Aircraft design requires a multitude of aerodynamic data and providing this solely based on high-quality methods such as computational fluid dynamics is prohibitive from a cost and time point of view. Deep learning methods have been proposed as surrogate models to predict aerodynamic quantities, showing great potential at significantly reduced cost. However, most approaches rely on a structured grid or are tested only for two-dimensional airfoil cases with a few thousand nodes. During aircraft programs, unstructured grids with millions of nodes are routinely used to model industrial-relevant complex physical systems. Hence, further investigation is required to study the applicability and extension of deep learning methods to industrial cases. In this paper, we use a graph neural network approach applicable to unstructured grids and extend it for the task of predicting surface pressure distributions for complex cases involving several hundreds of thousand of nodes. We compare this approach with proper orthogonal decomposition combined with an interpolation technique and with two other deep learning approaches, namely, a coordinate-based multilayer perceptron for pointwise predictions and its extension using surface normals as additional inputs. Results are first presented for a two-dimensional airfoil case and then for the NASA Common Research Model transport aircraft with an underlying mesh consisting of around $500,000$ surface points. The deep learning methods demonstrate in transonic flows the ability to capture shock location and strength more accurately. Furthermore, the proposed graph-based approach with the addition of more geometric information such as connectivity and surface normals seems to provide an additional boost in performance over the coordinate-based multilayer perceptron yielding more realistic pressure distributions.

飞机设计需要大量的空气动力学数据，并且从成本和时间的角度来看，仅基于计算流体动力学等高质量方法来提供这些数据是令人望而却步的。深度学习方法已被提议作为预测空气动力学量的替代模型，在显着降低成本的情况下显示出巨大的潜力。然而，大多数方法都依赖于结构化网格，或者仅针对具有几千个节点的二维机翼案例进行测试。在飞机项目中，通常使用具有数百万个节点的非结构化网格来模拟与工业相关的复杂物理系统。因此，需要进一步调查研究深度学习方法在工业案例中的适用性和扩展性。在本文中，我们使用适用于非结构化网格的图神经网络方法，并将其扩展到预测涉及数十万个节点的复杂情况的表面压力分布的任务。我们将这种方法与适当的正交分解与插值技术相结合，并与其他两种深度学习方法进行比较，即用于逐点预测的基于坐标的多层感知器及其使用表面法线作为附加输入的扩展。结果首先针对二维机翼案例呈现，然后针对 NASA 通用研究模型运输机呈现，其底层网格由周围组成 我们将这种方法与适当的正交分解与插值技术相结合，并与其他两种深度学习方法进行比较，即用于逐点预测的基于坐标的多层感知器及其使用表面法线作为附加输入的扩展。结果首先针对二维机翼案例呈现，然后针对 NASA 通用研究模型运输机呈现，其底层网格由周围组成 我们将这种方法与适当的正交分解与插值技术相结合，并与其他两种深度学习方法进行比较，即用于逐点预测的基于坐标的多层感知器及其使用表面法线作为附加输入的扩展。结果首先针对二维机翼案例呈现，然后针对 NASA 通用研究模型运输机呈现，其底层网格由周围组成$500,000$表面点。深度学习方法在跨音速流中展示了更准确地捕获冲击位置和强度的能力。此外，所提出的基于图形的方法添加了更多的几何信息，例如连通性和表面法线，似乎比基于坐标的多层感知器提供了额外的性能提升，从而产生更逼真的压力分布。