Cascaded lattice Boltzmann modeling and simulations of three-dimensional non-Newtonian fluid flows
Cascaded lattice Boltzmann modeling and simulations of three-dimensional non-Newtonian fluid flows
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DOI：
10.1016/j.cpc.2021.107858
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发表时间：
2019-08
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影响因子：
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通讯作者：
S. Adam;Farzaneh Hajabdollahi;K. Premnath
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文献类型：
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作者：
S. Adam;Farzaneh Hajabdollahi;K. Premnath
非牛顿流体流动，特别是三维（3D）的非牛顿流体流动，出现在物理学感兴趣的许多环境中。以前的研究，使用格子玻尔兹曼方法（LBM）的这种流动到目前为止，主要限于两个维度，并使用不太强大的碰撞模型。在本文中，我们开发了一个新的三维级联LBM的基础上的中心矩和多重弛豫时间（MRT）的三维，十九速度（D3Q19）格子模拟广义牛顿（幂律）流体流动。二阶矩的弛豫时间根据局部剪切速率局部变化，并由幂律流体的非线性本构关系的一致性系数和幂律指数参数化。数值验证研究的三维级联LBM的各种基准问题，包括复杂的三维非牛顿流在立方腔在不同的雷诺数和幂律指数的大小，包括剪切变稀和剪切增稠流体，提出。此外，为了证明所提出的3D级联LBM的中心矩的基础上的优点，数值稳定性与LBM的基础上，一个单一的弛豫时间模型和MRT模型，使用原始的时刻。数值结果表明，三维级联LBM的精度，二阶网格收敛性和显着改善数值稳定性的模拟三维非牛顿幂律流体的流动。
Non-Newtonian fluid flows, especially in three dimensions (3D), arise in numerous settings of interest to physics. Prior studies using the lattice Boltzmann method (LBM) of such flows have so far been limited mainly to two dimensions and used less robust collision models. In this paper, we develop a new 3D cascaded LBM based on central moments and multiple relaxation times (MRT) on a three-dimensional, nineteen velocity (D3Q19) lattice for simulation of generalized Newtonian (power law) fluid flows. The relaxation times of the second order moments are varied locally based on the local shear rate and parameterized by the consistency coefficient and the power law index of the nonlinear constitutive relation of the power law fluid. Numerical validation study of the 3D cascaded LBM for various benchmark problems, including the complex 3D non-Newtonian flow in a cubic cavity at different Reynolds numbers and power law index magnitudes encompassing shear thinning and shear thickening fluids, are presented. Furthermore, in order to demonstrate the advantages of the proposed 3D cascaded LBM based on central moments, numerical stability comparisons against the LBMs based on a single relaxation time model and a MRT model using raw moments are made. Numerical results demonstrate the accuracy, second order grid convergence and significant improvements in numerical stability of the 3D cascaded LBM for simulation of 3D non-Newtonian flows of power law fluids.