An improved multiphase lattice Boltzmann flux solver for three-dimensional flows with large density ratio and high Reynolds number
An improved multiphase lattice Boltzmann flux solver for three-dimensional flows with large density ratio and high Reynolds number
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DOI：
10.1016/j.jcp.2015.08.049
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发表时间：
2015-12
期刊：
影响因子：
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通讯作者：
Yu Wang;C. Shu;L. M. Yang
中科院分区：
文献类型：
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作者：
Yu Wang;C. Shu;L. M. Yang
提出了一种改进的多相格子Boltzmann通量求解器（MLBFS），以有效地模拟具有大密度比和高雷诺数的三维多相流。作为一种有限体积格式，最初在[27]中提出的MLBFS应用有限体积法直接求解宏观流动变量。通过使用标准的LBM解决方案，在每个单元界面处局部重建通量。由于标准LBM的建模误差，重建的通量偏离Navier-Stokes方程;为了补偿这种误差，在原始MLBFS中引入复张量。然而，张量的计算引入了额外的复杂性，并且通常需要相对较厚的界面厚度来保持数值稳定性，这使得求解器在3D情况下复杂且低效。为了克服这一缺点，在这项工作中，理论分析从查普曼-恩斯科格展开得到的配方进行。结果表明，通过修正平衡密度分布函数的计算方法，可以有效地消除模型误差。通过这种改进，所提出的三维MLBFS不仅避免了补偿张量的计算，而且能够在非常薄的界面厚度下保持数值稳定性。几个基准的情况下，包括具有挑战性的液滴在干燥的表面上的碰撞，迎面碰撞的二元液滴和液滴飞溅的薄膜密度比1000和雷诺数高达3000的研究，以验证所提出的求解器。所得结果与已发表的数据吻合较好。
An improved multiphase lattice Boltzmann flux solver (MLBFS) is proposed in this work for effective simulation of three-dimensional (3D) multiphase flows with large density ratio and high Reynolds number. As a finite volume scheme, the MLBFS originally proposed in [27] applies the finite volume method to solve for macroscopic flow variables directly. The fluxes are reconstructed locally at each cell interface by using the standard LBM solutions. Due to the modeling error of the standard LBM, the reconstructed fluxes deviate from those in the Navier–Stokes equations; and to compensate this error, a complex tensor is introduced in the original MLBFS. However, the computation of the tensor introduces additional complexity and usually needs a relatively thicker interface thickness to maintain numerical stability, which makes the solver be complex and inefficient in the 3D case. To remove this drawback, in this work, a theoretical analysis to the formulations obtained from the Chapman–Enskog expansion is conducted. It is shown that the modeling error can be effectively removed by modifying the computation of the equilibrium density distribution function. With this improvement, the proposed 3D MLBFS not only avoids the calculation of the compensation tensor but also is able to maintain numerical stability with very thin interface thickness. Several benchmark cases, including the challenging droplet impacting on a dry surface, head-on collisions of binary droplets and droplet splashing on a thin film with density ratio 1000 and Reynolds number up to 3000, are studied to validate the proposed solver. The obtained results agree well with the published data.