Turbulent flow consists of structures with a wide range of spatial and temporal scales which are hard to resolve numerically. Classical numerical methods as the Large Eddy Simulation (LES) are able to capture fine details of turbulent structures but come at high computational cost. Applying generative adversarial networks (GAN) for the synthetic modeling of turbulence is a mathematically well-founded approach to overcome this issue. In this work, we investigate the generalization capabilites of GAN-based synthetic turbulence generators when geometrical changes occur in the flow configuration (e.g. aerodynamic geometric optimization of structures such as airfoils). As training data, we use the flow around a low-pressure turbine (LPT) stator with periodic wake impact obtained from highly resolved LES. To simulate the flow around a LPT stator, we use the conditional deep convolutional GAN framework pix2pixHD conditioned on the position of a rotating wake in front of the stator. For the generalization experiments we exclude images of wake positions located at certain regions from the training data and use the unseen data for testing. We show the abilities and limits of generalization for the conditional GAN by extending the regions of the extracted wake positions successively. Finally, we evaluate the statistical properties of the synthesized flow field by comparison with the corresponding LES results.

翻译：湍流由包含广泛时空尺度的结构组成，这些结构在数值上难以解析。经典数值方法如大涡模拟（LES）能够捕捉湍流结构的精细细节，但计算成本高昂。将生成对抗网络（GAN）应用于湍流的合成建模是一种数学基础扎实的解决方案。本研究探讨了基于GAN的合成湍流生成器在流动几何构型发生变化时（例如机翼等结构的空气动力学几何优化）的泛化能力。训练数据采用高分辨率LES模拟的低压涡轮（LPT）静叶在周期性尾迹撞击下的流场。为模拟LPT静叶周围流场，我们使用条件深度卷积GAN框架pix2pixHD，该框架以静叶前方旋转尾迹的位置为条件。在泛化实验中，我们从训练数据中排除特定区域尾迹位置对应的图像，并用未见数据进行测试。通过逐步扩展提取尾迹位置的区域范围，我们揭示了条件GAN的泛化能力及其局限性。最后，通过与相应LES结果对比，评估了合成流场统计特性的准确性。