Physics-Informed Neural Networks for Transonic Flows around an Airfoil

Abstract

Physics-informed neural networks have gained popularity as a deep-learning based parametric partial differential equation solver. Especially for engineering applications, this approach is promising because a single neural network could substitute many classical simulations in multi-query scenarios. Only recently, researchers have successfully solved subsonic flows around airfoils with physics-informed neural networks by utilizing mesh transformations to precondition the training. However, compressible flows in the transonic regime could not be accurately approximated due to shock waves resulting in local discontinuities. In this article, we propose techniques to successfully approximate solutions of the compressible Euler equations for sub- and transonic flows with physics-informed neural networks. Inspired by classical numerical algorithms for solving conservation laws, the presented method locally introduces artificial dissipation to stabilize shock waves. We compare different viscosity variants such as scalar- and matrix-valued artificial viscosity, and validate the method at transonic flow conditions for an airfoil, obtaining good agreement with finite-volume simulations. Finally, the suitability for parametric problems is showcased by approximating transonic solutions at varying angles of attack with a single network. The presented work enables the application of parametric neural network based solvers to a new class of industrially relevant flow conditions in aerodynamics and beyond.