Generalization capabilities of conditional GAN for turbulent flow under changes of geometry

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.

Generative Modeling of Turbulence

We present a mathematically well founded approach for the synthetic modeling of turbulent flows using generative adversarial networks (GAN). Based on the analysis of chaotic, deterministic systems in terms of ergodicity, we outline a mathematical proof that GAN can actually learn to sample state snapshots form the invariant measure of the chaotic system. Based on this analysis, we study a hierarchy of chaotic systems starting with the Lorenz attractor and then carry on to the modeling of turbulent flows with GAN. As training data, we use fields of velocity fluctuations obtained from large eddy simulations (LES). Two architectures are investigated in detail: we use a deep, convolutional GAN (DCGAN) to synthesise the turbulent flow around a cylinder. We furthermore simulate the flow around a low pressure turbine stator using the pix2pixHD architecture for a conditional DCGAN being conditioned on the position of a rotating wake in front of the stator. The settings of adversarial training and the effects of using specific GAN architectures are explained. We thereby show that GAN are efficient in simulating turbulence in technically challenging flow problems on the basis of a moderate amount of training date. GAN training and inference times significantly fall short when compared with classical numerical methods, in particular LES, while still providing turbulent flows in high resolution.