Formulating turbulence closures using sparse regression with embedded form invariance
Formulating turbulence closures using sparse regression with embedded form invariance
复制标题
DOI：
10.1103/physrevfluids.5.084611
复制
发表时间：
2020-08-28
影响因子：
2.7
通讯作者：
Capecelatro, J.
中科院分区：
文献类型：
--
作者：
Beetham, S.;Capecelatro, J.
提出了一种数据驱动框架，用于求解Reynolds-average Navier-Stokes （RANS）方程的闭包。近年来，科学界已经转向机器学习技术，将数据转化为改进的RANS闭包。虽然该领域的工作主体主要利用神经网络（nn），但我们交替利用稀疏回归框架。这种方法有两个重要的特性：(1)所得模型是封闭的代数形式，允许绘制直接的物理推断并将其简单地集成到现有的计算流体动力学求解器中；(2)可以通过深思熟虑的特征空间剪裁来保证伽利略不变性。我们的方法证明了两类流动：均匀自由剪切湍流和波浪壁面上的湍流。基于波浪壁结构学习的模型，然后通过后向台阶的流动进行验证。这项工作展示了与现代神经网络相似的性能，但具有可解释性，易用性和传播性增加以及对稀疏和噪声训练数据集的鲁棒性的额外好处。
A data-driven framework for formulation of closures of the Reynolds-average Navier-Stokes (RANS) equations is presented. In recent years, the scientific community has turned to machine learning techniques to translate data into improved RANS closures. While the body of work in this area has primarily leveraged neural networks (NNs), we alternately leverage a sparse regression framework. This methodology has two important properties: (1) The resultant model is in a closed, algebraic form, allowing for direct physical inferences to be drawn and naive integration into existing computational fluid dynamics solvers, and (2) Galilean invariance can be guaranteed by thoughtful tailoring of the feature space. Our approach is demonstrated for two classes of flows: homogeneous free shear turbulence and turbulent flow over a wavy wall. The model learned based upon the wavy wall configuration is then validated against flow over a backward-facing step. This work demonstrates similar performance to that of modern NNs but with the added benefits of interpretability, increased ease of use and dissemination, and robustness to sparse and noisy training data sets.