Physics-Informed Neural Solver for High-Speed Flow Over Airfoils

While there is significant research interest in physics-informed deep learning, it remains challenging to model high-speed flow over airfoils accurately and efficiently, particularly in the presence of flow discontinuities such as shock waves in the transonic regime. In this article, we introduce a novel deep learning method, the Neural Euler Solver, to tackle this problem. In contrast to the original physics-informed neural network (PINN) approach that attempts to learn flow variables at each point in a physical domain, our method constructs an irregular computational mesh transformed from a point cloud in the physical domain and trains a multilayered-perceptron architecture to fit the 2-D Euler Equations over the constructed mesh. As training proceeds, the computational mesh is self-refined over higher-error region to achieve numerical efficiency as well as accuracy to capture shock waves. The results are analyzed and compared against the surface pressure measurement for the RAE2822 section in transonic flow conditions.