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本文基于具有守恒性与相容性的N相相场模型，发展了一种用于高效模拟N相非混溶不可压流体流动的正则化格子Boltzmann方法。通过设计辅助矩，该方法能够精确恢复二阶Allen-Cahn方程与修正的动量方程。通过数值模拟三相液滴透镜铺展与三相Kelvin-Helmholtz不稳定性现象，验证了所发展的N相正则化格子Boltzmann方法的正确性与有效性。最后，对三相Rayleigh-Taylor不稳定性进行了数值模拟与分析，重点探究了雷诺数在500 ≤Re≤ 20000范围内（特别是高雷诺数Re=20000工况下）相界面的演化过程，定量分析了两个界面处气泡与尖钉的振幅以及无量纲化速度的变化规律。
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关键词:
- 相场模型 /
- N相不可压流体 /
- 格子Boltzmann方法 /
- Rayleigh-Taylor不稳定性
This paper develops a regularized lattice Boltzmann method for efficiently simulating the flow of N-phase immiscible incompressible fluids based on the phase field model that satisfies conservation and compatibility. By designing auxiliary moments, this method can accurately recover the second-order Allen-Cahn equation and the modified momentum equation. The correctness and effectiveness of the developed N-phase regularized lattice Boltzmann method are validated through numerical simulations of three-phase liquid lens spreading and Kelvin-Helmholtz instability phenomena. Finally, numerical simulations and analyses of three-phase Rayleigh-Taylor instabilities (RTI) were conducted, focusing on the evolution of the phase interface within the Reynolds number range of 500 ≤ Re ≤ 20000 (particularly under high Reynolds number condition of Re = 20000). Quantitative analyses were performed on the amplitude variations of bubbles and spikes at the two interfaces, as well as the changes in dimensionless velocity. We found that as the Reynolds number increases, the phase interface curls up at multiple locations due to Kelvin-Helmholtz instability, making the fluid more prone to dispersion and fragmentation. This study also simulated the evolution of RTI under different interface perturbations. The results indicate that RTI first develops at the perturbed interface, and its evolution gradually triggers instability at another interface.-
Keywords:
- Phase field model /
- N-phase incompressible fluid /
- lattice Boltzmann method /
- Rayleigh-Taylor instability
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[1] Barber J L, Kadau K, Germann T C, Alder B J 2008 Eur. Phys. J. B 64 271
[2] Celani A, Mazzino A, Bjorkholm J E, Vozella L 2006 Phys. Rev. Lett. 96 134504
[3] Moin P 1991 Comput. Methods Appl. Mech. Eng. 87 329
[4] Guo Z L, Zheng C G 2009 Theory and Applications of Lattice Boltzmann Method (Beijing:Science Press)(in Chinese)[郭照立,郑楚光2009格子Boltzmann方法的原理及应用(北京:科学出版社)]
[5] He Y L, Wang Y, Li Q 2009 Lattice Boltzmann Method:Theory and Applications (Beijing:Science 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)]
[6] He X Y, Chen S Y, Zhang R Y 1999 J. Comput. Phys. 152 642
[7] Liang H, Shi B C, Guo Z L, Chai Z H 2014 Phys. Rev. E 89 053320
[8] Liang H, Li Q X, Shi B C, Chai Z H 2016 Phys. Rev. E 93 033133
[9] Liang H, Xia Z H, Huang H W 2021 Phys. Fluids 33 082103
[10] Li Y, Su T, Liang H, Xu J R 2022 Acta Phys. Sin. 67 224701(in Chinese)[李洋,苏婷,梁宏,徐江 荣2022 67 224701]
[11] Ma C, Liu B, Liang H 2022 Acta Phys. Sin. 71 044701(in Chinese)[马聪,刘斌,梁宏2022物理 学报71 044701]
[12] Li D M, Lai H L, Chen S Y, Zhang G C, Lin C D, Gan Y B 2018 Acta Phys. Sin. 67 080501(in Chinese)[李德梅,赖惠林,许爱国,张广财,林传栋,甘延标2018 67 080501]
[13] Zhang R Y, He X Y, Chen S Y 2000 Comput. Phys. Commun. 129 121
[14] Hu X L, Liang H, Wang H L 2020 Acta Phys. Sin. 69 044701(in Chinese)[胡晓亮,梁宏,王会利 2020 69 044701]
[15] Zhan C J, Liu X, Chai Z H, Shi B C 2024 Commun. Comput. Phys 36 850
[16] Kalantarpour R, Ebadi A, Hosseinalipour S M, Liang H 2020 Comput.&Fluids 204 104480
[17] Boyer F, Lapuerta C 2006 ESAIM:Math. Model. Numer. Anal. 40 653
[18] Boyer F, Lapuerta C, Minjeaud S et al. 2010 Transp. Porous Media 82 463
[19] Dong S 2018 J. Comput. Phys. 361 1
[20] Zheng L, Zheng S, Zhai Q L 2020 Phys. Rev. E 101 043302
[21] Mirjalili S, Mani A 2024 J. Comput. Phys. 498 112657
[22] Xia Q, Yang J X, Li Y B 2023 Phys. Fluids 35 012120
[23] Latt J, Chopard B 2006 Math. Comput. Simulat. 72 165
[24] Montessori A, Falcucci G, Prestininzi P, et al. 2014 Phys. Rev. E 89 053317
[25] Liu X, Chen Y, Chai Z H, Shi B C 2024 Phys. Rev. E 109 025301
[26] Huang Y H, Chen X M, Chai Z H, Shi B C 2025 Adv. Appl. Math. Mech. 17 1370
[27] Huang H W, Liang H, Xu J R 2021 Acta Phys. Sin. 70 114701(in Chinese)[黄皓伟,梁宏,徐江荣 2021 70 114701]
[28] Li C Y, Guo Z L 2025 Acta Phys. Sin. 74 064702(in Chinese)[李春熠,郭照立2025 74 064702]
[29] Huang Z Y, Lin G, Ardekani A M 2021 J. Comput. Phys. 434 110229
[30] Mirjalili S, Mani A 2021 J. Comput. Phys. 426 109918
[31] Qian Y H, d'Humieres D, Lallemand P 1992 Europhys. Lett. 17 479
[32] Yang X F, Zhao J, Wang Q, Shen J 2017 Math. Models Methods Appl. Sci. 27 1993
[33] Hu Y, Li D C, He Q 2020 Int. J. Multiph. Flow 132 103432
[34] Yuan X L, Shi B C, Zhan C J, Chai Z H 2022 Phys. Fluids 34 023311
[35] Wu J W, Yang J X, Tan Z J 2022 Comput. Methods Appl. Mech. Eng. 398 115291
[36] Zhang S T, Xiao H W, Zhou H X, Niu X D 2022 Acta Aerodyn. Sin. 40 75(in Chinese)[章诗婷,肖 鸿威,周锦翔,牛小东2022空气动力学学报40 75]
[37] Fakhari A, Lee T 2013 Phys. Rev. E 87 023304
[38] Fakhari A, Geier M, Lee T 2016 J. Comput. Phys. 315 434
[39] Zhou X, Dong B, Zhan C J, Li W Z 2020 Int. J. Aerosp. Eng. 2020 8885226
[40] Ramaprabhu P, Dimonte G, Lee T 2016 Phys. Rev. E 74 066308
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