Lattice Boltzmann modeling and simulation of compressible flows

Abstract

In this mini-review we summarize the progress of Lattice Boltzmann(LB) modeling and simulating compressible flows in our group in recentyears. Main contents include (i) Single-Relaxation-Time (SRT) LB modelsupplemented by additional viscosity, (ii) Multiple-Relaxation-Time(MRT) LB model, and (iii) LB study on hydrodynamic instabilities.The former two belong to improvements of physical modeling and thethird belongs to simulation or application. The SRT-LB model supplementedby additional viscosity keeps the original framework of Lattice Bhatnagar–Gross–Krook(LBGK). So, it is easier and more convenient for previous SRT-LB users.The MRT-LB is a completely new framework for physical modeling. Itsignificantly extends the range of LB applications. The cost is longercomputational time. The developed SRT-LB and MRT-LB are complementaryfrom the sides of convenience and applicability.

Keywords

lattice Boltzmann modeling / compressible flows / shock waves / hydrodynamic instability

References

[1] S. Succi, The Lattice Boltzmann Equation for Fluid Dynamics and Beyond, New York: Oxford University Press, 2001

[2] S. Y. Chen, H. D. Chen, D. Martinez, and W. Matthaeus, Phys. Rev. Lett., 1991, 67(27): 3776

[3] G. Vahala, B. Keating, M. Soe, J. Yepezand, and L. Vahala, Comm. Comp. Phys., 2008, 4(3): 624

[4] A. J. C. Ladd, J. Fluid Mech., 1994, 271: 311

[5] A. Gunstensen, D. Rothman, S. Zaleski, and G. Zanetti, Phys. Rev. A, 1991, 43(8): 4320

[6] X. Shan and H. Chen, Phys. Rev. E, 1993, 47(3): 1815

[7] M. R. Swift, W. R. Osborn, and J. M. Yeomans, Phys. Rev. Lett., 1995, 75(5): 830

[8] X. He, S. Chen, and R. Zhang, J. Comput. Phys., 1999, 152(2): 642

[9] A. Xu, G. Gonnella, and A. Lamura, Phys. Rev. E, 2003, 67(5): 056105

[10] A. Xu, G. Gonnella, and A. Lamura, Phys. Rev. E, 2006, 74(1): 011505

[11] A. Xu, G. Gonnella, A. Lamura, G. Amati, and F. Massaioli, Europhys. Lett., 2005, 71(4): 651

[12] M. Sbragaglia, R. Benzi, L. Biferale, S. Succi, K. Sugiyama, and F. Toschi, Phys. Rev. E, 2007, 75(2): 026702

[13] V. Sofonea, A. Lamura, G. Gonnella, and A. Cristea, Phys. Rev. E, 2004, 70(4): 046702

[14] A. Cristea, G. Gonnella, A. Lamura, and V. Sofonea, Commun. Comput. Phys., 2010, 7(2): 350

[15] S. Succi, E. Foti, and F. Higuera, Europhys. Lett., 1989, 10(5): 433

[16] Y. Xu, Y. Liu, X. Yang, and F. Wu, Commun.Theor. Phys., 2008, 49(5): 1319

[17] C. Wang, X. Zhang, C. W. Shu, and J. Ning, J. Comput. Phys., 2012, 231(2): 653

[18] S. Tan, C. Wang, C. W. Shu, and J. Ning, J. Comput. Phys., 2012, 231(6): 2510

[19] F. J. Alexander, H. Chen, S. Chen, and G. D. Doolen, Phys. Rev. A, 1992, 46(4): 1967

[20] G. W. Yan, Y. S. Chen, and S. X. Hu, Phys. Rev. E, 1999, 59(1): 454

[21] C. H. Sun, Phys. Rev. E, 1998, 58(6): 7283

[22] C. H. Sun and A. T. Hsu, Phys. Rev. E, 2003, 68(1): 016303

[23] T. Kataoka and M. Tsutahara, Phys. Rev. E, 2004, 69(5): 056702

[24] T. Kataoka and M. Tsutahara, Phys. Rev. E, 2004, 69(3): 035701(R)

