Solving nonlinear subsonic compressible flow in infinite domain via multi-stage neural networks

TL;DR

This paper introduces a multi-stage physics-informed neural network framework to accurately solve nonlinear subsonic compressible flow in infinite domains, overcoming traditional domain truncation and linearization limitations with high precision results.

Contribution

It presents a novel multi-stage PINN approach with coordinate transformation and asymptotic constraints to solve nonlinear compressible flow in unbounded domains, improving accuracy over traditional methods.

Findings

Achieves near machine precision accuracy in flow simulations.

Quantifies errors from domain truncation and linearization.

Demonstrates robustness for high Mach number flows.

Abstract

In aerodynamics, accurately modeling subsonic compressible flow over airfoils is critical for aircraft design. However, solving the governing nonlinear perturbation velocity potential equation presents computational challenges. Traditional approaches often rely on linearized equations or finite, truncated domains, which introduce non-negligible errors and limit applicability in real-world scenarios. In this study, we propose a novel framework utilizing Physics-Informed Neural Networks (PINNs) to solve the full nonlinear compressible potential equation in an unbounded (infinite) domain. We address the unbounded-domain and convergence challenges inherent in standard PINNs by incorporating a coordinate transformation and embedding physical asymptotic constraints directly into the network architecture. Furthermore, we employ a Multi-Stage PINN (MS-PINN) approach to iteratively minimize residuals, achieving solution accuracy approaching machine precision. We validate this framework by simulating flow over circular and elliptical geometries, comparing our results against traditional finite-domain and linearized solutions. Our findings quantify the noticeable discrepancies introduced by domain truncation and linearization, particularly at higher Mach numbers, and demonstrate that this new framework is a robust, high-fidelity tool for computational fluid dynamics.