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

目前正在开发一种新的框架，旨在将湍流的稀疏观测（流体的速度混乱地变化）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。尽管存在这些局限性，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无数领域都是至关重要的，可以从稀疏的数据中得到丰富的解释。将这些观测结果与复杂的模拟（称为数据同化）相结合的过程，由于湍流的复杂性质和广泛的尺度范围，带来了重大挑战。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，旨在跨多个分辨率桥接模拟，同时考虑到不同尺度的稀疏测量。该项目可以大大提高我们对湍流的理解，并改善数值模拟和现场测试之间的协同作用，从而提高这些模拟的保真度。该项目将开发封装分层伴随数据同化（HADA）框架的开源软件工具。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发展。文档和教程将随软件一起提供，以便于使用。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。我们的目标是采用一个最佳的涡流粘度模型来稳定伴随场，解决现有的挑战，如能源增长和缓慢的收敛速度通常与伴随为基础的技术。建议的分层数据同化框架逐步重建流场的时空分辨率的层次结构，使用涡粘性场作为不同的网格分辨率之间的桥梁。这种方法提高了伴随数据同化在湍流中的性能，同时减少了传统方法经常产生的计算需求。通过提供一个可靠的，高效的，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问题。它提供的对湍流中伴随敏感性的增强理解可以显着改善天气预报，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，该研究还将促进跨学科合作，并作为一个宝贵的教育资源。该奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

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.