A multiple-relaxation-time lattice Boltzmann method for high-speed compressible flows

doi:10.1088/1674-1056/24/5/050501

中国物理B ›› 2015, Vol. 24 ›› Issue (5): 50501-050501.doi: 10.1088/1674-1056/24/5/050501

A multiple-relaxation-time lattice Boltzmann method for high-speed compressible flows

李凯, 钟诚文

National Key Laboratory of Science and Technology on Aerodynamic Design and Research, Northwestern Polytechnical University, Xi'an 710072, China

收稿日期:2014-08-16 修回日期:2014-12-29 出版日期:2015-05-05 发布日期:2015-05-05
基金资助:
Project supported by the Innovation Fund for Aerospace Science and Technology of China (Grant No. 2009200066) and the Aeronautical Science Fund of China (Grant No. 20111453012).

A multiple-relaxation-time lattice Boltzmann method for high-speed compressible flows

Li Kai (李凯), Zhong Cheng-Wen (钟诚文)

National Key Laboratory of Science and Technology on Aerodynamic Design and Research, Northwestern Polytechnical University, Xi'an 710072, China

Received:2014-08-16 Revised:2014-12-29 Online:2015-05-05 Published:2015-05-05
Contact: Zhong Cheng-Wen E-mail:zhongcw@nwpu.edu.cn
About author:05.20.Dd; 47.11.Df; 47.40.-x
Supported by:
Project supported by the Innovation Fund for Aerospace Science and Technology of China (Grant No. 2009200066) and the Aeronautical Science Fund of China (Grant No. 20111453012).

摘要/Abstract

摘要：

This paper presents a coupling compressible model of the lattice Boltzmann method. In this model, the multiple-relaxation-time lattice Boltzmann scheme is used for the evolution of density distribution functions, whereas the modified single-relaxation-time (SRT) lattice Boltzmann scheme is applied for the evolution of potential energy distribution functions. The governing equations are discretized with the third-order Monotone Upwind Schemes for scalar conservation laws finite volume scheme. The choice of relaxation coefficients is discussed simply. Through the numerical simulations, it is found that compressible flows with strong shocks can be well simulated by present model. The numerical results agree well with the reference results and are better than that of the SRT version.

关键词: lattice Boltzmann method, multi-relaxation-time, compressible flow, finite volume method

Abstract:

Key words: lattice Boltzmann method, multi-relaxation-time, compressible flow, finite volume method

中图分类号: (Kinetic theory)

05.20.Dd

47.11.Df (Finite volume methods) 47.40.-x (Compressible flows; shock waves)

李凯, 钟诚文. A multiple-relaxation-time lattice Boltzmann method for high-speed compressible flows[J]. 中国物理B, 2015, 24(5): 50501-050501.

Li Kai (李凯), Zhong Cheng-Wen (钟诚文). A multiple-relaxation-time lattice Boltzmann method for high-speed compressible flows[J]. Chin. Phys. B, 2015, 24(5): 50501-050501.

