基于人工神经网络的可压缩湍流大涡模拟模型

在国家数值风洞（NNW）工程项目的指导下，空间人工神经网络（SANN）模型被用于强可压缩湍流大涡模拟（LES）研究，其中流场的湍流马赫数分别为0.6、0.8、1.0。基于湍流的多尺度空间结构特性和人工神经网络方法发展的高精度空间神经网络（SANN）模型适用于不可压缩湍流和弱可压缩湍流。对于强可压缩湍流，流场中会出现激波结构，给大涡模拟带来了挑战。本文的研究结果表明：SANN模型适用于强可压缩湍流的大涡模拟。在先验分析中，SANN模型预测的亚格子应力和亚格子热流的相关系数超过0.995，远远高于梯度模型和近似反卷积模型等传统模型；传统模型的相对误差大于30%，而SANN模型在这方面有很大的改进，相对误差低于11%。在后验分析中，与隐式大涡模拟（ILES）、动态Smagorinsky模型（DSM）、动态混合模型（DMM）相比，SANN模型能更精确地预测能谱、各类湍流统计特性以及瞬态流动结构。因此，基于湍流多尺度空间结构特性的人工神经网络模型加深了人们对强可压缩湍流亚格子建模的认识，同时可以服务于NNW工程的流体力学模型构造。

Artificial neural network model for large-eddy simulation of compressible turbulence

The Spatial Artificial Neural Network (SANN) model is applied to perform Large Eddy Simulations (LES) of highly compressible turbulence at high turbulent Mach numbers of 0.6, 0.8 and 1.0 under the National Numerical Windtunnel (NNW) Project. In our previous studies, we developed the SANN model for incompressible and weakly compressible turbulence based on multi-scale spatial structures of turbulence. However, generations of shock waves in highly compressible turbulence pose great challenges to LES. This paper discusses the applicability of the SANN models for LES of highly compressible turbulence. It has been demonstrated that the correlation coefficients of the SANN model can be larger than 0.995. The relative errors of the SANN model can be smaller than 11%, which are much smaller than those of the traditional gradient model and the approximate deconvolution model in an a priori analysis for highly compressible turbulence. In an a posteriori analysis, we make a comparison of the results of the SANN model, the Implicit Large Eddy Simulation (ILES), the Dynamic Smagorinsky Model (DSM) and the Dynamic Mixed Model (DMM). It is shown that the SANN model performs better in the prediction of spectra and statistical properties of velocity and temperature, and instantaneous flow structures for highly compressible turbulence. The artificial neural network model with consideration of spatial features can deepen our understanding of subgrid-scale modeling for LES of highly compressible turbulence. At the same time, the model can contribute to the construction of the turbulence models of the NNW Project.