Improving Statistical Convergence in Direct Numerical Simulations by Exploring Large-Scale Structures Organization and Symmetry

计算流体动力学(CFD)用于描述、解释和预测飞机、火箭和地面车辆外部以及发动机和建筑通风系统内部的湍流流动。由于湍流中的非定常结构，这样的计算可能会很昂贵。这个项目将专注于开发模拟技术，使这种计算更实用。通过亚利桑那州立大学社区连接基础设施开展的外联活动将侧重于通过简短的教程和演示，让高中生了解湍流及其与现实生活应用的联系，这些演示涉及湍流的高级可视化和大规模的有组织的运动。该项目的目标是开发相应的策略，以缓解在有限时间的数值模拟过程中，在流动区域的某些部分存在缓慢移动的相干结构或锁定的问题。在这些情况下，收集的流量统计数据可能会受到这些结构的局部和临时影响的严重偏差，并且不能可靠地代表长期的系统动态。目前的建议致力于设计简单但有效的策略，在大大减少计算时间的情况下，显著改善数值模拟中的统计收敛。这些策略包括在模拟的有限时间内对流的多个实现和多个状态进行有效采样。这将通过在运行时设计计算的流场的特定数学变换来实现，该变换可以被认为是在本质上触发状态转变的扰动。将探索系统的对称性，以设计(I)服从于促进快速转变为所需的未采样流动状态的变换，(Ii)在数学上保持一致并保持控制流体动力学方程。除了改进统计收敛，该项目还试图回答以下科学问题：(I)在某些对称系统中观察到的非常长寿命的非对称流动状态，例如横流中的射流和钝体尾迹，是否是相干结构锁定类似现象的产物，以及当前的技术是否将产生对称平均场，(Ii)增加来自新重建状态的样本是否改善了通过低阶模型对系统动力学的长期预测，例如适当的正交分解。这项研究与教育计划相结合，该计划包括在当地凤凰城地区高中开展外展活动，让本科生参与研究，并改进研究生课程。

Computational Fluid Dynamics (CFD) is used to describe, explain, and predict turbulent fluid flow externally around airplanes, rockets, and ground vehicles and internally in engines and building ventilation systems. Such computations can be expensive because of the unsteady structures in the turbulence. This project will focus on developing simulation techniques to make such computations more practical. Outreach activities through ASU community-connect infrastructure will focus on educating high-school students about turbulence and its connection to real-life applications through short tutorials and demonstrations involving advanced visualization of turbulent flows and large-scale organized motions. The goal of this project is to develop the strategies that mitigate the problem associated with the persistence of slow moving coherent structures in certain portions of the flow domain, or locking, during the finite time of numerical simulations. In these situations, the collected flow statistics can be significantly biased by the localized and temporary effect of these structures and cannot reliably represent a long-term system dynamics. The current proposal is devoted to designing simple but efficient strategies that will yield significantly improved convergence of statistics in numerical simulations over a much reduced computational time. These strategies include efficient sampling over multiple realizations and multiple states of the flow during the finite time of the simulations. This will be achieved by designing specific mathematical transformations of the computed flow field at a runtime that can be thought of as disturbances that trigger the state transitions in nature. The symmetries of the system will be explored to design the transformations that (i) amenable to promoting quick transitions into desired unsampled flow states, (ii) mathematically consistent and preserve the governing fluid dynamics equations. In addition to improving statistical convergence, the project seeks to answer the following scientific questions: (i) whether the observation of very long-lived asymmetric flow states in certain symmetric systems, such as jets in crossflow and bluff-body wakes, is an artifact of a similar phenomenon of coherent structure locking and whether the current techniques will yield symmetric average fields, (ii) whether addition of the samples from the newly reconstructed states improve a long-term prediction of the system dynamics by low-order models, such as Proper Orthogonal Decomposition. The research is coupled to the educational plan that includes outreach activities at local Phoenix district high schools, involvement of undergraduates in research, and improving graduate curriculum.