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使用离散Boltzmann模型模拟了可压流体系统中多模初始情况下的Rayleigh-Taylor不稳定性.该离散Boltzmann模型等效于一个Navier-Stokes模型外加一个关于热动非平衡行为的粗粒化模型.通过模拟Riemann问题：Sod激波管、冲击波碰撞和热Couette流问题验证模型的有效性，所得数值结果与解析解一致.利用该模型对界面间断随机多模初始扰动的可压Rayleigh-Taylor不稳定性进行数值模拟研究，得到不稳定性界面演化过程的基本图像.由于黏性和热传导共同作用，一开始扰动界面被“抹平”，演化较慢；随着模式互相耦合而减少，演化开始加速，并经历非线性小扰动阶段和不规则非线性阶段，而后发展成典型的“蘑菇状”，后期进入湍流混合阶段.由于扰动模式的耦合与发展，轻重流体的重力势能、压缩能与动能相互转化，系统先是趋于热动平衡态，而后偏离热动平衡态以线性形式增长，接着再次趋于热动平衡态，最后慢慢远离热动平衡态.
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关键词:
- 离散Boltzmann方法 /
- Rayleigh-Taylor不稳定性 /
- 可压流体 /
- 动理学模型
We use a discrete Boltzmann model (DBM) to simulate the multi-mode Rayleigh-Taylor instability (RTI) in a compressible flow.This DBM is physically equivalent to a Navier-Stokes model supplemented by a coarse-grained model for thermodynamic nonequilibrium behavior.The validity of the model is verified by comparing simulation results of Riemann problems,Sod shock tube,collision between two strong shock waves,and thermal Couette flow with analytical solutions.Grid independence is verified.The DBM is utilized to simulate the nonlinear evolution of the RTI from multi-mode initial perturbation with discontinuous interface.We obtain the basic process of the initial disturbance interface which develops into mushroom graphs.The evolution of the system is relatively slow at the beginning,and the interface moves down on a whole.This is mainly due to the fact that the heat transfer plays a leading role,and the exchange of internal energy occurs near the interface of fluid.The overlying fluid absorbs heat,which causes the volume to expand,and the underlying fluid releases heat,which causes the volume to shrink,consequently the fluid interface moves downward.Meanwhile,due to the effects of viscosity and thermal conduction,the perturbed interface is smoothed.The evolution rate is slow at the initial stage.As the modes couple with each other,the evolution begins to grow faster.As the interface evolves gradually into the gravity dominated stage,the overlying and underlying fluids begin to exchange the gravitational potentials via nonlinear evolution.Lately,the two parts of fluid permeate each other near the interface.The system goes through the nonlinear disturbance and irregular nonlinear stages,then develops into the typical “mushroom” stage.Afterwards,the system evolves into the turbulent mixing stage.Owing to the coupling and development of perturbation modes,and the transformation among the gravitational potential energy,compression energy and kinetic energy,the system first approaches to a transient local thermodynamic equilibrium,then deviates from it and the perturbation grows linearly.After that,at the beginning,the fluid system tends to approach to an equilibrium state,which is caused by the adjustment of the system,and the disturbance of the multi-mode initial interface moves toward a process of the eigenmode stage.Then,the system deviates from the equilibrium state linearly,which is due to the flattening of the system interface and