A novel machine learning algorithm is presented, serving as a data-driven turbulence modeling tool for Reynolds Averaged Navier-Stokes (RANS) simulations. This machine learning algorithm, called the Tensor Basis Random Forest (TBRF), is used to predict the Reynolds-stress anisotropy tensor, while guaranteeing Galilean invariance by making use of a tensor basis. By modifying a random forest algorithm to accept such a tensor basis, a robust, easy to implement, and easy to train algorithm is created. The algorithm is trained on several flow cases using DNS/LES data, and used to predict the Reynolds stress anisotropy tensor for new, unseen flows. The resulting predictions of turbulence anisotropy are used as a turbulence model within a custom RANS solver. Stabilization of this solver is necessary, and is achieved by a continuation method and a modified $k$-equation. Results are compared to the neural network approach of Ling et al. [J. Fluid Mech, 807(2016):155-166, (2016)]. Results show that the TBRF algorithm is able to accurately predict the anisotropy tensor for various flow cases, with realizable predictions close to the DNS/LES reference data. Corresponding mean flows for a square duct flow case and a backward facing step flow case show good agreement with DNS and experimental data-sets. Overall, these results are seen as a next step towards improved data-driven modelling of turbulence. This creates an opportunity to generate custom turbulence closures for specific classes of flows, limited only by the availability of LES/DNS data.

中文翻译：

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使用具有不变性的随机森林对雷诺应力张量进行数据驱动建模

提出了一种新颖的机器学习算法，用作雷诺平均纳维-斯托克斯 (RANS) 模拟的数据驱动湍流建模工具。这种称为张量基础随机森林 (TBRF) 的机器学习算法用于预测雷诺应力各向异性张量，同时通过使用张量基础来保证伽利略不变性。通过修改随机森林算法以接受这样的张量基，创建了一个健壮、易于实现且易于训练的算法。该算法使用 DNS/LES 数据在几种流动情况下进行训练，并用于预测新的、看不见的流动的雷诺应力各向异性张量。湍流各向异性的结果预测用作自定义 RANS 求解器中的湍流模型。这个求解器的稳定是必要的，并且是通过延续方法和修改后的 $k$-equation 实现的。结果与 Ling 等人的神经网络方法进行了比较。[J. 流体机械，807（2016）：155-166，（2016）]。结果表明，TBRF算法能够准确预测各种流动情况下的各向异性张量，可实现的预测接近DNS/LES参考数据。方形管道流情况和后向阶梯流情况的相应平均流量显示出与 DNS 和实验数据集的良好一致性。总体而言，这些结果被视为改进湍流数据驱动建模的下一步。这为特定类别的流生成自定义湍流闭合创造了机会，仅受 LES/DNS 数据的可用性限制。807(2016):155-166, (2016)]。结果表明，TBRF算法能够准确预测各种流动情况下的各向异性张量，可实现的预测接近DNS/LES参考数据。方形管道流动案例和后向阶梯流动案例的相应平均流量显示出与 DNS 和实验数据集的良好一致性。总体而言，这些结果被视为改进湍流数据驱动建模的下一步。这为特定类别的流生成自定义湍流闭合创造了机会，仅受 LES/DNS 数据的可用性限制。807(2016):155-166, (2016)]。结果表明，TBRF算法能够准确预测各种流动情况下的各向异性张量，可实现的预测接近DNS/LES参考数据。方形管道流动案例和后向阶梯流动案例的相应平均流量显示出与 DNS 和实验数据集的良好一致性。总体而言，这些结果被视为改进湍流数据驱动建模的下一步。这为特定类别的流生成自定义湍流闭合创造了机会，仅受 LES/DNS 数据的可用性限制。方形管道流动案例和后向阶梯流动案例的相应平均流量显示出与 DNS 和实验数据集的良好一致性。总体而言，这些结果被视为改进湍流数据驱动建模的下一步。这为特定类别的流生成自定义湍流闭合创造了机会，仅受 LES/DNS 数据的可用性限制。方形管道流情况和后向阶梯流情况的相应平均流量显示出与 DNS 和实验数据集的良好一致性。总体而言，这些结果被视为改进湍流数据驱动建模的下一步。这为特定类别的流生成自定义湍流闭合创造了机会，仅受 LES/DNS 数据的可用性限制。