CBET-EPSRC: Deep Learning Closure Models for Large-Eddy Simulation of Unsteady Aerodynamics

计算模拟越来越多地使设计更轻、更高效和更高性能的飞行器成为可能。目前的计算能力已经成功地帮助了航空航天设计的许多进步，但在选择用于表示湍流的模型方面仍然存在挑战。由于计算资源的实际限制，工程设计的计算模拟通常忽略了湍流的复杂特征。用于近似缺失物理的模型包含必须根据数据校准的参数，这对于未知流来说是具有挑战性的。这些模型中简单的数学形式限制了它们的准确性。近年来，利用机器学习和约束优化技术开发了有效的数值方法来校准流动模拟过程中复杂模型的参数。这些方法对简单的湍流流动是成功的，但还没有应用于空气动力学中遇到的复杂流动。该项目的主要目标是开发方法，通过校准湍流模型来模拟实际气动流动，这将提高它们对具有挑战性的配置的预测精度。所开发的优化方法将广泛适用于各个工程领域，而不仅仅局限于空气动力学领域，并且将以开源、高性能软件包的形式公开提供。该项目将通过开发深度学习闭包和优化方法，为湍流分离流和再循环流的大涡模拟提供准确、高效的计算流体动力学模型。该模型将使用基于伴随的方法在可压缩的Navier-Stokes方程上进行优化，这将通过避免构建高维梯度来实现有效的数据同化。与成本相当的最先进的模型相比，由此产生的模型将能够显著提高精度，或者等效地，显著降低计算成本以达到相当的精度。高保真的数值数据集，为几种尾迹几何形状和分离翼型流动将产生的目标数据，为优化过程。此外，将开发一类新的在线优化方法，以实现动态的、无数据的封闭模型，该模型将直接从控制方程中学习，并将开发一种混合的、多尺度深度学习公式来模拟近壁湍流。科学界更广泛地对利用大型数据集和机器学习技术感兴趣；因此，该项目有潜力开发出跨学科广泛采用的方法。由此产生的算法、方法、数据集和代码将被传播，以促进空气动力学社区和跨学科的采用。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。

Computational simulations increasingly enable the design of lighter, more efficient, and higher-performance flight vehicles. Current computational capabilities have successfully aided many advances in aerospace design, but challenges remain in the selection of the models used to represent turbulence. Due to practical limits on computing resources, computational simulations for engineering design typically neglect the intricate features of turbulence. The models used to approximate the missing physics contain parameters that must be calibrated to data, which is challenging for unknown flows. Simple mathematical forms in these models limit their accuracy. Recently, efficient numerical methods to calibrate the parameters of complex models during flow simulations have been developed using techniques from machine learning and constrained optimization. These methods have been successful for simple turbulent flows but have not been applied to the complex flows encountered in aerodynamics. The principal objective of this project is to develop methods by which to calibrate turbulence models for simulations of practical aerodynamic flows, which will enhance their predictive accuracy for challenging configurations. The optimization methods to be developed will be broadly applicable across engineering fields, not limited to aerodynamics, and will be made publicly available in an open-source, high-performance software package.This project will address the need for accurate, efficient computational fluid dynamics models by developing deep learning closures and optimization methods for large-eddy simulations of turbulent separated and recirculating flows. The models will be optimized over the compressible Navier–Stokes equations using an adjoint-based approach, which will enable efficient data assimilation by avoiding the need to construct high-dimensional gradients. The resulting models will enable significant accuracy improvements compared to state-of-the-art models for comparable cost, or equivalently, significantly reduced computational cost for comparable accuracy. High-fidelity numerical datasets for several wake geometries and separated airfoil flows will be generated as target data for the optimization procedure. Additionally, a new class of online optimization methods will be developed to enable dynamic, data-free closure models that will learn directly from the governing equations, and a hybrid, multiscale deep learning formulation will be developed to model near-wall turbulent flows. The scientific community more broadly is interested in leveraging large datasets and machine learning techniques; this project therefore has potential to develop methods to be widely adopted across disciplines. The resulting algorithms, methods, datasets, and codes will be disseminated to foster adoption within the aerodynamics community and across scientific disciplines.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.