A discrete Boltzmann model with symmetric velocity discretization for compressible flow

doi:10.1088/1674-1056/acea6b

中国物理B ›› 2023, Vol. 32 ›› Issue (11): 110503-110503.doi: 10.1088/1674-1056/acea6b

A discrete Boltzmann model with symmetric velocity discretization for compressible flow

Chuandong Lin(林传栋)^1,†, Xiaopeng Sun(孙笑朋)^1,‡, Xianli Su(苏咸利)^1,§, Huilin Lai(赖惠林)^2,¶, and Xiao Fang(方晓)^1,||

1 Sino-French Institute of Nuclear Engineering and Technology, Sun Yat-sen University, Zhuhai 519082, China;
2 School of Mathematics and Statistics, the Key Laboratory of Analytical Mathematics and Applications(Ministry of Education), Fujian Key Laboratory of Analytical Mathematics and Applications(FJKLAMA), and Center for Applied Mathematics of Fujian Province(FJNU), Fujian Normal University, Fuzhou 350117, China

收稿日期:2023-06-03 修回日期:2023-07-12 接受日期:2023-07-26 出版日期:2023-10-16 发布日期:2023-10-26
通讯作者: Chuandong Lin, Xiaopeng Sun, Xianli Su, Huilin Lai, Xiao Fang E-mail:linchd3@mail.sysu.edu.cn;sunxp6@mail2.sysu.edu.cn;suxli@mail2.sysu.edu.cn;hllai@fjnu.edu.cn;fangx26@mail.sysu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 51806116, U2242214, and 11875329), Guangdong Basic and Applied Basic Research Foundation (Grant No. 2022A1515012116), and the Natural Science Foundation of Fujian Province, China (Grant Nos. 2021J01652 and 2021J01655).

A discrete Boltzmann model with symmetric velocity discretization for compressible flow

Chuandong Lin(林传栋)^1,†, Xiaopeng Sun(孙笑朋)^1,‡, Xianli Su(苏咸利)^1,§, Huilin Lai(赖惠林)^2,¶, and Xiao Fang(方晓)^1,||

1 Sino-French Institute of Nuclear Engineering and Technology, Sun Yat-sen University, Zhuhai 519082, China;
2 School of Mathematics and Statistics, the Key Laboratory of Analytical Mathematics and Applications(Ministry of Education), Fujian Key Laboratory of Analytical Mathematics and Applications(FJKLAMA), and Center for Applied Mathematics of Fujian Province(FJNU), Fujian Normal University, Fuzhou 350117, China

Received:2023-06-03 Revised:2023-07-12 Accepted:2023-07-26 Online:2023-10-16 Published:2023-10-26
Contact: Chuandong Lin, Xiaopeng Sun, Xianli Su, Huilin Lai, Xiao Fang E-mail:linchd3@mail.sysu.edu.cn;sunxp6@mail2.sysu.edu.cn;suxli@mail2.sysu.edu.cn;hllai@fjnu.edu.cn;fangx26@mail.sysu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 51806116, U2242214, and 11875329), Guangdong Basic and Applied Basic Research Foundation (Grant No. 2022A1515012116), and the Natural Science Foundation of Fujian Province, China (Grant Nos. 2021J01652 and 2021J01655).

摘要/Abstract

摘要： A discrete Boltzmann model (DBM) with symmetric velocity discretization is constructed for compressible systems with an adjustable specific heat ratio in the external force field. The proposed two-dimensional (2D) nine-velocity scheme has better spatial symmetry and numerical accuracy than the discretized velocity model in literature [Acta Aerodyn. Sin. 40 98108 (2022)] and owns higher computational efficiency than the one in literature [Phys. Rev. E 99 012142 (2019)]. In addition, the matrix inversion method is adopted to calculate the discrete equilibrium distribution function and force term, both of which satisfy nine independent kinetic moment relations. Moreover, the DBM could be used to study a few thermodynamic nonequilibrium effects beyond the Euler equations that are recovered from the kinetic model in the hydrodynamic limit via the Chapman-Enskog expansion. Finally, the present method is verified through typical numerical simulations, including the free-falling process, Sod's shock tube, sound wave, compressible Rayleigh-Taylor instability, and translational motion of a 2D fluid system.

关键词: discrete Boltzmann method, compressible flow, nonequilibrium effect, kinetic method

Abstract: A discrete Boltzmann model (DBM) with symmetric velocity discretization is constructed for compressible systems with an adjustable specific heat ratio in the external force field. The proposed two-dimensional (2D) nine-velocity scheme has better spatial symmetry and numerical accuracy than the discretized velocity model in literature [Acta Aerodyn. Sin. 40 98108 (2022)] and owns higher computational efficiency than the one in literature [Phys. Rev. E 99 012142 (2019)]. In addition, the matrix inversion method is adopted to calculate the discrete equilibrium distribution function and force term, both of which satisfy nine independent kinetic moment relations. Moreover, the DBM could be used to study a few thermodynamic nonequilibrium effects beyond the Euler equations that are recovered from the kinetic model in the hydrodynamic limit via the Chapman-Enskog expansion. Finally, the present method is verified through typical numerical simulations, including the free-falling process, Sod's shock tube, sound wave, compressible Rayleigh-Taylor instability, and translational motion of a 2D fluid system.