[25] M. Watari and M. Tsutahara, Phys. Rev. E, 2003, 67(3): 036306

[26] M. Watari and M. Tsutahara, Phys. Rev. E, 2004, 70(1): 016703

[27] M. Watari, Physica A, 2007, 382(2): 502

[28] A. Xu, Europhys. Lett., 2005, 69(2): 214

[29] A. Xu, Phys. Rev. E, 2005, 71(6): 066706

[30] S. Ansumali and I. V. Karlin, J. Stat. Phys., 2002, 107(1-2): 291

[31] S. Ansumali, I. V. Karlin, and H. C. Ottinger, Europhys. Lett., 2003, 63(6): 798

[32] Y. Li, R. Shock, R. Zhang, and H. Chen, J. Fluid Mech., 2004, 519: 273

[33] V. Sofonea, A. Lamura, G. Gonnella, and A. Cristea, Phys. Rev. E, 2004, 70(4): 046702

[34] X. F. Pan, A. Xu, G. Zhang, and S. Jiang, Int. J. Mod. Phys. C, 2007, 18(11): 1747

[35] Y. Gan, A. Xu, G. Zhang, X. Yu, and Y. Li, Physica A, 2008, 387(8-9): 1721

[36] Y. Gan, A. Xu, G. Zhang, and Y. Li, Commun.Theor. Phys., 2008, 50(1): 201

[37] F. Chen, A. Xu, G. Zhang, Y. Gan, C. Tao, and Y. Li, Commun. Theor. Phys., 2009, 52(4): 681

[38] F. Chen, A. Xu, G. Zhang, and Y. Li, Commun.Theor. Phys., 2010, 54(6): 1121

[39] Y. Gan, A. Xu, G. Zhang, and Y. Li, Commun.Theor. Phys., 2011, 56(3): 490

[40] F. Chen, A. Xu, G. Zhang, and Y. Li, Phys.Lett. A, 2011, 375(21): 2129

[41] F. Chen, A. Xu, G. Zhang, Y. Li, and S. Succi, Europhys. Lett., 2010, 90(5): 54003

[42] F. Chen, A. Xu, G. Zhang, and Y. Li, Commun.Theor. Phys., 2011, 55(2): 325

[43] F. Chen, A. Xu, G. Zhang, and Y. Li, Commun.Theor. Phys., 2011, 56(2): 333

[44] F. Chen, A. Xu, G. Zhang, and Y. Li, Thero.& Appl. Mech. Lett., 2011, 1(5): 052004

[45] F. J. Higuera, S. Succi, and R. Benzi, Europhys. Lett., 1989, 9(4): 345

[46] F. J. Higuera, and J. Jiménez, Europhys. Lett., 1989, 9(7): 663

[47] P. Lallemand and L. S. Luo, Phys. Rev. E, 2000, 61(6): 6546

[48] P. Lallemand and L. S. Luo, Phys. Rev. E, 2003, 68(3): 036706

[49] P. Lallemand, D. d’Humières, L. S. Luo, and R. Rubinstein, Phys. Rev. E, 2003, 67(2): 021203

[50] Y. Gan, A. Xu, G. Zhang, and Y. Li, Phys.Rev. E, 2011, 83(5): 056704

[51] A. L. Velikovich, J. P. Dahlburg, A. J. Schmitt, J. H. Gardner, L. Phillips, F. L. Cochran, Y. K. Chong, G. Dimonte, and N. Metzler, Phys. Plasmas, 2000, 7(5): 1662

[52] R. D. Richtmyer, Comm. Pure Appl. Math., 1960, 13(2): 297

[53] E. E. Meshkov, Sov. Fluid Dyn., 1969, 4(5): 101

[54] R. F. Benjamin, Advances in Compressible Turbulent Mixing, U. S. Government PrintingOffice, 1992

[55] Q. Zhang and S. Sohn, Phys. Fluids, 1997, 9(4): 1106

[56] L. F. Wang, W. H. Ye, and Y. J. Li, Phys. Plasma, 2010, 17(4): 042103

[57] Y. Gan, A. Xu, G. Zhang, Y. Li, and H. Li, Phys. Rev. E, 2011, 84(4): 046715

[58] Y. Gan, A. Xu, G. Zhang, and Y. Li, Europhys.Lett., 2012, 97(4): 44002

[59] Y. Gan, A. Xu, G. Zhang, and Y. Li, Front.Phys., 2012, 7(4): 481

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