A multi-energy-level lattice Boltzmann model for the compressible Navier-Stokes equations. (English) Zbl 1119.76049
Summary: We propose a new lattice Boltzmann model for compressible Navier-Stokes equations. The new model is based on a three-energy-level and three-speed lattice Boltzmann equation by using the method of higher moments of equilibrium distribution functions. As in the 25-bit model, we obtain equilibrium distribution functions and solve compressible Navier-Stokes equations with the second-order accuracy of truncation errors. Numerical examples show that the model can be used to simulate shock waves, contact discontinuities and supersonic flows around circular cylinders. The numerical results are compared with those obtained by traditional methods.
References:
| [1] | Frisch, Physical Review Letters 56 pp 1505– (1986) |
| [2] | Chen, Annual Review of Fluid Mechanics 3 pp 314– (1998) |
| [3] | Qian, Europhysics Letters 17 pp 479– (1992) |
| [4] | Chen, Physical Review A 45 pp 5339– (1992) |
| [5] | Benzi, Physics Reports 222 pp 147– (1992) |
| [6] | Yan, Journal of Computational Physics 161 pp 61– (2000) |
| [7] | Yan, Chinese Physics Letters 16 pp 109– (1999) |
| [8] | Yan, Physica D 154 pp 43– (2001) |
| [9] | . An introduction to computational fluid dynamics–the finite volume method. Longman: New York, 1995. |
| [10] | Harten, SIAM Journal on Numerical Analysis 21 pp 1– (1984) |
| [11] | Harten, Journal of Computational Physics 131 pp 3– (1997) |
| [12] | Zhang, Journal of Computational Physics 176 pp 483– (2002) |
| [13] | Theory, algorithms, and applications of level set methods for propagating interface. Acta Numerica. Cambridge University Press: Cambridge, U.K., 1995. |
| [14] | Woodward, Journal of Computational Physics 54 pp 115– (1984) |
| [15] | Yan, Physical Review E 59 pp 454– (1999) |
| [16] | Alexander, Physical Review A 46 pp 1967– (1992) |
| [17] | Nadiga, Journal of Statistical Physics 81 pp 129– (1995) |
| [18] | Huang, International Journal of Modern Physics C 8 pp 827– (1997) |
| [19] | Prendergast, Journal of Computational Physics 109 pp 53– (1993) |
| [20] | Kim, International Journal for Numerical Methods in Fluids 25 pp 21– (1997) |
| [21] | Kotelnikov, Journal of Computational Physics 134 pp 364– (1997) |
| [22] | Renda, Europhysics Letters 41 pp 279– (1998) |
| [23] | Vahala, International Journal of Modern Physics C 9 pp 1247– (1998) |
| [24] | Sun, Physical Review E 58 pp 7283– (1998) |
| [25] | De Cicco, SIAM Journal on Scientific Computing 21 pp 366– (1999) |
| [26] | Mason, Bulletin of the American Physical Society 45 pp 168– (2000) |
| [27] | Mason, Journal of Statistical Physics 107 pp 385– (2002) |
| [28] | Yan, International Journal for Numerical Methods in Fluids 51 pp 1407– (2006) |
| [29] | Kataoka, Physial Review E 69 pp 056702– (2004) |
| [30] | Kataoka, Physical Review E 69 pp 035701– (2004) |
| [31] | McNamara, Journal of Statistical Physics 81 pp 395– (1995) |
| [32] | Wolfram, Journal of Statistical Physics 45 pp 471– (1986) |
| [33] | . The Mathematical Theory of Non-uniform Gas. Cambridge University Press: Cambridge, 1939. |
| [34] | Nessyahu, Journal of Computational Physics 87 pp 408– (1990) |
| [35] | Wang, Computational Fluid Dynamics Journal 12 pp 191– (2004) |
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