参考文献 60

[1]	Succi S 2001 The Lattice Boltzmann Equation for Fluid Dynamics and Beyond (1st edn.) (New York: Oxford University Press)
[2]	Lim C Y, Shu C, Niu X D and Chew Y T 2002 Phys. Fluids 14 2299
[3]	Toschi F and Succi S 2005 Europhys. Lett. 69 549
[4]	Zhuo C and Zhong C 2013 Phys. Rev. E 88 053311
[5]	Liu C F and Ni Y S 2008 Chin. Phys. B 17 4554
[6]	Sun D K, Xiang N, Jiang D, Chen K, Yi H and Ni Z H 2013 Chin. Phys. B 22 114704
[7]	Yu H, Girimaji S S and Luo L S 2005 Phys. Rev. E 71 016708
[8]	Chen S 2009 Appl. Math. Comput. 215 591
[9]	Zhuo C, Zhong C, Li K, Xiong S, Chen X and Cao J 2010 Commun. Comput. Phys. 8 1208
[10]	Zhuo C and Zhong C 2013 Int. J. Heat Fluid Flow 42 10
[11]	Inamuro T, Ogata T, Tajima S and Konishi N 2004 J. Comput. Phys. 198 628
[12]	Premnath K N and Abraham J 2007 J. Comput. Phys. 224 539
[13]	Xie H Q, Zeng Z, Zhang L Q, Liang G Y, Hiroshi M and Yoshiyuki K 2012 Chin. Phys. B 21 124703
[14]	Kang X Y, Ji Y P, Liu D H and Jin Y J 2008 Chin. Phys. B 17 1041
[15]	Yi H H, Yang X F, Wang C F and Li H B 2009 Chin. Phys. B 18 2878
[16]	Ji Y P, Kang X Y and Liu D H 2010 Chin. Phys. Lett. 27 094701
[17]	Zhao M, Ji Z Z and Feng T 2004 Acta Phys. Sin. 53 671 (in Chinese)
[18]	Zhong C, Xie J, Zhuo C, Xiong S and Yin D 2009 Chin. Phys. B 18 4083
[19]	Zhuo C, Zhong C and Cao J 2012 Phys. Rev. E 85 046703
[20]	Karlin I V, Ferrante A and Öttinger H C 1999 Europhys. Lett. 47 182
[21]	Ansumali S, Karlin I V and Öttinger H C 2003 Europhys. Lett. 63 798
[22]	Ginzburg I 2005 Adv. Water Resour. 28 1171
[23]	Ginzburg I, Verhaeghe F and d'Humiéres D 2008 Commun. Comput. Phys. 3 427
[24]	d'Humiéres D 1992 Prog. Astronaut. Aeronaut. 159 450
[25]	Lallemand P and Luo L S 2000 Phys. Rev. E 61 6546
[26]	Alexander F J, Chen S and Sterling J D 1993 Phys. Rev. E 47 R2249
[27]	Qian Y H 1993 J. Sci. Comput. 8 231
[28]	Chen Y, Ohashi H and Akiyama M 1994 Phys. Rev. E 50 2776
[29]	Yan G, Zhang J, Liu Y and Dong Y 2007 Int. J. Numer. Meth. Fluids 55 41
[30]	Sun C 1998 Phys. Rev. E 58 7283
[31]	Sun C 2000 Phys. Rev. E 61 2645
[32]	Sun C H 2000 Chin. Phys. Lett. 17 209
[33]	Shi W, Shyy W and Mei R 2001 Numer. Heat Transfer, Part B 40 1
[34]	Kataoka T and Tsutahara M 2004 Phys. Rev. E 69 056702
[35]	Kataoka T and Tsutahara M 2004 Phys. Rev. E 69 035701
[36]	Watari M 2007 Physica A 382 502
[37]	He X, Chen S and Doolen G D 1998 J. Comput. Phys. 146 282
[38]	Guo Z, Zheng C, Shi B and Zhao T S 2007 Phys. Rev. E 75 036704
[39]	Li Q, He Y L, Wang Y and Tao W Q 2007 Phys. Rev. E 76 056705
[40]	Li K and Zhong C 2015 Int. J. Numer. Meth. Fluids 77 334
[41]	Zheng L, Shi B and Guo Z 2008 Phys. Rev. E 78 026705
[42]	Chen F, Xu A, Zhang G, Li Y and Succi S 2010 Europhys. Lett. 90 54003
[43]	Chen F, Xu A, Zhang G and Li Y 2011 Phys. Lett. A 375 2129
[44]	Chen F, Xu A, Zhang G and Li Y 2011 Theor. Appl. Mech. Lett. 1 052004
[45]	Bhatnagar P L, Gross E P and Krook M 1954 Phys. Rev. 94 511
[46]	Qu K 2009 Development of Lattice Boltzmann Method for Compressible Flows (Ph. D. Thesis) (Singapore: National University of Singapore)
[47]	Mei R, Luo L S, Lallemand P and d'Humiéres D 2006 Comput. Fluids 35 855
[48]	d'Humiéres D 2002 Philos. Trans. R. Soc. London, Ser. A 360 437
[49]	Mei R and Shyy W 1998 J. Comput. Phys. 143 426
[50]	Xi H, Peng G and Chou S H 1999 Phys. Rev. E 59 6202
[51]	He Y L, Liu Q and Li Q 2013 Physica A 392 4884
[52]	Patil D V 2013 Physica A 392 2701
[53]	van Leer B 1979 J. Comput. Phys. 32 101
[54]	Kermani M J, Gerber A G and Stockie J M 2003 4th Conference of Iranian Aerospace Society, January 27-29, Tehran, Iran
[55]	van Albada G D, van Leer B and Roberts Jr W W 1982 Astron. Astrophys. 108 76
[56]	Li Q, He Y L and Gao Y J 2008 Int. J. Mod. Phys. C 19 1581
[57]	Guo Z, Zheng C and Shi B 2002 Chin. Phys. 11 366
[58]	De Tullio M D, De Palma P, Iaccarino G, Pascazio G and Napolitano M 2007 J. Comput. Phys. 225 2098
[59]	Belotserkovskii O M 1959 Flow Past a Circular Cylinder with a Detached Shock Wave (Technical Memorandum) (Wilmington: AVCO Corporation)
[60]	Modesto-Madera N A 2011 A Numerical Study of Supersonic Flow Past a Circular Cylinder (MS Thesis) (Hartford: Rensselaer Polytechnic Institute)

