arXiv subjects

Simon Wassing

Publications and source records attributed to Simon Wassing.

2 recordsLinked to original sources

arXiv2024

Physics-Informed Neural Networks for Transonic Flows around an Airfoil

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.

physics.flu-dyn↗

arXiv2023

Physics-Informed Neural Networks for Parametric Compressible Euler Equations

The numerical approximation of solutions to the compressible Euler and Navier-Stokes equations is a crucial but challenging task with relevance in various fields of science and engineering. Recently, methods from deep learning have been successfully employed for solving partial differential equations by incorporating the equations into a loss function that is minimized during the training of a neural network. This approach yields a so-called physics-informed neural network. It is not based upon classical discretizations, such as finite-volume or finite-element schemes, and can even address parametric problems in a straightforward manner. This has raised the question, whether physics-informed neural networks may be a viable alternative to conventional methods for computational fluid dynamics. In this article we introduce an adaptive artificial viscosity reduction procedure for physics-informed neural networks enabling approximate parametric solutions for forward problems governed by the stationary two-dimensional Euler equations in sub- and supersonic conditions. To the best of our knowledge, this is the first time that the concept of artificial viscosity in physics-informed neural networks is successfully applied to a complex system of conservation laws in more than one dimension. Moreover, we highlight the unique ability of this method to solve forward problems in a continuous parameter space. The presented methodology takes the next step of bringing physics-informed neural networks closer towards realistic compressible flow applications.

physics.flu-dyn↗