Reduction of spurious velocity in the free-energy-based lattice Boltzmann method for large density ratio
Reduction of spurious velocity in the free-energy-based lattice Boltzmann method for large density ratio
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DOI：
10.1299/jtst.2015jtst0004
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发表时间：
2015
影响因子：
1.2
通讯作者：
J. Gong;N. Oshima;Yutaka Tabe
中科院分区：
文献类型：
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作者：
J. Gong;N. Oshima;Yutaka Tabe
采用基于自由能的格子Boltzmann方法（LBM）求解大密度比的两相流，消除了交错网格下泊松方程计算中产生的弯曲界面附近的伪速度。结果表明，采用交错网格的逐次超松弛法计算泊松方程的压力，会引入各向异性离散误差，导致计算值与理论预测值的偏差。此外，各向异性的压力将导致大量的虚假速度，这是液滴形状变形的驱动力。通过混合两种交错网格的泊松方程离散方程中的速度分量，分别利用正交方向和对角方向的速度分量，减小了伪速度和液滴变形的大小。结果表明，通过适当选择混合因子，可以将伪速度的大小减小到原来的一半，并使形状变形和压力与理论预测的偏差最小。等人（2004年）扩展了该模型，以允许模拟具有大密度比的不可压缩两相流，即使在密度比高达1000：1的情况下也能产生稳定的结果。此外，Lee and Lin（2005）和Lee and Fischer（2006）基于He等人（1999）设计的模型，提出了两种模型，它们可以使用格子Boltzmann方程的稳定离散方案来模拟大密度比下的两相流。Zheng等人（2006）也提出了一个基于Swift模型的伽利略不变自由能模型，并声称它能够模拟具有大密度差异的两相流。寄生速度，也称为寄生电流，是一种具有小幅度的人造速度，存在于模拟中的界面附近。这种人工速度场是扩散界面法的两相流模拟技术中常见的问题，如LBM、流体体积（VOF）、
The spurious velocity around curved interface, arising from the calculation of the Poisson equation with staggered grids, is reduced in the free-energy-based two-phase flow lattice Boltzmann method (LBM) for large density ratios. It is found that the pressure calculation from the Poisson equation, using the successive over-relaxation method with staggered grids, would introduce anisotropic discretization errors and lead to deviations of its calculated value from the theoretical prediction. Moreover, the anisotropic pressure would induce a large magnitude of spurious velocity, which is the driving force for droplet shape deformation. By blending the velocity components in the discretization equations of the Poission equation from two types of staggered grids that separately make use of the velocity components in the orthogonal and the diagonal directions, the magnitude of the spurious velocity and the droplet deformation are diminshed. It is found that, by appropriate choice of the blending factor, the magnitude of the spurious velocity can be reduced to half of its original value, and the shape deformation and pressure deviation from the theoretical prediction can be minimized. et al. (2004) extended the model to permit simulations of incompressible two-phase flows with large density ratios yielding stable results, even in the cases where the ratio was as high as 1000:1. Moreover, Lee and Lin (2005) and Lee and Fischer (2006), based on the model devised by He et al. (1999), proposed two models that can simulate two-phase flows at a large density ratio using a stable discretization scheme of the lattice Boltzmann equation. Zheng et al. (2006) also proposed a Galilean-invariant free-energy model, based on Swift’s model, and claimed that it is able to mimic two-phase flows with large density differences. The spurious velocity, also referred to as parasitic current, is an artificial velocity with a small amplitude, that exists in the vicinity of an interface in the simulation. This artificial velocity field is a common problem in the two-phase flow simulation techniques of diffuse interface methods, such as the LBM, the volume of fluid (VOF), the