Fast simulations of turbulent flows based on spatiotemporal statistical information

1337000 Vedula该项目的总体目标是使用新的建模框架显著提高湍流大涡模拟的速度、精度和时空预测能力。这种对在多个时间情况下跨越空间多个点的大规模涡旋相互作用的预测的这种增强在几个应用中具有重要意义，包括(1)破坏性龙卷风路径的统计预测和(2)远离震源的不同位置的喷流噪声强度的预测和控制。虽然这种湍流模型的发展需要对湍流中时空相互作用的统计性质有一个基本的了解，但目前在这方面缺乏足够的知识(例如，关于高雷诺数下的多点时空相关性)。为了解决各向同性和壁面有界湍流的这一知识空白，并开发基于时空结构的拟议框架，PI将专注于实现以下目标：(1)利用传统和新的计算方法，全面研究(1D)Burgers湍流、(3D)各向同性湍流和高雷诺数下湍流通道流动结构的时空波动的统计特性，(2)基于湍流的时空结构，开发新的、具有极高预测能力的Burgers和各向同性湍流的最优湍流模型，以及(3)推广所提议的湍流通道流动框架。通过解决现有模型由于不能准确地捕捉湍流的大尺度时空结构而产生的主要缺陷，所提出的框架将极大地提高湍流建模的技术水平。假设大涡模拟的速度和精度可以显著提高，如果相关的亚网格尺度的应力模式是基于与湍流的基本时空统计一致的信息构建的。根据这一假设，基于最优预报形式、误差最小化原理、随机估计和时空相关性的相关信息，通过新的亚网格尺度模型，在过滤(或粗粒度)控制方程中仔细考虑了未分辨的时空尺度对分辨尺度的影响。由此产生的亚格子尺度模式不仅试图保持湍流的时空结构，而且由于时空相关性中包含了粗粒度的时间信息，因此在数值模拟中允许更大的时间步长，从而能够更快地模拟湍流。由于PI的初步研究表明，该方法在应用于广泛的其他正则非线性动力系统时是成功的，因此该框架在快速和可靠的湍流模拟方面似乎是有希望的。通过拟议的测试问题和目标，私人投资促进计划还计划展示拟议的湍流框架的效用，并为更复杂的流动的应用获得见解。就更广泛的影响而言，该项目不仅有望对湍流的基本理解做出重要贡献，而且还有望对各种科学和工程应用中快速可靠的湍流模拟以及与喷射噪声声学、流固耦合、湍流控制、燃气轮机、污染物扩散和天气现象相关的产品创新产生影响。为了向来自不同学科的学生传播有关基本概念和研究成果的知识，专业督导计划提供一项新的研究生水平的多学科课程，内容涉及湍流模拟和降阶建模，并将通过网站向公众提供课堂讲稿。为了产生进一步的影响，私人投资者还建议在美国全国计算力学大会上组织一个关于湍流建模最新进展的小型研讨会，以将框架和结果传达给该领域的其他研究人员。该项目将支持包括博士和本科生在内的研究人员的培训，他们将通过俄克拉荷马大学的多样性丰富计划从代表性不足的群体中积极招募。

1337000 VedulaThe overall goal of this project is to significantly enhance the speed, accuracy, and spatiotemporal prediction capabilities of large eddy simulations of turbulent flows using a new modeling framework. Such enhancements in prediction of large-scale eddy interactions across multiple points in space at multiple time instances are of importance in several applications including (i) statistical prediction of the path of a destructive tornado and (ii) prediction and control of jet-noise intensities at various locations away from the source. While the development of such models for turbulent flows requires a fundamental understanding of the statistical nature of spatiotemporal interactions in turbulence, sufficient knowledge in this context (e.g., regarding multi-point space-time correlations at high Reynolds numbers) is currently lacking. To address this knowledge gap for isotropic and wall-bounded turbulent flows and to develop the proposed framework based on space-time structure, the PIs will focus on achieving the following objectives: (1) conduct a comprehensive study of statistical properties of spatiotemporal fluctuations in (1D) Burgers turbulence, (3D) isotropic turbulence and turbulent channel flow configurations at high Reynolds numbers using traditional and novel computational approaches, (2) develop new, optimal turbulence models for Burgers and isotropic turbulence with highly improved prediction capabilities, based on space-time structure of turbulence, and (3) generalize the proposed framework for turbulent channel flows. The proposed framework would significantly advance the state of the art in turbulence modeling by addressing a major drawback of existing models arising from their inability to accurately capture the large-scale spatiotemporal structure of turbulent flows. The hypothesis is that the speed and accuracy of large eddy simulations can be significantly improved if the relevant subgrid-scale stress models are constructed based on information that is consistent with the underlying spatiotemporal statistics of the turbulent flow. In accordance with this hypothesis, the effects of unresolved spatial and temporal scales on the resolved scales are carefully considered in the filtered (or coarse-grained) governing equations via new subgrid scale models, based on the optimal prediction formalism, principles of error minimization, stochastic estimation, and relevant information on spatiotemporal correlations. The resulting subgrid scale models will not only attempt to preserve the spatiotemporal structure of the turbulent flow but will also enable faster simulations of turbulent flows by allowing for larger time steps in numerical simulations due to inclusion of coarse-grained temporal information contained in the space-time correlations. The proposed framework appears to be promising for fast and reliable turbulent flow simulations, as preliminary studies by the PIs demonstrated that the method was successful when applied to a broad range of other canonical nonlinear dynamical systems. Through the proposed test problems and objectives, the PIs also plan to demonstrate the utility of the proposed framework for turbulent flows and gain insights for applications for more complex flows. In terms of the broader impacts, this project is not only expected to make important contributions to the fundamental understanding of turbulence, but is also expected to have an impact on fast and reliable turbulence simulations in various scientific and engineering applications and product innovations relevant to jet noise acoustics, fluid-structure interaction, turbulence control, gas turbines, pollutant dispersion, and weather phenomena. In order to disseminate knowledge about the underlying basic concepts and research results to students from different disciplines, the PIs plan to offer a new graduate level multi-disciplinary course on turbulence simulation and reduced order modeling, with lecture notes to be made available to the general public through a website. For further impact, the PIs also propose to organize a minisymposium on recent advances in turbulence modeling at the US National Congress on Computational Mechanics to communicate the framework and results to other researchers in the field. This project will support the training of researchers including Ph.D. and undergraduate students, who will be actively recruited from underrepresented groups through Diversity Enrichment Programs at U. Oklahoma.