CAREER: Scale-dependent reduced-order models for turbulent flows

湍流在科学和工程中无处不在，其广泛的空间和时间尺度使其模拟成本高，建模具有挑战性。 为了加速科学发现、工程设计和湍流控制，迫切需要有效的降阶模型来代替昂贵的模拟。 该项目将通过开发一类新的降阶模型来满足这一需求，通过尊重湍流物理学的关键方面，克服以前方法的长期局限性。 这些新工具将适用于各种湍流，并可由学术界，政府实验室和工业界的研究人员应用，以实现以下目标，例如通过减轻喷气发动机和风力涡轮机的声发射来防止过度噪声暴露对健康的不利影响，并通过增强地质流动的预测建模能力来提高我们对气候变化的理解。 该研究项目与综合教育项目紧密结合，其核心组成部分是一系列专业制作的视频，每个视频都突出了流体动力学领域的关键贡献者以及他们所研究的影响力问题。通过突出多样化的研究人员，不仅关注科学，而且关注科学家，这些视频将帮助来自代表性不足人群的学生将自己设想为未来的流体动力学研究人员，扩大STEM的参与并使劳动力多样化。 该项目的技术目标是开发一对新模型，用于湍流的长期和短期预测。 关键的观察是，典型的降阶模型的基础上扩展到空间模式和时变系数的流动状态，如标准的伽辽金模型和他们的现代替代品，违反了密切的物理关系的空间和时间尺度的流动。 通过在一个新生的空间-时间建模框架内工作，在该框架中，流动状态扩展为依赖于空间和时间的模式，并战略性地选择时间基函数，所提出的方法尊重空间和时间尺度之间的物理关系。 使这个框架成熟的关键任务包括开发最佳的空间基础，稀疏三元非线性相互作用，并得出误差估计。 为了加速和简化他们的采用，在这个项目中开发的方法将被纳入由桑迪亚国家实验室维护的开源平台Pressio。这个奖项反映了NSF的法定使命，并被认为值得通过使用基金会的知识价值和更广泛的影响审查标准进行评估来支持。

Turbulent flows are ubiquitous in science and engineering, and their wide range of spatial and temporal scales make them simultaneously expensive to simulate and challenging to model. Effective reduced-order models that can be used in place of costly simulations are urgently needed to accelerate scientific discovery, engineering design, and control of turbulent flows. This project will fill this need by developing a new class of reduced-order models that, by respecting key aspects of turbulent flow physics, overcome longstanding limitations of previous methods. These new tools will be applicable to a wide range of turbulent flows and can be applied by researchers in academia, government labs, and industry to achieve objectives such as preventing the adverse health effects of excessive noise exposure by mitigating acoustic emissions of jet engines and wind turbines and improving our understanding of climate change by enhancing predictive modeling capabilities of geological flows. The research program is closely integrated with a comprehensive education program, the central component of which is a series of professionally produced videos, each spotlighting a key contributor to the field of fluid dynamics and the impactful problems they work on. By highlighting a diverse set of researchers and focusing on not just the science, but also the scientist, the videos will help empower students from underrepresented populations to envision themselves as future fluid-dynamics researchers, broadening participation in STEM and diversifying the workforce. The technical goal of the project is to develop a pair of new models tailored for long- and short-time prediction of turbulent flows. The critical observation is that typical reduced-order models based on expansion of the flow state into spatial modes and time-varying coefficients, such as standard Galerkin models and their modern alternatives, violate the intimate physical relationship between spatial and temporal scales of the flow. By working within a nascent space-time modeling framework, in which the flow state is expanded into modes that depend on both space and time, and strategically selecting the temporal basis functions, the proposed approach respects the physical relationship between spatial and temporal scales. Critical tasks to bring this framework to maturation include developing optimal spatial bases, sparsifying triadic nonlinear interactions, and deriving error estimates. To accelerate and streamline their adoption, the methods developed during this project will be incorporated into the open-source platform Pressio maintained by Sandia National Laboratory.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.