Advection–Diffusion Lattice Boltzmann Method With and Without Dynamical Filter
Advection–Diffusion Lattice Boltzmann Method With and Without Dynamical Filter
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DOI：
10.3389/fphy.2022.875628
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发表时间：
2022-05
期刊：
影响因子：
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通讯作者：
Zhihong Zhang;Zhiqiang Li;Yunke Wu
中科院分区：
文献类型：
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作者：
Zhihong Zhang;Zhiqiang Li;Yunke Wu
在多组分流动和/或热流中，当对流扩散方程的扩散系数相对较小时，格子Boltzmann方法中的弛豫系数将接近0.5，这将导致数值不稳定。当计算区域中存在高梯度区域时，稳定性条件将变得更加严格。为了提高对流扩散格子Boltzmann方法模拟复杂流动标量输运的稳定性，提出了一种适用于对流扩散格子Boltzmann方法的混合正则化碰撞算子和动态滤波方法.对流扩散格子Boltzmann方法首先在均匀流中进行测试，具有光滑和不连续的初始条件。然后对双周期剪切层流中对数值稳定性敏感的标量输运进行了检验。并对自适应动态滤波方法进行了试验。结果进行了比较，经典的有限差分法和晶格玻尔兹曼方法使用基于投影的正则化和标准的Bahtnagar-Gross-Krook碰撞算子。结果表明，混合正则碰撞算子在模拟扩散系数较小的标量对流扩散问题时具有优势。此外，自适应滤波方法还可以提高有限数值耗散的格子Boltzmann方法的数值稳定性。
In multi-component flow and/or thermal flows, when the diffusion coefficient of the advection–diffusion equation is relatively small, the relaxation coefficient in the lattice Boltzmann method will be close to 0.5, which will lead to numerical instability. The stability conditions will become more severe, when there are high gradient regions in the computational domain. In order to improve the stability of advection–diffusion lattice Boltzmann method to simulate scalar transport in complex flow, a hybrid regularized collision operators and a dynamic filtering method which is suitable for the convection-diffusion lattice Boltzmann method are proposed in this paper. The advection–diffusion lattice Boltzmann method is first tested in uniform flow with smooth and discontinuous initial conditions. Then the scalar transport in doubly periodic shear layer flow is tested, which is sensitive to numerical stability. The adaptive dynamic filtering method is also tested. The results are compared to the classical finite difference method and to the lattice Boltzmann method using the projection-based regularized and standard Bahtnagar-Gross-Krook collision operator. The results show that the hybrid regularized collision operator has advantages in simulating the scalar advection-diffusion problem with small diffusion coefficient. In addition, the adaptive filtering method can also improve the numerical stability of the lattice Boltzmann method with limited numerical dissipation.