A, Zhang G, Succi S 2015 Soft Matter 11 5336

    [86]

    Chen F, Xu A, Zhang G, Wang Y 2014 Front Phys. 9 246

    [87]

    Lin C, Xu A, Zhang G, Li Y, Succi S 2014 Phys. Rev. E 89 013307

    [88]

    Lai H 2015 Postdoctoral Research Report (Beijing: Institute of Applied Physics and Computational Mathematics) (in Chinese) [赖惠林 2015 博士后出站报告(北京: 应用物理与计算数学研究所)]

    [89]

    Lai H, Xu A, Zhang G, Gan Y, Ying Y, Succi S 2015 arXiv:1507.01107

    [90]

    Gan Y B, Xu A G, Zhang G C 2015 Guest Professor Research Report (Beijing: Institute of Applied Physics and Computational Mathematics) (in Chinese) [甘延标, 许爱国, 张广财 2015 Kelvin-Helmholtz不稳定性的离散Boltzmann建模、模拟与非平衡效应研究 (北京: 北京应用物理与计算数学研究所客座研究报告)]

    [91]

    Succi S, Bella G, Papetti F 1997 J. Sci. Comput. 12 395

    [92]

    Filippova O, Hanel D 1998 Int. J. Mod. Phys. C 9 1439

    [93]

    Filippova O, Hanel D 2000 J. Comput. Phys. 158 139

    [94]

    Filippova O, Hanel D 2000 Comput. Phys. Commun. 129 267

    [95]

    Yu H, Luo L, Girimaji S 2002 Int. J. Comput. Eng. Sci. 3 73

    [96]

    Yamamoto K, He X, Doolen G 2002 J. Stat. Phys. 107 367

    [97]

    Yamamoto K 2003 Int. J. Mod. Phys. B 17 197

    [98]

    Yamamoto K, Takada N, Misawa M 2005 Proc. Comb. Inst. 30 1509

    [99]

    Lee T, Lin C, Chen L 2006 J. Comput. Phys. 215 133

    [100]

    Chiavazzo E, Karlin I V, Gorban A N, Boulouchos K 2009 J. Stat. Mech.: Theory and Experiment P06013

    [101]

    Chiavazzo E, Karlin I V, Gorban A N, Boulouchos K 2010 Combust. Flame 157 1833

    [102]

    Chiavazzo E, Karlin IV, Gorban A N, Boulouchos K 2011 Int.J. Numerical Methods for Heat & Fluid Flow 21 494

    [103]

    Chen S, Liu Z, Zhang C, He Z, Tian Z, Shi B, Zheng C 2007 Appl. Math. Comput. 193 266

    [104]

    Chen S, Liu Z, Tian Z, Shi B, Zheng C 2008 Comput. Math. Appl. 55 1424

    [105]

    Chen S, Krafczyk M 2009 Int. J. Therm. Sci. 48 1978

    [106]

    Chen S 2010 Int. J. Hydrogen Energ. 35 1401

    [107]

    Chen S, Li J, Han H, Liu Z, Zheng C 2010 Int. J. Hydrogen Energ. 35 3891

    [108]

    Chen S, Han H, Liu Z, Li J, Zheng C 2010 Int. J. Hydrogen. Energ. 35 4736

    [109]

    Chen S, Zheng C 2011 Int. J. Hydrogen Energ. 36 15403

    [110]

    Chen S, Mi J, Liu H, Zheng C 2012 Int. J. Hydrogen. Energ. 37 5234

    [111]

    Sun J S, Zhu J S 1995 Theoretical Explosion Physics (Beijing: National Defense Industry Press) (in Chinese) [孙锦山, 朱建士 1995 理论爆轰物理(北京: 国防工业出版社)]

    [112]

    Cochran S G, Chan J 1979 Lawrence Livermore National Laboratory Report UCID-18024

    [113]

    Lee E L, Tarver C M 1980 Phys. Fluids 23 2362

    [114]

    Gou X, Sun W, Chen Z, Ju Y 2010 Combust. Flame 157 1111

    [115]

    Pan X, Xu A, Zhang G, Jiang S 2007 Int. J. Mod. Phys. C 18 1747

    [116]

    Gan Y, Xu A, Zhang G, Yu X, Li Y 2008 Physica A 387 1721

    [117]

    Chen F, Xu A, Zhang G, Li Y, Succi S 2010 EPL 90 54003

    [118]

    Chen F, Xu A, Zhang G, Li Y 2011 Commun. Theore. Phys. 55 325

    [119]

    Gan Y, Xu A, Zhang G, Yang Y 2013 EPL 103 24003

    [120]

    Chen F, Xu A, Zhang G, Li Y 2011 Commun. Theore. Phys. 56 333

    [121]

    Chen F, Xu A, Zhang G, Li Y 2011 Theore. & Appl. Mech. Lett. 1 052004

    [122]

    Gan Y, Xu A, Zhang G, Li Y 2011 Commun. Theore. Phys. 56 490

    [123]

    Chen F, Xu A, Zhang G, Li Y 2011 Commun. Theore. Phys. 55 325

    [124]

