Solving compressible Navier-Stokes equations using the feature-enhanced neural network

TL;DR

This paper extends the feature-enhanced neural network (FENN) to effectively solve compressible Navier-Stokes equations, demonstrating its superiority over existing methods in handling complex compressible viscous flow problems.

Contribution

The study introduces the first successful application of a PINN-like method to forward and parametric problems involving compressible viscous flows.

Findings

FENN outperforms existing methods in compressible flow scenarios.

FENN accurately solves multiple flow problems with different conditions.

The approach effectively handles parametric variations such as angle of attack.

Abstract

Physics-informed neural networks (PINNs) have shown remarkable prospects in solving partial differential equations (PDEs) involving fluid mechanics. However, the method has so far succeeded only in inviscid flows and incompressible viscous flows, while the solution of compressible viscous flows still faces significant challenges. In previous work, we proposed a feature-enhanced neural network (FENN), which enhances the ability of PINNs to approximate flows by introducing beneficial features into the network inputs, thereby improving the performance in solving PDEs. In this study, we extend FENN to compressible viscous flows, which are governed by the compressible Navier-Stokes equations including the continuity, momentum, and energy equations. By solving four forward problems under different flow conditions and geometries together with a parametric problem involving angle of attack, we validate the effectiveness of FENN. In contrast, existing advanced methods that are well established for inviscid flows and incompressible viscous flows fail in this scenario. To the best of our knowledge, this is the first time that a PINN-like method has successfully solved forward and parametric problems involving compressible viscous flows.