Theory of the lattice Boltzmann method: Dispersion, dissipation, isotropy, Galilean invariance, and stability
Theory of the lattice Boltzmann method: Dispersion, dissipation, isotropy, Galilean invariance, and stability
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DOI：
10.1103/physreve.61.6546
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发表时间：
2000-06-01
影响因子：
2.4
通讯作者：
Luo, LS
中科院分区：
文献类型：
--
作者：
Lallemand, P;Luo, LS
研究了广义格子Boltzmann方程（LBE）的广义流体力学（输运系数与波矢的关系）。广义格子Boltzmann方程是在矩空间而不是离散速度空间中构造的。模型的广义流体动力学是通过求解线性化LEE的色散方程得到的，无论是通过使用微扰技术的解析解还是数值解。建议的LEE模型具有最大数量的可调参数为给定的一组离散速度。广义流体力学的特点分散，耗散（高粘度），各向异性，缺乏伽利略不变性的模型，并可以应用于选择的可调参数，优化模型的属性值。建议的广义水动力分析也提供了一些见解的稳定性和适当的初始条件LEE模拟。在平均流动速度和粘性弛豫时间的参数空间中，分析和比较了几种二维LEE模型的稳定性。本文所述的方法可用于分析其它LEE模型。作为例子，LEE模型与各种插值方案进行了分析。剪切如何与初始不连续的速度分布（冲击）与或不具有恒定的流动速度的数值结果表明，在LEE模型中的色散效应：与我们的理论分析的结果比较有利。我们还表明，而线性分析的LEE演化算子是等价的查普曼-Enskog分析在长波长的限制（波矢量k=0），它也可以提供结果为大值的k。这些结果对于LEE方法的稳定性和其他流体动力学性质是重要的，并且不能通过Chapman-Enskog分析获得。
The generalized hydrodynamics (the wave vector dependence of the transport coefficients) of a generalized lattice Boltzmann equation (LBE) is studied in detail. The generalized lattice Boltzmann equation is constructed in moment space rather than in discrete velocity space. The generalized hydrodynamics of the model is obtained by solving the dispersion equation of the linearized LEE either analytically by using perturbation technique or numerically. The proposed LEE model has a maximum number of adjustable parameters for the given set of discrete velocities. Generalized hydrodynamics characterizes dispersion, dissipation (hyperviscosities), anisotropy, and lack of Galilean invariance of the model, and can be applied to select the values of the adjustable parameters that optimize the properties of the model. The proposed generalized hydrodynamic analysis also provides some insights into stability and proper initial conditions for LEE simulations. The stability properties of some two-dimensional LEE models are analyzed and compared with each Ether in the parameter space of the mean streaming velocity and the viscous relaxation time. The procedure described in this work can be applied to analyze other LEE models. As examples, LEE models with various interpolation schemes are analyzed. Numerical results on shear how with an initially discontinuous velocity profile (shock) with or without a constant streaming velocity are shown to demonstrate the dispersion effects in the LEE model: the results compare favorably with our theoretical analysis. We also show that whereas linear analysis of the LEE evolution operator is equivalent to Chapman-Enskog analysis in the long-wavelength limit (wave vector k=0), it can also provide results for large values of k. Such results are important for the stability and other hydrodynamic properties of the LEE method and cannot be obtained through Chapman-Enskog analysis.