用于Ginzburg-Landau超流体流动的格子Boltzmann模型
Lattice Boltzmann Model for the Ginzburg-Landau Superfluid Flows
DOI: 10.12677/IJFD.2013.11002, PDF, 下载: 3,034  浏览: 11,914  国家科技经费支持
作者: 张建影：北京大学工学院，北京；闫广武*：吉林大学数学学院
关键词: 格子Boltzmann模型；的Ginzburg-Landau超流体；位势流《br》 Lattice Boltzmann Model; Ginzburg-Landau Superfluid; Potential Flow
摘要: 本文构造了用于模拟Ginzburg-Landau超流体流动的格子Boltzmann模型。通过给出复格子Boltzmann方程，以及应用复Chapman-Enskog展开，我们得到了复平衡分布函数满足的不同时间尺度上的系列偏微分方程。利用这些系列方程，我们得到了具有二阶截断误差的复Ginzburg-Landau方程。进一步引入速度势函数，得到了Ginzburg-Landau超流体流动的动力学方程。   In this paper, a lattice Boltzmann model for the Ginzburg-Landau superfluid flow is proposed. By using complex lattice Boltzmann equation and complex Chapman-Enskog expansion, we obtain a series of partial differential equations on the complex equilibrium distribution function in the different time scales, and the complex Ginzburg- Landau equation with the second-order truncation error. By employing the velocity potential function, we get the kinetic equations of the Ginzburg-Landau superfluid flow.

文章引用：张建影, 闫广武. 用于Ginzburg-Landau超流体流动的格子Boltzmann模型[J]. 流体动力学, 2013, 1(1): 10-14. http://dx.doi.org/10.12677/IJFD.2013.11002

参考文献

[1] Qian YH, d'Humieres D and Lallemand P, Lattice BGK Model for Navier- Stokes Equations, Europhys. Lett., 1992, 17, 6: 479- 484.
[2] Chen SY, Doolen G.D, Lattice Boltzmann method for fluid flows, Annu. Fluid Mech., 1998, 3: 314- 322.
[3] Chen HD, Chen SY and Matthaeus MH, Recovery of the Navier- Stokes Equations Using a Lattice Boltzmann gas Method, Phys. Rev. A, 1992, 45: 5339- 5342.
[4] Benzi R, Succi S and Vergassola M, The Lattice Boltzmann Equation: Theory and Applications, Phys. Rep., 1992, 222: 147- 197.
[5] Shan XW, Chen HD, Lattice Boltzmann model of simulating flows with multiple phases and components, Phys. Rev. E, 1993, 47: 1815- 1819.
[6] Luo LS, Theory of the lattice Boltzmann method: lattice Boltzmann method for nonideal gases, Phys. Rev. E, 2000, 62: 4982- 4996.
[7] Ladd A, Numerical simulations of particle suspensions via a discretized Boltzmann equation, Part 2.Numerical results, J. Fluids Mech., 1994, 271: 311- 339.
[8] Chen SY, Chen HD, Martinez D, et al, Lattice Boltzmann Model for simulation of Magneto- hydrodynamics, Phys. Rev. Lett., 1991, 67: 3776- 3779.
[9] Dawson SP, Chen SY, Doolen GD, Lattice Boltzmann computations for reaction- diffusion equations, J. Chem. Phys., 1993, 98: 1514- 1523.
[10] Succi S, Foti E, Higuera FJ, 3- Dimensional flows in complex geometries with the lattice Boltzmann method, Europhys. Lett., 1989, 10: 433- 438.
[11] Yan GW, Chen YS, Hu SX, Simple lattice Boltzmann model for simulating flows with shock wave, Phys. Rev. E, 1999, 59: 454- 459.
[12] Qu K, Shu Q, Chew YT, Alternative method to construct equilibrium distribution function in lattice- Boltzmann method simulation of inviscid compressible flows at high Mach number, Phys. Rev. E, 2007, 75: 036706.
[13] Gan YB, Xu AG, Zhang GC, Yu XJ, Li YJ, Two- dimensional lattice Boltzmann model for compressible flows with high Mach number, Physica A, 2008, 387: 1721- 1732.
[14] Succi S, Lattice quantum mechanics: an application to Bose- Einstein condensation, Int. J. Mod. Phys. C, 1998, 9: 1577- 1585.
[15] Zhang JY, Yan GW, A lattice Boltzmann model for the nonlinear Schrödinger equation, J. Phys. A, 2007, 40: 10393- 10405.
[16] Palpacelli S, Succi S, Quantium lattice Boltzmann simulation of expanding Bose- Einstein condensates in random potentials, Phys. Rev. E, 2008, 77: 066708.
[17] Zhang JY and Yan GW, Lattice Boltzmann model for the complex Ginzburg- Landau equation, Phys. Rev. E, 2010, 81: 066705.

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