Prediction of surface pressure distributions of non-parametric airfoils using geometric deep learning methods

Computational Fluid Dynamics (CFD) simulations are one of the cornerstones in providing aerodynamic data required for aircraft design and optimization. However, using these simulations extensively is limited by their high computational demands. Therefore, it is essential to create efficient data-driven surrogate models for CFD solvers. In many practical scenarios an explicit unifying parameterization of aircraft configurations is not available. This highlights the need for models that operate directly on raw geometric representations. Geometric deep learning has emerged as a class of deep learning techniques capable of operating on such data, enabling predictive modeling without the need of an explicit parameterization. In this paper, we extend and investigate two geometric deep learning approaches for the prediction of surface pressure distributions of non-parametric airfoils. These methods are Bi-Stride Multi-Scale Graph Neural Network and Implicit Neural Representation of the signed distance function coupled with a Multi-Layer Perceptron. To enhance both of these methods, we propose the use of area-weighted loss functions to better account for variations in node density in the meshes. Moreover, in the formulation of the graph neural network we introduce edge completion at the coarsest level to account for interactions between different connected components, such as flap, main element and slat in a 3-element high-lift airfoil. These methods are compared to the well-established method Proper Orthogonal Decomposition coupled with Interpolation, which is allowed to use an explicit parameterization and serves as a baseline. Two high-fidelity datasets with CFD simulations solving the Reynold-Averaged Navier Stokes equations are created. The first one features a varied set of single-element airfoils with simulations in the subsonic and transonic regime, while the second one features high-lift multi-element airfoils with a variable flap position with simulations in the subsonic regime. The results show that both geometric deep learning approaches outperform the established baseline across various data regimes. These approaches can capture shocks and flow separation with more accuracy. The use of an area-weighted loss function enhances area-weighted performance and leads to faster performance gains in the early training epochs. These findings support the potential of geometric deep learning methods as data-driven surrogates of CFD solvers for varying geometries.