2026 Cengizci SUPG High Speed Flow

This study presents a hybrid computational framework for simulating non-reacting inviscid high-speed flows of nitrogen gas (N2) around a circular cylinder. Owing to the strongly convection-dominated nature of the compressible Euler equations, the compressible-flow streamline-upwind/Petrov–Galerkin (SUPG) formulation is combined with the YZ shock-capturing technique to stabilize the finite element discretization in the presence of strong discontinuities. Building upon the stabilized solution, a physics-informed neural network (PINN) is employed as a post-processing correction stage (PINN-Augmented SUPG with Shock-Capturing—PASSC). The network, anchored to the finite element solution through a shock-weighted data-consistency loss, significantly enhances the numerical representation of shocks by reducing localized discretization-induced oscillations while preserving the agreement of the stabilized solution with reference quantities. Two-dimensional simulations confirm that, across the considered Mach-number range, the corrections remain closely aligned with the stabilized solution, inducing only small absolute changes in the detected shock position and maintaining stagnation-pressure ratios within approximately 2.5% of the corresponding Rayleigh pitot values. This innovative approach ensures both stability and accurate feature representation in high-speed flow simulations.