the conversing of the compression energy into internal energy.Moreover, the system tends to approach to the equilibrium state again,and this is because the modes couple and the disturbance interface is further “screened”.The system is in a relatively stable state.Furthermore,the system is farther away from the equilibrium state because of the gravitational potential energy of the fluid system transformation.The compression energy of the system is released further,and the kinetic energy is further increased.After that,the nonequilibrium intensity decreases,and then the system is slowly away from thermodynamic equilibrium.The interface becomes more and more complicated,and the nonequilibrium modes also become more and more abundant.-
Keywords:
- discrete Boltzmann method /
- Rayleigh-Taylor instability /
- compressible flows /
- kinetic model
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[5] Wang L F, Ye W H, Wu J F, Liu J, Zhang W Y, He X T 2016 Phys. Plasmas 23 052713
[6] Wang L F, Ye W H, He X T, Wu J F, Fan Z F, Xue C, Guo H Y, Miao W Y, Yuan Y T, Dong J Q, Jia G, Zhang J, Li Y J, Liu J, Wang L M, Ding Y K, Zhang W Y 2017 Sci. China:Phys. Mech. Astron. 60 055201
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[14] Li Q, Luo K H, Gao Y J, He Y L 2012 Phys. Rev. E 85 026704
[15] Liu G J, Guo Z L 2013 Int. J. Numer. Method H. 23 176
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[26] Lin C D, Xu A G, Zhang G C, Li Y J, Succi S 2014 Phys. Rev. E 89 013307
[27] Lai H L, Xu A G, Zhang G C, Gan Y B, Ying Y J, Succi S 2016 Phys. Rev. E 94 023106
[28] Liu H, Kang W, Zhang Q, Zhang Y, Duan H L, He X T 2016 Front. Phys. 11 115206
[29] Gan Y B, Xu A G, Zhang G C, Yang Y 2013 Europhys. Lett. 103 24003
[30] Gan Y B, Xu A G, Zhang G C, Succi S 2015 Soft Matter 11 5336
[31] Watari M, Tsutahara M 2004 Phys. Rev. E 70 016703
[32] Zhang H X 1988 Acta Aerodyn. Sin. 6 43 (in Chinese)[张涵信 1988 空气动力学学报 6 43]
[33] Guo Z L, Zheng C G, Shi B C 2002 Phys. Fluids 14 2007
[34] Xu A G, Zhang G C 2016 The 9th National Conference on Fluid Mechanics Nanjing, China Oct. 20-23, 2016 (in Chinese)[许爱国, 张广财 2016 第九届全国流体力学学术会议, 南京, 2016年10月20–23 日]
[35] Xu A G, Zhang G C 2016 Special Academic Report of Electromechanical College of Nanjing Forestry University Nanjing, China, Oct. 25, 2016 (in Chinese)[许爱国, 张广财 2016 南京林业大学机电学院专题学术报告, 中国南京, 2016年10月25日]
[36] Xu A G, Zhang G C 2016 Academic Report on Physics Department of Renmin University of China Beijing, China, Nov. 23, 2016 (in Chinese)[许爱国, 张广财 2016 中国人民大学物理系专题学术报告, 中国北京, 2016 年11 月23日]
[37] Xu A G, Zhang G C 2016 The 4th Academic Seminar of LBM and Its Applications Beijing, China, Nov. 26, 2016 (in Chinese)[许爱国, 张广财 2016 第四届LBM及其应用学术研讨会, 中国北京, 2016年11月26日]
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[1] Rayleigh L 1882 Proc. London Math. Soc. s1-14 170
[2] Lamb H 1932 Hydrodynamics (6th Ed.) (London:Cambridge University press) p501
[3] Taylor G 1950 Proc. R. Soc. London A 201 192
[4] Betti R, Goncharov V, McCrory R, Verdon C 1998 Phys. Plasmas (1994-present) 5 1446