Key words: discrete Boltzmann method, compressible flow, nonequilibrium effect, kinetic method

中图分类号: (Nonequilibrium and irreversible thermodynamics)

05.70.Ln

47.11.-j (Computational methods in fluid dynamics) 47.45.Ab (Kinetic theory of gases) 51.10.+y (Kinetic and transport theory of gases)

Chuandong Lin(林传栋), Xiaopeng Sun(孙笑朋), Xianli Su(苏咸利),Huilin Lai(赖惠林), and Xiao Fang(方晓). A discrete Boltzmann model with symmetric velocity discretization for compressible flow[J]. 中国物理B, 2023, 32(11): 110503-110503.

参考文献

[1] Anderson J D 2021 Modern compressible flow:With historical perspective, 4th edn. (Boston:McGraw-Hill) pp. 36-37
[2] Martys N S, Shan X W and Chen H D 1998 Phys. Rev. E 58 6855
[3] Guo Z L, Zheng C G and Shi B C 2002 Phys. Rev. E 65 046308
[4] Mohamad A and Kuzmin A 2010 Int. J. Heat Mass Transfer 53 990996
[5] Zhang J F 2011 Microfluid. Nanofluid. 10 128
[6] Li Q, Luo K H, Kang Q J, He Y L, Chen Q and Liu Q 2016 Prog. Energy Combust. Sci. 52 62105
[7] Shan M L, Zhu C P, Yao C, Yin C and Jiang X Y 2016 Chin. Phys. B 25 104701
[8] Sun D K, Chai Z H, Li Q and Lin G 2018 Chin. Phys. B 27 088105
[9] Fei L L, Luo K H and Li Q 2018 Phys. Rev. E 97 053309
[10] Zuo H, Deng S C and Li H B 2019 Chin. Phys. B 28 030202
[11] Wang H, Tian F B and Liu X D 2022 Chin. Phys. B 31 024701
[12] Bai L, Shan M L, Yang Y, Su N N, Qian J W and Han Q B 2022 Chin. Phys. B 31 034701
[13] Zhong X G, Liu Y S, Yao Y C, He B and Wen B H 2023 Chin. Phys. B 32 054701
[14] Qin F F, Fei L L, Zhao J L, Kang Q J, Derome D and Carmeliet J 2023 J. Fluid Mech. 963 A26
[15] Xu A G and Zhang Y D 2022 Complex media kinetics (Beijing:Science Press) pp. 67-229 (in Chinese)
[16] Xu A G, Zhang G C, Gan Y B, Chen F and Yu X J 2012 Front. Phys. 7 582600
[17] Lin C D, Xu A G, Zhang G C, Li Y J and Succi S 2014 Phys. Rev. E 89 013307
[18] Xu A G, Lin C D, Zhang G C and Li Y J 2015 Phys. Rev. E 91 043306
[19] Lai H L, Xu A G, Zhang G C, Gan Y B, Ying Y J and Succi S 2016 Phys. Rev. E 94 023106
[20] Lin C D, Xu A G, Zhang G C and Li Y J 2016 Combust. Flame 164 137151
[21] Lin C D, Xu A G, Zhang G C, Luo K H and Li Y J 2017 Phys. Rev. E 96 053305
[22] Lin C D and Luo K H 2018 Combust. Flame 198 356362
[23] Lin C D and Luo K H 2018 Comput. Fluids 166 176183
[24] Lin C D and Luo K H 2019 Phys. Rev. E 99 012142
[25] Zhang Y D, Xu A G, Zhang G C, Gan Y B, Chen Z H and Succi S 2019 Soft matter 15 22452259
[26] Lin C D, Luo K H, Xu A G, Gan Y B and Lai H L 2021 Phys. Rev. E 103 013305
[27] Lin C D 2022 Acta Aerodyn. Sin. 40 98108
[28] Gan Y B, Xu A G, Zhang G C and Succi S 2015 Soft Matter 11 53365345
[29] Gan Y B, Xu A G, Zhang G C, Zhang Y D and Succi S 2018 Phys. Rev. E 97 053312
[30] Ji Y, Lin C D and Luo K H 2022 J. Comput. Phys. 455 111002
[31] Zhang D J, Xu A G, Zhang Y D, Gan Y B and Li Y J 2022 Phys. Fluids 34 086104
[32] Zhang Y D, Xu A G, Zhang G C, Chen Z H and Wang P 2019 Comput. Phys. Commun. 238 5065
[33] Zhang H X and Zhuang F G 1991 Adv. Appl. Mech. 29 193256
[34] Gan Y B, Xu A G, Lai H L, Li W, Sun G L and Succi S 2022 J. Fluid Mech. 951 A8

A discrete Boltzmann model with symmetric velocity discretization for compressible flow

A discrete Boltzmann model with symmetric velocity discretization for compressible flow

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