CDS&E: Physics Guided Super-Resolution for Turbulent Transport

了解湍流现象是我们理解空气动力学、水力学、天体物理、推进、大气、海洋、医学等多个领域中许多自然和技术过程的关键。Navier-Stokes方程的直接数值模拟被广泛认为是在捕捉复杂的湍流输运过程中具有最高保真度的主要计算方法。然而，流的时间和长度范围很广，这使得即使在最先进的高性能超级计算机上，域名系统也昂贵得令人望而却步。大涡模拟(LES)过滤掉了小尺度的输运，提供了一种计算量小得多的替代方法。然而，由于相关联的过滤，由LES生成的数据具有较低的精度，并且期望从过滤后的LES数据重构原始真实的DNS结果。这项建议描述了一种新的物理指导的机器学习方法来执行这种重建，并对各种湍流进行系统评估。该项目旨在通过三项创新推进高保真湍流的恢复。首先，开发了一种新的物理引导的深度学习模型，用于从低分辨率的粗大涡模拟数据中重建精细的湍流数据。将纳入额外的物理学习目标和关系，以确保建议的模型满足与流程相关的特定物理约束，并且它也可推广到大规模模拟。其次，将开发一种新的深度学习方案，并利用该方案从目前可以进行的最可靠的大涡模拟构造高保真超分辨率场。最后，将考虑各种各样的湍流，从被动不可压缩到化学反应可压缩，以进行全面的模型评估。这个项目有可能提高我们在许多科学和工程领域有效地模拟高分辨率湍流的能力。研究结果将用于开发本科生和研究生教育以及K-12外游的材料。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Understanding turbulence phenomenon is the key to our comprehension of many natural and technological processes in diverse fields including aerodynamics, hydraulics, astrophysics, propulsion, atmospherics, oceanics, medicine, and many others. Direct numerical simulation (DNS) of the Navier-Stokes equations is widely recognized as the prime computational methodology with the highest fidelity in capturing the intricacies of turbulent transport. However, the wide range of flow's time and length scales makes DNS prohibitively expensive and time consuming even on the most advanced high-performance supercomputers. Large eddy simulation (LES), which filters out the very small-scale transport, provides an alternative with a much lower computational cost. However, the data generated by LES are of lower accuracy due to the associated filtering, and it is desirable to reconstruct the original true DNS results from the filtered LES data. This proposal describes a novel physics-guided machine learning methodology to perform this reconstruction with a systematic assessment for a variety of turbulent flows. This project aims to advance the restoration of high-fidelity turbulent flows via three innovations. First, a new physics-guided deep learning model will be developed to reconstruct fine-resolution turbulent flow data from low-resolution coarse LES data. Additional physical learning objectives and relationships will be incorporated to ensure that the proposed model meets specific physical constraints associated with the flow, and it is also generalizable for large scale simulations. Second, a novel deep learning scheme will be developed and utilized to construct high fidelity super-resolution fields from the most reliable LES that can be currently conducted. Finally, a wide variety of turbulent flows will be considered, ranging from passive incompressible, to chemically reactive compressible for comprehensive model assessments. This project has the potential to improve our capability to efficiently simulate high-resolution turbulent flows in many scientific and engineering domains. The research results will be used to develop materials for both undergraduate and graduate education, and for K-12 outreach.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.