[5] Wang L F, Ye W H, Wu J F, Liu J, Zhang W Y, He X T 2016 Phys. Plasmas 23 052713
[6] Wang L F, Ye W H, He X T, Wu J F, Fan Z F, Xue C, Guo H Y, Miao W Y, Yuan Y T, Dong J Q, Jia G, Zhang J, Li Y J, Liu J, Wang L M, Ding Y K, Zhang W Y 2017 Sci. China:Phys. Mech. Astron. 60 055201
[7] Cabot W, Cook A 2006 Nat. Phys. 2 562
[8] Berthoud G 2000 Annu. Rev. Fluid Mech. 32 573
[9] Barber J L, Kadau K, Germann T C, Alder B J 2008 Eur. Phys. J. B 64 271
[10] Celani A, Mazzino A, Vozella L 2006 Phys. Rev. L. 96 134504
[11] Moin P 1991 Comput. Meth. Appl. Mech. Eng. 87 329
[12] Succi S 2001 The Lattice Boltzmann Equation for Fluid Dynamics and Beyond (New York:Oxford University Press) pp179-255
[13] He X Y, Chen S Y, Zhang R Y 1999 J. Comput. Phys. 152 642
[14] Li Q, Luo K H, Gao Y J, He Y L 2012 Phys. Rev. E 85 026704
[15] Liu G J, Guo Z L 2013 Int. J. Numer. Method H. 23 176
[16] Scagliarini A, Biferale L, Sbragaglia M, Sugiyama K, Toschi F 2010 Phys. Fluids 22 055101
[17] Xu A G, Zhang G C, Gan Y B, Chen F, Yu X J 2012 Front. Phys. 7 582
[18] Xu A G, Zhang G C, Gan Y B 2016 Mech. Eng. 38 361 (in Chinese)[许爱国, 张广财, 甘延标 2016 力学与实践 38 361]
[19] Gan Y B, Xu A G, Zhang G C, Yu X J, Li Y J 2008 Physica A 387 1721
[20] Gan Y B, Xu A G, Zhang G C, Li Y J 2011 Phys. Rev. E 83 056704
[21] Gan Y B, Xu A G, Zhang G C, Li Y J, Li H 2011 Phys. Rev. E 84 046715
[22] Yan B, Xu A G, Zhang G C, Ying Y J, Li H 2013 Front. Phys. 8 94
[23] 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]
[24] Xu A G, Zhang G C, Ying Y J 2015 Acta Phys. Sin. 64 184701 (in Chinese)[许爱国, 张广财, 应阳君 2015 64 184701]
[25] Xu A G, Zhang G C, Ying Y J, Wang C 2016 Sci. China:Phys. Mech. Astron. 59 650501
[26] Lin C D, Xu A G, Zhang G C, Li Y J, Succi S 2014 Phys. Rev. E 89 013307
[27] Lai H L, Xu A G, Zhang G C, Gan Y B, Ying Y J, Succi S 2016 Phys. Rev. E 94 023106
[28] Liu H, Kang W, Zhang Q, Zhang Y, Duan H L, He X T 2016 Front. Phys. 11 115206
[29] Gan Y B, Xu A G, Zhang G C, Yang Y 2013 Europhys. Lett. 103 24003
[30] Gan Y B, Xu A G, Zhang G C, Succi S 2015 Soft Matter 11 5336
[31] Watari M, Tsutahara M 2004 Phys. Rev. E 70 016703
[32] Zhang H X 1988 Acta Aerodyn. Sin. 6 43 (in Chinese)[张涵信 1988 空气动力学学报 6 43]
[33] Guo Z L, Zheng C G, Shi B C 2002 Phys. Fluids 14 2007
[34] Xu A G, Zhang G C 2016 The 9th National Conference on Fluid Mechanics Nanjing, China Oct. 20-23, 2016 (in Chinese)[许爱国, 张广财 2016 第九届全国流体力学学术会议, 南京, 2016年10月20–23 日]
[35] Xu A G, Zhang G C 2016 Special Academic Report of Electromechanical College of Nanjing Forestry University Nanjing, China, Oct. 25, 2016 (in Chinese)[许爱国, 张广财 2016 南京林业大学机电学院专题学术报告, 中国南京, 2016年10月25日]
[36] Xu A G, Zhang G C 2016 Academic Report on Physics Department of Renmin University of China Beijing, China, Nov. 23, 2016 (in Chinese)[许爱国, 张广财 2016 中国人民大学物理系专题学术报告, 中国北京, 2016 年11 月23日]
[37] Xu A G, Zhang G C 2016 The 4th Academic Seminar of LBM and Its Applications Beijing, China, Nov. 26, 2016 (in Chinese)[许爱国, 张广财 2016 第四届LBM及其应用学术研讨会, 中国北京, 2016年11月26日]
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