Deep neural networks for data-driven LES closure models
Deep neural networks for data-driven LES closure models
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DOI：
10.1016/j.jcp.2019.108910
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发表时间：
2019-12-01
影响因子：
4.1
通讯作者：
Munz, Claus-Dieter
中科院分区：
文献类型：
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作者：
Beck, Andrea;Flad, David;Munz, Claus-Dieter
在这项工作中，我们提出了一种新的基于数据的大涡模拟(LES)人工神经网络湍流模拟方法。我们定义了包括离散化算子在内的完全大涡模拟公式，并导出了相应的完全闭包项。然后，我们从衰减的均匀各向同性湍流的直接数值模拟中产生这些项的训练数据。我们设计和训练了基于局部卷积滤波的人工神经网络，以预测从粗网格量到闭包项的潜在未知非线性映射，而不需要先验假设。结果表明，同时选择粗网格基元变量和粗网格LES算子作为输入特征可以显著提高训练效果。所有被调查的网络都能够从数据中概括并学习近似，内部元素的交叉相关性高达47%，甚至73%，这表明完全闭合确实可以从所提供的粗格网数据中学习。由于学习的闭包项是近似的，直接应用会导致稳定性问题。我们展示了如何利用人工神经网络的输出来构建稳定和准确的模型。数据信息、时间和空间自适应涡粘性闭合得到了最好的结果。虽然有必要进一步研究该方法的普适性，但这项工作为进一步研究数据驱动的最优湍流模型提供了一个起点。(C)2019 Elsevier Inc.保留所有权利。
In this work, we present a novel data-based approach to turbulence modeling for Large Eddy Simulation (LES) by artificial neural networks. We define the perfect LES formulation including the discretization operators and derive the associated perfect closure terms. We then generate training data for these terms from direct numerical simulations of decaying homogeneous isotropic turbulence. We design and train artificial neural networks based on local convolution filters to predict the underlying unknown non-linear mapping from the coarse grid quantities to the closure terms without a priori assumptions. We show that selecting both the coarse grid primitive variables as well as the coarse grid LES operator as input features significantly improves training results. All investigated networks are able to generalize from the data and learn approximations with a cross correlation of up to 47% and even 73% for the inner elements, demonstrating that the perfect closure can indeed be learned from the provided coarse grid data. Since the learned closure terms are approximate, a direct application leads to stability issues. We show how to employ the artificial neural network output to construct stable and accurate models. The best results have been achieved with a data-informed, temporally and spatially adaptive eddy viscosity closure. While further investigations into the generalizability of the approach is warranted, this work thus represents a starting point for further research into data-driven, optimal turbulence models. (C) 2019 Elsevier Inc. All rights reserved.