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• A novel and robust model based on the idea of GAN, BiFlowAN, is proposed to precisely predict the flow field. • A general deep TL framework is designed as an effective way to increase the generalization of the BiFlowAN on a limited flow field dataset. • The proposed methods can be used as a deep learning framework to cope with the difficulties in learning from small-scale data in airfoil design, lightening the burden of expensive data. The flow field under different flow conditions contains abundant structure information and is of great significance for aerodynamic analysis and aircraft design. Deep learning (DL) techniques have received great interest for flow field prediction due to their high capability of capturing structure characteristics in recent years. However, successful training of DL models usually requires a large amount of data, whose acquisition is prohibitively expensive and learning from insufficient flow field data still remains underexplored for DL models. This paper proposes a general deep transfer learning framework to predict the flow field of airfoils with insufficient data by transferring knowledge learned from other conditions with a large amount of data. A novel and robust flow field prediction model based on the idea of generative adversarial networks, BiFlowAN, is first proposed to precisely predict the flow field over an airfoil under a condition with sufficient data. Transfer learning technique is then introduced to transfer the learned knowledge of BiFlowAN to a new model, BiFlowAN-TL, for improving the generalization of the model under another condition with a small-scale dataset. Compared with other alternatives, the flow field predictions of supercritical airfoils show that BiFlowAN achieves higher accuracy and generalization in predicting the flow fields with sufficient data and BiFlowAN-TL significantly improves the prediction accuracy than BiFlowAN on the small-scale dataset, exhibiting the potential applicability of the proposed methods to solve the problem of rapidly and accurately evaluating aerodynamic performance with insufficient data. [ABSTRACT FROM AUTHOR]

• Taking the place of the time-consuming CFD simulation and the expensive wind-tunnel experiments in flow field prediction. • The method is based on the generative adversarial networks with the deep learning framework. • The method is validated on the supercritical airfoils for efficiently and accurately evaluating the flow field. The efficient and accurate access to the aerodynamic performance is important for the design and optimization of supercritical airfoils. The aerodynamic performance is usually obtained by using computational fluid dynamics (CFD) methods or wind-tunnel experiments. But the computations of CFD are very time intensive and expensive, and the prior knowledge in wind-tunnel experiments plays a decisive role in engineering. Though many surrogate methods were proposed to alleviate the costs of these traditional approaches, most of them can only calculate the low-dimensional aerodynamic performance, and is not able to provide the accurate prediction of transonic flow fields for supercritical airfoils. Since the flow fields are equipped with its own discipline as a physical system in fluid dynamics, it is therefore possible to learn this discipline via data-driven machine learning approaches. Deep learning is witness to expansive growth into diverse applications due to its immense ability to extract essential features from complicated physical systems. Generative adversarial networks (GANs) as a recent popular method in deep leaning are capable of efficiently capturing the distribution of training data. In this work, we proposed a surrogate model, ffsGAN, which leverage the property of GANs combined with convolution neural networks (CNNs) to directly establish a one-to-one mapping from a parameterized supercritical airfoil to its corresponding transonic flow field profile over the parametric space. Compared with the most existing surrogate models, the ffsGAN is superior in efficiently and accurately predicting the high-dimensional flow field rather than the low-dimensional aerodynamic characteristics. The ffsGAN method is first trained using 500 airfoils that sampled based on RAE2822. The flow fields are then predicted for unseen airfoils to evaluate the generalization of the model in terms of prediction accuracy. An investigation of the effects of various hyper-parameters in the network architectures and loss functions is performed. The experimental results show that ffsGAN is a promising tool for rapid evaluation of detailed aerodynamic performance. The elaborate flow field predicted by ffsGAN is possible to be considered in airfoil design to further improve the design and optimization quality in the future. [ABSTRACT FROM AUTHOR]

Mesh quality is critical for the numerical accuracy of CFD (Computational Fluid Dynamics). Although various techniques have been developed to improve mesh applicability to complex flows, r-adaptive methods have received far too little attention. This paper introduces an r-adaptive algorithm based on the self-organizing maps (SOM) of Kohonen and applies it to unsteady CFD applications using the Discontinuous Galerkin (DG) method. Inspired by the properties of the DG method, the numerical discontinuity over the element interface is quantified as an adaptation indicator. The method requires only one adaptation, followed by solution projection onto the new mesh to save computational costs in unsteady cases. A significant advantage of this method is its higher efficiency without solving complex equations during the adaptation. The performance of the developed mesh adaptation algorithm is tested on the steady laminar viscous flow past a circular cylinder at R e = 40 and the unsteady laminar viscous flow past a circular cylinder at R e = 100 and two circular cylinders in a side-by-side arrangement at R e = 200. Significant improvements in flow contours and coefficients are obtained after adaptation. • The SOM method is adopted for unstructured mesh r-adaptation with the DG method. • The method avoids auxiliary mesh PDEs in traditional r-adaptation methods. • A one-time adaptation in unsteady cases saves computational costs. • The improvement of results in CFD applications validates method performance. [ABSTRACT FROM AUTHOR]

As more powerful computing hardware enables higher resolution simulations, a fast and flexible mesh optimization method is becoming increasingly indispensable for Computational Fluid Dynamics (CFD), which unfortunately remains a bottleneck in the current CFD workflows. In this paper, a novel mesh optimization method based on an improved self-organizing map (SOM) neural network is proposed to improve the accuracy and efficiency of numerical simulation while maintaining constant computational cost. During an improved competitive learning procedure in SOM, the node distribution with constant connectivity rapidly matches the characteristics of the flow field, which is predicted by a Multilayer Perceptron (MLP). Based on the local element volume and flow solution variations, annealing schemes for self-adaptation of important SOM parameters are designed to ensure the convergence of the proposed algorithm. Specially, a feasible region constraint and a smoothing constraint are embedded into the node movement to avoid mesh tangling and excessive mesh skewness, and make the transition between nodes gradual. The proposed approach is applicable to various types of meshes and is easy to implement without code intrusiveness. Comparative results on benchmark examples and typical CFD examples demonstrate that the proposed method attributes to both the improvement in the computational accuracy and efficiency. It exhibits the potential to be a flexible and promising tool for rapid mesh optimization in CFD and other engineering fields. • A novel self-organizing mesh optimization method based entirely on neural networks. • Improved learning mechanism avoids mesh tangling and excessive mesh skewness problem. • The method enhances SOM based on mesh optimization and avoids auxiliary mesh PDEs. • Benchmark results show method flexibility in optimizing various geometric meshes. • Various CFD examples validate method performance in diverse flow conditions. [ABSTRACT FROM AUTHOR]