A multiple-relaxation-time lattice Boltzmann method for high-speed compressible flows

A multiple-relaxation-time lattice Boltzmann method for high-speed compressible flows

RichHTML

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 60

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Pei-Feng Lin(林培锋), Xiao Hu(胡箫), and Jian-Zhong Lin(林建忠). Inertial focusing and rotating characteristics of elliptical and rectangular particle pairs in channel flow[J]. 中国物理B, 2022, 31(8): 80501-080501.
[2]	Peichan Wu(吴锫婵), Yuhan Yan(严妤函), Huan Zhu(朱欢), Juan Shi(施娟), and Zhenqian Chen(陈振乾). Hemodynamics of aneurysm intervention with different stents[J]. 中国物理B, 2022, 31(6): 64701-064701.
[3]	Le Bai(柏乐), Ming-Lei Shan(单鸣雷), Yu Yang(杨雨), Na-Na Su(苏娜娜), Jia-Wen Qian(钱佳文), and Qing-Bang Han(韩庆邦). Effect of viscosity on stability and accuracy of the two-component lattice Boltzmann method with a multiple-relaxation-time collision operator investigated by the acoustic attenuation model[J]. 中国物理B, 2022, 31(3): 34701-034701.
[4]	He Wang(王贺), Fang-Bao Tian(田方宝), and Xiang-Dong Liu(刘向东). Lattice Boltzmann model for interface capturing of multiphase flows based on Allen-Cahn equation[J]. 中国物理B, 2022, 31(2): 24701-024701.
[5]	张庆宇, 孙东科, 章顺虎, 王辉, 朱鸣芳. Modeling of microporosity formation and hydrogen concentration evolution during solidification of an Al-Si alloy[J]. 中国物理B, 2020, 29(7): 78104-078104.
[6]	覃章荣, 陈燕雁, 凌风如, 孟令娟, 张超英. A mass-conserved multiphase lattice Boltzmann method based on high-order difference[J]. 中国物理B, 2020, 29(3): 34701-034701.
[7]	左鸿, 邓守春, 李海波. Boundary scheme for lattice Boltzmann modeling of micro-scale gas flow in organic-rich pores considering surface diffusion[J]. 中国物理B, 2019, 28(3): 30202-030202.
[8]	赵书霞, 丰曌. Gas flow characteristics of argon inductively coupled plasma and advections of plasma species under incompressible and compressible flows[J]. 中国物理B, 2018, 27(12): 124701-124701.
[9]	欧阳振宇, 林建忠, 库晓珂. Dynamics of a self-propelled particle under different driving modes in a channel flow[J]. 中国物理B, 2017, 26(1): 14701-014701.
[10]	张若洋, 赵清, 葛墨林. Achieving acoustic cloak by using compressible background flow[J]. 中国物理B, 2016, 25(8): 84702-084702.
[11]	张庆宇, 孙东科, 张友法, 朱鸣芳. Numerical modeling of condensate droplet on superhydrophobic nanoarrays using the lattice Boltzmann method[J]. 中国物理B, 2016, 25(6): 66401-066401.
[12]	Esmaeil Dehdashti. Development of a new correlation to calculate permeability for flows with high Knudsen number[J]. 中国物理B, 2016, 25(2): 24702-024702.
[13]	单鸣雷, 朱昌平, 姚澄, 殷澄, 蒋小燕. Pseudopotential multi-relaxation-time lattice Boltzmann model for cavitation bubble collapse with high density ratio[J]. 中国物理B, 2016, 25(10): 104701-104701.
[14]	谢海琼, 曾忠, 张良奇. Three-dimensional multi-relaxation-time lattice Boltzmann front-tracking method for two-phase flow[J]. 中国物理B, 2016, 25(1): 14702-014702.
[15]	宋保维, 任峰, 胡海豹, 黄桥高. Lattice Boltzmann simulation of liquid–vapor system by incorporating a surface tension term[J]. , 2015, 24(1): 14703-014703.