Solving nonlinear subsonic compressible flow in infinite domain via multi-stage neural networks
This provides a robust, high-fidelity tool for computational fluid dynamics in aircraft design, addressing errors from domain truncation and linearization, though it is incremental as it builds on existing PINN methods.
The study tackled solving the nonlinear compressible potential equation for subsonic flow in infinite domains, a challenge in aerodynamics, by proposing a multi-stage PINN framework with coordinate transformations and physical constraints, achieving solution accuracy near machine precision and quantifying errors from traditional methods.
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.