A physics-informed SUPG-stabilized finite element framework with shock-capturing for simulating inviscid high-speed flows around a cylinder

[2608.14883] A physics-informed SUPG-stabilized finite element framework with shock-capturing for simulating inviscid high-speed flows around a cylinder Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Physics > Fluid Dynamics arXiv:2608.14883 (physics) [Submitted on 14 Aug 2026] Title: A physics-informed SUPG-stabilized finite element framework with shock-capturing for simulating inviscid high-speed flows around a cylinder Authors: Süleyman Cengizci , Ömür Uğur View a PDF of the paper titled A physics-informed SUPG-stabilized finite element framework with shock-capturing for simulating inviscid high-speed flows around a cylinder, by S\"uleyman Cengizci and 1 other authors View PDF HTML (experimental) Abstract: This study presents a hybrid computational framework for simulating non-reacting inviscid high-speed flows of nitrogen gas (N$_2$) 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$\beta$ 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 (\underline{P}INN-\underline{A}ugmented \underline{S}UPG with \underline{S}hock-\underline{C}apturing---PASSC). The network is anchored to the finite element solution through a shock-weighted data-consistency loss, while the governing equations are enforced in a conservative space--time control-volume form supplemented by macroscopic conservation windows, an entropy-admissibility penalty, and the boundary conditions of the underlying problem. Two-dimensional simulations are performed for free-stream Mach numbers ranging from $2.0$ to $12.0$, and the results are assessed against analytical normal-shock and stagnation relations, the semi-empirical Billig correlation, and reference solutions from the literature. The correction is designed to improve the numerical representation of shocks by reducing localized discretization-induced oscillations and mesh-scale serrations while preserving the agreement of the stabilized solution with the analytical and semi-empirical reference quantities. Subjects: Fluid Dynamics (physics.flu-dyn) ; Numerical Analysis (math.NA) Cite as: arXiv:2608.14883 [physics.flu-dyn] (or arXiv:2608.14883v1 [physics.flu-dyn] for this version) https://doi.org/10.48550/arXiv.2608.14883 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Suleyman Cengizci Ph.D. [ view email ] [v1] Fri, 14 Aug 2026 20:46:18 UTC (29,340 KB) Full-text links: Access Paper: View a PDF of the paper titled A physics-informed SUPG-stabilized finite element framework with shock-capturing for simulating inviscid high-speed flows around a cylinder, by S\"uleyman Cengizci and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: physics.flu-dyn < prev | next > new | recent | 2026-08 Change to browse by: cs cs.NA math math.NA physics References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... 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