    Lin C, Xu A, Zhang G, Li Y 2014 arXiv:1405.5500

  • [1] 张恒, 任峰, 胡海豹. 基于格子Boltzmann方法的幂律流体二维顶盖驱动流转捩研究. 物理学报, 2021, 70(18): 184703. doi: 10.7498/aps.70.20210451
    [2] 臧益鹏, 许振宇, 黄安, 艾苏曼, 夏晖晖, 阚瑞峰. 基于改进模拟退火算法的非均匀燃烧场分布重建. 物理学报, 2021, 70(13): 134205. doi: 10.7498/aps.70.20202124
    [3] 李宁, TuXin, 黄孝龙, 翁春生. 基于Tikhonov正则化参数矩阵的激光吸收光谱燃烧场二维重建光路设计方法. 物理学报, 2020, 69(22): 227801. doi: 10.7498/aps.69.20201144
    [4] 张贝豪, 郑林. 倾斜多孔介质方腔内纳米流体自然对流的格子Boltzmann方法模拟. 物理学报, 2020, 69(16): 164401. doi: 10.7498/aps.69.20200308
    [5] 叶欢锋, 金頔, 匡波, 杨燕华. 平衡分布正值性对格子Boltzmann方法数值表现影响分析. 物理学报, 2019, 68(20): 204701. doi: 10.7498/aps.68.20190624
    [6] 娄钦, 李涛, 杨茉. 复杂微通道内气泡在浮力作用下上升行为的格子Boltzmann方法模拟. 物理学报, 2018, 67(23): 234701. doi: 10.7498/aps.67.20181311
    [7] 李德梅, 赖惠林, 许爱国, 张广财, 林传栋, 甘延标. 可压流体Rayleigh-Taylor不稳定性的离散Boltzmann模拟. 物理学报, 2018, 67(8): 080501. doi: 10.7498/aps.67.20171952
    [8] 王佐, 张家忠, 王恒. 非正交多松弛系数轴对称热格子Boltzmann方法. 物理学报, 2017, 66(4): 044701. doi: 10.7498/aps.66.044701
    [9] 臧晨强, 娄钦. 复杂微通道内非混相驱替过程的格子Boltzmann方法. 物理学报, 2017, 66(13): 134701. doi: 10.7498/aps.66.134701
    [10] 陈福振, 强洪夫, 苗刚, 高巍然. 燃料抛撒成雾及其燃烧爆炸的光滑离散颗粒流体动力学方法数值模拟研究. 物理学报, 2015, 64(11): 110202. doi: 10.7498/aps.64.110202
    [11] 史冬岩, 王志凯, 张阿漫. 任意复杂流-固边界的格子Boltzmann处理方法. 物理学报, 2014, 63(7): 074703. doi: 10.7498/aps.63.074703
    [12] 郭亚丽, 徐鹤函, 沈胜强, 魏兰. 利用格子Boltzmann方法模拟矩形腔内纳米流体Raleigh-Benard对流. 物理学报, 2013, 62(14): 144704. doi: 10.7498/aps.62.144704
    [13] 冯玉霄, 黄群星, 梁军辉, 王飞, 严建华, 池涌. 三维燃烧介质和壁面温度的非接触联合重建研究. 物理学报, 2012, 61(13): 134702. doi: 10.7498/aps.61.134702
    [14] 杨汝, 张波, 赵寿柏, 劳裕锦. 基于符号时间序列方法的开关变换器离散映射算法复杂度分析. 物理学报, 2010, 59(6): 3756-3762. doi: 10.7498/aps.59.3756
    [15] 张超英, 李华兵, 谭惠丽, 刘慕仁, 孔令江. 椭圆柱体在牛顿流体中运动的格子Boltzmann方法模拟. 物理学报, 2005, 54(5): 1982-1987. doi: 10.7498/aps.54.1982
    [16] 韩祥临. 一个燃烧模型的近似解. 物理学报, 2004, 53(12): 4061-4064. doi: 10.7498/aps.53.4061
    [17] 俞慧丹, 赵凯华. 模拟可压缩流体的格子Boltzmann模型. 物理学报, 1999, 48(8): 1470-1476. doi: 10.7498/aps.48.1470
    [18] 范安辅, 高智. 非平衡气流与化学激光的增益饱和效应. 物理学报, 1993, 42(3): 407-416. doi: 10.7498/aps.42.407
    [19] 李富斌. 用细胞自动机方法模拟计算二维流体的平衡与非平衡相关函数. 物理学报, 1992, 41(9): 1448-1451. doi: 10.7498/aps.41.1448
    [20] 庆承瑞, 周玉美. 环形非圆截面等离子体自由界面的磁流体平衡方程解. 物理学报, 1980, 29(1): 106-110. doi: 10.7498/aps.29.106
计量
  • 文章访问数:  6829
  • PDF下载量:  577
  • 被引次数: 0
出版历程
  • 收稿日期:  2015-02-04
  • 修回日期:  2015-04-02
  • 刊出日期:  2015-09-05

/

返回文章
返回