Physics-informed neural networks for the Reynolds-Averaged Navier-Stokes modeling of Rayleigh-Taylor turbulent mixing
Physics-informed neural networks for the Reynolds-Averaged Navier-Stokes modeling of Rayleigh-Taylor turbulent mixing
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DOI：
10.1016/j.compfluid.2023.106025
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发表时间：
2023-08-17
影响因子：
2.8
通讯作者：
Yong, Heng
中科院分区：
文献类型：
--
作者：
Xiao, Meng-Juan;Yu, Teng-Chao;Yong, Heng
最近，物理信息神经网络（PINNs）已被证明是一种有效的机器学习方法来解决偏微分方程。然而，这种方法在解决具有激波/材料不连续性或多尺度特征（如湍流）的复杂问题时可能非常具有挑战性。在本文中，我们提出了一个改进的PINNs框架求解雷诺平均Navier-Stokes（RANS）方程的瑞利-泰勒（RT）不稳定性诱导的湍流混合。RANS模型基于K-L模型的闭合形式。然而，湍流动能K和湍流长度尺度L的传输方程不包括在内，而是直接由神经网络预测，从而导致反问题。对原有的PINN进行了一些修改，以提高其对RT湍流混合的适用性，并加快训练优化过程。我们首先研究的适用性PINNs解决多材料欧拉方程不考虑湍流。然后，PINNs应用于RT湍流混合问题使用传统的K-L模型的训练数据。结果证实了PINN使用有限的训练数据预测整个时空场的能力。接下来，我们使用隐式大涡模拟（ILES）的数据进一步训练PINN，这产生了一个基于PINN的湍流模型，其性能优于传统的K-L模型。这些结果揭示了进一步的应用PINNs复杂的问题，特别是那些有限的测量数据和未知的物理模型。
Recently, Physics-informed neural networks (PINNs) have proven to be an efficient machine-learning method for solving partial differential equations. However, this method can be quite challenging when solving complex problems with shock/material discontinuities or multi-scale features, such as turbulence. In this paper, we propose an improved PINNs framework for solving the Reynolds-averaged Navier-Stokes (RANS) equations for turbulent mixing induced by the Rayleigh-Taylor (RT) instability. The RANS model is based on the closure form of the K-L model. However, the transport equations of the turbulent kinetic energy K and turbulent length scale L are not included and are instead predicted directly by neural networks, thus resulting in an inverse problem. Several modifications are made to the original PINNs to improve its applicability to RT turbulent mixing and accelerate the training optimization process. We first examine the applicability of the PINNs for solving multi-material Euler equations without considering turbulence. Then, PINNs is applied to the RT turbulent mixing problem using training data from the traditional K-L model. The results confirm the ability of the PINNs to predict the entire spatiotemporal field using limited training data. Next, we further train the PINNs using data from the implicit large eddy simulation (ILES), which yields a PINN-based turbulence model that performs better than the traditional K-L model. These results shed light on further applications of PINNs for complex problems, particularly those with limited measurement data and unknown physical models.