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、火箭和地面车辆周围的外部湍流，以及发动机和建筑通风系统的内部湍流。由于湍流中的非定常结构，这样的计算可能是昂贵的。这个项目将侧重于开发模拟技术，使这种计算更加实用。通过亚利桑那州立大学社区连接基础设施开展的外展活动将侧重于教育高中生湍流及其与现实应用的联系，通过简短的教程和演示，包括湍流的高级可视化和大规模有组织的运动。该项目的目标是制定策略，以减轻在有限的数值模拟时间内，流域某些部分缓慢移动的相干结构持续存在或锁定相关的问题。在这些情况下，收集到的流量统计数据可能会受到这些结构的局部和暂时影响的显著偏差，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而有效的策略，这些策略将在大大减少的计算时间内显著改善数值模拟中的统计收敛性。这些策略包括在有限的模拟时间内对多个实现和流的多个状态进行有效采样。这将通过在运行时设计计算流场的特定数学变换来实现，可以将其视为触发自然状态转换的干扰。将探索系统的对称性，以设计(i)易于促进快速过渡到所需的未采样流动状态的转换，（ii）数学上一致并保持控制流体动力学方程。除了改进统计趋同外，该项目还寻求回答以下科学问题：(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，如横流和坡体尾迹中的射流，是否是相干结构锁定的类似现象的产物，以及当前的技术是否会产生对称的平均场，（ii）从新重建状态中添加的样本是否会改善低阶模型对系统动力学的长期预测，如适当正交分解。这项研究与教育计划相结合，该计划包括在凤凰城地区当地高中开展外展活动，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.