Computational fluid dynamics models based on Reynolds-averaged Navier--Stokes equations with turbulence closures still play important roles in engineering design and analysis. However, the development of turbulence models has been stagnant for decades. With recent advances in machine learning, data-driven turbulence models have become attractive alternatives worth further explorations. However, a major obstacle in the development of data-driven turbulence models is the lack of training data. In this work, we survey currently available public turbulent flow databases and conclude that they are inadequate for developing and validating data-driven models. Rather, we need more benchmark data from systematically and continuously varied flow conditions (e.g., Reynolds number and geometry) with maximum coverage in the parameter space for this purpose. To this end, we perform direct numerical simulations of flows over periodic hills with varying slopes, resulting in a family of flows over periodic hills which ranges from incipient to mild and massive separations. We further demonstrate the use of such a dataset by training a machine learning model that predicts Reynolds stress anisotropy based on a set of mean flow features. We expect the generated dataset, along with its design methodology and the example application presented herein, will facilitate development and comparison of future data-driven turbulence models.

中文翻译：

---

参数化几何的周期性山丘上的流动：直接模拟数据驱动湍流建模的数据集

基于具有湍流闭合的雷诺平均 Navier-Stokes 方程的计算流体动力学模型仍然在工程设计和分析中发挥重要作用。然而，湍流模型的发展几十年来一直停滞不前。随着机器学习的最新进展，数据驱动的湍流模型已成为值得进一步探索的有吸引力的替代方案。然而，数据驱动湍流模型开发的一个主要障碍是缺乏训练数据。在这项工作中，我们调查了当前可用的公共湍流数据库并得出结论，它们不足以开发和验证数据驱动模型。相反，我们需要更多来自系统和连续变化的流动条件（例如，雷诺数和几何形状）的基准数据，为此目的在参数空间中具有最大的覆盖范围。为此，我们对具有不同坡度的周期性山丘上的流动进行了直接数值模拟，从而产生了一系列从初期到轻度和大规模分离的周期性山丘上的流动。我们通过训练基于一组平均流特征预测雷诺应力各向异性的机器学习模型，进一步证明了此类数据集的使用。我们期望生成的数据集及其设计方法和此处介绍的示例应用程序将促进未来数据驱动湍流模型的开发和比较。我们通过训练基于一组平均流特征预测雷诺应力各向异性的机器学习模型，进一步证明了此类数据集的使用。我们期望生成的数据集及其设计方法和此处介绍的示例应用程序将促进未来数据驱动湍流模型的开发和比较。我们通过训练基于一组平均流特征预测雷诺应力各向异性的机器学习模型，进一步证明了此类数据集的使用。我们期望生成的数据集及其设计方法和此处介绍的示例应用程序将促进未来数据驱动湍流模型的开发和比较。