High fidelity computational fluid dynamics (CFD) is increasingly being used to enable deeper understanding of turbulence or to aid in the design of practical engineering systems. While such CFD approaches can predict complex turbulence phenomena, the computational grid often needs to be sufficiently refined to accurately capture the flow, especially at high Reynolds number. As a result, the computational cost of the CFD can become very high. It therefore becomes impractical to adopt such simulations for parametric investigations. To mitigate this, we propose a framework where coarse grid simulations can be used to predict the fine grid results through machine learning. Coarsening the computational grid increases the grid-induced error and affects the prediction of turbulence. This requires an approach that can generate a data-driven surrogate model capable of predicting the local error distribution and correcting for the turbulence quantities. The proposed framework is tested using a turbulent bluff-body flow in an enclosed duct. We first highlight the flow field differences between the fine grid and coarse grid simulations. We then consider a set of scenarios to investigate the capability of the surrogate model to interpolate and extrapolate outside the training data range. The impact of operating conditions and grid sizes are considered. A Random Forest regression algorithm is used to construct the surrogate model. Two different sets of input features are investigated. The first only takes into account the grid-induced error and local flow properties. The second supplements the first using additional variables that serve to capture and generalise turbulence. The global and localised errors for the predictions are quantified. We show that the second set of input features is better at correcting for the biases due to insufficient resolution and spurious flow behaviour, providing more accurate and consistent predictions. The proposed method has proven to be capable of correcting the coarse-grid results and obtaining reasonable predictions for new, unseen cases. Based on the investigated cases, we found this method maximises the benefit of the available data and shows potential for a good predictive capability.

高保真计算流体动力学 (CFD) 越来越多地用于加深对湍流的理解或帮助设计实际工程系统。虽然这种 CFD 方法可以预测复杂的湍流现象，但计算网格通常需要足够细化才能准确捕获流动，特别是在高雷诺数时。因此，CFD 的计算成本可能会变得非常高。因此，采用这种模拟进行参数研究变得不切实际。为了缓解这个问题，我们提出了一个框架，可以使用粗网格模拟通过机器学习来预测细网格结果。粗化计算网格会增加网格引起的误差并影响湍流的预测。这需要一种能够生成数据驱动的代理模型的方法，该模型能够预测局部误差分布并校正湍流量。所提出的框架使用封闭管道中的湍流钝体流进行测试。我们首先强调细网格和粗网格模拟之间的流场差异。然后，我们考虑一组场景来研究代理模型在训练数据范围之外进行插值和外推的能力。考虑了运行条件和电网尺寸的影响。随机森林回归算法用于构建代理模型。研究了两组不同的输入特征。第一个仅考虑网格引起的误差和局部流动特性。第二个使用额外的变量来补充第一个，这些变量用于捕获和概括湍流。预测的全局和局部误差被量化。我们表明，第二组输入特征能够更好地纠正由于分辨率不足和虚假流行为而导致的偏差，从而提供更准确和一致的预测。事实证明，所提出的方法能够纠正粗网格结果，并为新的、未见过的情况获得合理的预测。根据调查的案例，我们发现这种方法最大限度地利用了可用数据，并显示出良好预测能力的潜力。