Post-processing subsonic flows using physics-informed neural networks

Abstract

The conservation equations describe the physics of flow and sound and one is possibly interested in what are vortical and compressible flow structures. For instance, the compressible flow velocity is analyzed to study acoustic waves. Another reason might be computing the compressible source structures of the aeroacoustic wave equation based on Pierce's operator. This work shows how neural networks can leverage physical knowledge to perform the inverse task of post-processing a compressible subsonic flow field into subparts by Helmholtz's decomposition. The Helmholtz decomposition of a velocity field into vortical and compressible structures is implemented using a finite element framework and physics-informed neural networks. These two implementations of Helmholtz's decomposition are compared. A verification example demonstrates the applicability of the methods by comparing the results to the analytical solution. The physics-informed neural network formulation results on the verification example outline promising directions for further applications to post-process compressible flow fields and the development of acoustic boundaries in fluid dynamics.