Laminar and Turbulent Behavior Captured by A 3-D Kinetic-Based Discrete Dynamic System
Laminar and Turbulent Behavior Captured by A 3-D Kinetic-Based Discrete Dynamic System
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通讯作者：
Xiaoyu Zhang;J. M. McDonough
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作者：
Xiaoyu Zhang;J. M. McDonough
我们通过伽辽金过程，从晶格玻尔兹曼方程（LBE）导出了不可压缩流动的三维动力学离散动力系统（DDS）。它由一个贫人晶格玻尔兹曼方程（PMLBE）表示，涉及五个分岔参数，包括LBE的松弛时间、大网格和亚网格运动尺度的分裂因子以及傅里叶空间的波矢量分量。数值实验表明，DDS可以捕捉到周期、次谐波、n周期和准周期的层流行为，以及具有谐波、噪声次谐波、噪声准周期和宽带功率谱的噪声周期的湍流行为。在这项工作中，我们从时间序列的收敛性和功率谱模式的角度研究了分岔参数对层流和湍流捕获的影响。我们发现二阶和三阶PMLBEs都能够捕获层流和湍流的流动行为，但二阶DDS性能更好，计算成本更低，捕获的流动行为更多。在给定的分岔参数范围内，我们确定了层流和湍流两种最优分岔参数集。除了这项工作，我们正在探索状态图，以更深入地了解分岔参数对捕获层流和湍流行为的贡献。替代模型（取代PMLBE）正在使用深度学习技术开发，以克服状态图的压倒性计算成本。同时，DDS也被应用于湍流脉动流的大涡模拟中，以提供动态的亚网格尺度信息
: We have derived a 3-D kinetic-based discrete dynamic system (DDS) from the lattice Boltzmann equation (LBE) for incompressible flows through a Galerkin procedure. Expressed by a poor-man lattice Boltzmann equation (PMLBE), it involves five bifurcation parameters including relaxation time from the LBE, splitting factor of large and sub-grid motion scales, and wavevector components from the Fourier space. Numerical experiments have shown that the DDS can capture laminar behaviors of periodic, subharmonic, n-period, and quasi-periodic and turbulent behaviors of noisy periodic with harmonic, noisy subharmonic, noisy quasi-periodic, and broadband power spectra. In this work, we investigated the effects of bifurcation parameters on the capturing of the laminar and turbulent flows in terms of the convergence of time series and the pattern of power spectra. We have found that the 2nd order and 3rd order PMLBEs are both able to capture laminar and turbulent flow behaviors but the 2nd order DDS performs better with lower computation cost and more flow behaviors captured. With the specified ranges of the bifurcation parameters, we have identified two optimal bifurcation parameter sets for laminar and turbulent behaviors. Beyond this work, we are exploring the regime maps for a deeper understanding of the contributions of the bifurcation parameters to the capturing of laminar and turbulent behaviors. Surrogate models (to replace the PMLBE) are being developed using deep learning techniques to overcome the overwhelming computation cost for the regime maps. Meanwhile, the DDS is being employed in the large eddy simulation of turbulent pulsatile flows to provide dynamic sub-grid scale information