Towards efficient state estimation in wall-bounded flows: hierarchical adjoint data assimilation

目前正在开发一种新的框架，旨在将对湍流的稀疏观测（流体的速度变化混乱）转化为对这种流动的准确、详细的预测。现场试验的观测结果往往受到空间和分辨率的限制。尽管存在这些限制，但从这些观测中得出的预测在气象学、海洋学和航空航天工程等众多领域至关重要，从稀疏的数据中产生丰富的解释。将这些观测结果与复杂的模拟相结合的过程，即所谓的数据同化，由于湍流中存在复杂的性质和广泛的尺度，提出了重大的挑战。为了解决这个问题，我们的项目计划开发一个基于分层伴随的数据同化框架，旨在跨越多个分辨率的模拟，同时考虑到不同尺度的稀疏测量。该项目将极大地促进我们对湍流的认识，提高数值模拟与现场试验之间的协同作用，从而提高模拟的保真度。该项目将开发开源软件工具，封装基于层次的数据同化（HADA）框架。这些工具将提供给研究人员和从业人员，促进更广泛的使用和进一步的发展。文档和教程将随软件一起提供，以方便使用。该项目的技术核心围绕着基于伴随的数据同化技术和分层方法的独特组合。我们的目标是采用最优的涡流粘度模型来稳定伴随油田，解决现有的挑战，如能量增长和缓慢的收敛速度通常与基于伴随技术相关。提出的分层数据同化框架利用涡流黏度场作为不同网格分辨率之间的桥梁，在时空分辨率层次上逐步重建流场。该方法提高了湍流中基于伴随的数据同化的性能，同时减少了传统方法经常产生的计算需求。通过提供可靠、高效和可扩展的状态估计工具，该框架可以推进工程和环境系统的逆向问题。它提供的对湍流伴随敏感性的增强理解可以显著改善天气预报、气候建模、污染扩散和其他相关领域的预测和决策过程。此外，这项研究也将促进跨学科的合作，并作为宝贵的教育资源。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。

A novel framework is currently under development, aiming to translate sparse observations of turbulent flows - where a fluid's speed varies chaotically - into accurate, detailed predictions of such flows. Observations from field tests are often limited by space and resolution. Despite these limitations, the predictions derived from such observations are crucial in a myriad of fields such as meteorology, oceanography, and aerospace engineering, yielding rich interpretations from sparse data. The process of merging these observations with complex simulations, known as Data Assimilation, poses significant challenges due to the intricate nature and wide range of scales present in turbulence. To address this, our project plans to develop a Hierarchical Adjoint-based Data Assimilation framework aiming to bridge simulations across multiple resolutions, while taking into account the sparse measurements at different scales. This project could significantly advance our understanding of turbulence and improve the synergy between numerical simulation and field tests, thereby enhancing the fidelity of these simulations. The project will develop open-source software tools encapsulating the Hierarchical Adjoint-based Data Assimilation (HADA) framework. These tools will be made available to researchers and practitioners alike, promoting broader usage and further development. Documentation and tutorials will accompany the software to facilitate ease of use. The technical core of this project revolves around a unique combination of adjoint-based data assimilation techniques and hierarchical methodology. We aim to employ an optimal eddy viscosity model to stabilize the adjoint fields, addressing existing challenges such as energy growth and slow convergence rates typically associated with adjoint-based techniques. The proposed Hierarchical Data Assimilation framework gradually reconstructs flow fields across a hierarchy of spatiotemporal resolutions, using eddy-viscosity fields as a bridge between different grid resolutions. This approach enhances the performance of adjoint-based data assimilation in turbulent flows, while simultaneously reducing the computational demands that conventional methods often incur. By delivering a reliable, efficient, and scalable state estimation tool, this framework can advance inverse problems for engineering and environmental systems. The enhanced understanding of adjoint sensitivity in turbulent flows it provides could significantly improve predictions and decision-making processes in areas such as weather forecasting, climate modeling, pollution dispersion, and other relevant areas. Moreover, the research will also foster interdisciplinary collaborations and serve as an invaluable educational resource.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.