基于人工神经网络的湍流大涡模拟方法

大涡模拟方法(LES)是研究复杂湍流问题的重要工具,在航空航天、湍流燃烧、气动声学、大气边界层等众多工程领域中具有广泛的应用前景.大涡模拟方法采用粗网格计算大尺度上的湍流结构,并用亚格子(SGS)模型近似表达滤波尺度以下的流动结构对大尺度流场的作用.传统的亚格子模型由于只利用了单点流场信息和简单的函数关系,在先验验证中相对误差较大, 在后验验证中耗散过强. 近几年来,机器学习方法在湍流建模问题中得到了越来越多的应用.本文介绍了基于人工神经网络(ANN)的湍流亚格子模型的最新进展.详细地讨论了人工神经网络混合模型、空间人工神经网络模型和反卷积人工神经网络模型的构造方法.借助于人工神经网络强大的数据插值能力,新的亚格子模型的先验精度和后验精度均有显著提升. 在先验验证中,新模型所预测的亚格子应力的相关系数超过了0.99,在预测精度上远高于传统的大涡模拟模型. 在后验验证中,新模型对各类湍流统计量和瞬态流动结构的预测都优于隐式大涡模拟方法、动态Smagorinsky模型、动态混合模型等传统模型.因此, 人工神经网络方法在发展复杂湍流的先进大涡模拟模型中具有很大的潜力. 

ARTIFICIAL NEURAL NETWORK-BASED SUBGRID-SCALE MODELS FOR LARGE-EDDY SIMULATION OF TURBULENCE 1)

Large eddy simulation (LES) is an important method to investigate different types of complex turbulent flows, which has been widely applied to the turbulent flows in aerospace, combustion, acoustics, atmospheric boundary layer, etc. Large eddy simulation effectively solves the large-scale motions of turbulence and models the effects of small-scale dynamics on the large-scale structures by using subgrid-scale (SGS) models. Traditional SGS models only use the single-point information based on some simple forms of analytical functions to approximate the SGS terms. Thus, traditional models exhibit quite large relative errors in the a priori study, and have excessive dissipations in the a posteriori study. Recently, machine learning approaches have been widely used to develop turbulence models, including the Reynolds-averaged Navier-Stokes (RANS) models and LES models. In this paper, we review the recent developments of artificial neural network (ANN) methods for SGS models in LES of turbulence. We discuss three different ANN-based SGS models, including artificial neural network mixed model (ANNMM), spatial artificial neural network (SANN) model and deconvolutional artificial neural network (DANN) model. Due to the strong data interpolation capability of artificial neural networks, the new SGS models exhibit improved accuracy in both a priori study and a posteriori study. In the a priori study, the new SGS models can predict the SGS stress much more accurately than the traditional SGS models: the correlation coefficients predicted by new SGS models can be made larger than 99%. In the a posteriori study, the new SGS models can give better predictions on turbulence statistics and instantaneous flow structures, as compared to a variety of traditional SGS models including the implicit LES (ILES), dynamic Smagorinsky model (DSM), and dynamic mixed model (DMM). It is shown that artificial neural network-based methods have strong potentials for the developments of advanced SGS models in the LES of complex turbulence.