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昂，同时也具有挑战性。为了加速湍流的科学发现、工程设计和控制，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，该模型通过尊重湍流物理的关键方面，克服了以前方法的长期局限性。这些新工具将适用于大范围的湍流，可以被学术界、政府实验室和工业界的研究人员应用，以实现诸如通过减少喷气发动机和风力涡轮机的声发射来防止过度噪音暴露对健康的不利影响，以及通过增强地质流的预测建模能力来提高我们对气候变化的理解等目标。该研究计划与一个全面的教育计划紧密结合，该计划的核心部分是一系列专业制作的视频，每个视频都聚焦于流体动力学领域的关键贡献者及其工作中的影响问题。通过突出不同的研究人员，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的人群的学生将自己想象成未来的流体动力学研究人员，扩大STEM的参与，使劳动力多样化。该项目的技术目标是为湍流的长期和短期预测开发一对新的模型。关键的观察是，典型的基于流动状态扩展为空间模态和时变系数的降阶模型，如标准伽辽金模型及其现代替代品，违反了流动的空间和时间尺度之间的密切物理关系。通过在一个新生的时空建模框架内工作，其中流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。使该框架成熟的关键任务包括开发最佳空间基础，稀疏化三元非线性相互作用，以及推导误差估计。为了加速和简化它们的采用，在这个项目中开发的方法将被纳入桑迪亚国家实验室维护的开源平台Pressio。该奖项反映了美国国家科学基金会的法定使命，并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，被认为值得支持。

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.