Use of Physics-Informed Neural Networks to compute velocity and pressure fields around an airfoil in transonic flow

Resumo

This work presents a novel application of Physics-Informed Neural Networks (PINNs) to simulate transonic (Mach 0.8–1.2) flow around an airfoil. The transonic regime features coexisting subsonic and supersonic zones, which generate shock waves and possibly boundary layer separation. This makes it a highly nonlinear and challenging flow condition for conventional Computational Fluid Dynamics (CFD) methods. Traditional finite-volume and finite-element solvers often require extremely fine shock-aligned meshes and significant computational cost to resolve transonic shocks and complex wave interactions. In contrast, our approach employs a PINN that embeds the compressible Navier–Stokes and continuity equations directly into the network’s loss function, enabling the flow field solution without a predefined mesh. PINN was implemented using DeepXDE library in a two-dimensional wind tunnel domain, with no-slip boundary conditions on the airfoil surface and far-field conditions on the outer boundaries. The mesh-free formulation avoids the grid generation burden and inherently sidesteps mesh-dependency in the solution, while working with residual-based adaptive collocation points sampling in the domain. We assess how well the PINN captures key transonic flow features—particularly the shock wave pattern and pressure field—by comparing its predictions to a high-fidelity finite-volume CFD solution. Applying PINNs to shock-dominated transonic flows remains largely uncharted, and previous attempts have struggled to resolve normal shock waves without special numerical treatments. To address this challenge by drawing on recent PINN advances, such as adaptive loss weighting and adding localized artificial viscosity at the shock was done. These help stabilize training and improve convergence for shock resolution. Preliminary results show that the PINN reproduces the flowfield accurately, capturing the shock location and overall pressure distribution in close agreement with the CFD benchmark. This study demonstrates the potential of PINNs as a promising, mesh-independent solver for complex aerodynamic simulations. It may offer advantages in regimes where traditional solvers encounter prohibitive meshing requirements or stability issues.