A SUPG-Stabilized Reduced-Order Model with Difference Quotients for the Navier–Stokes Equations
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Reduced-order modeling of incompressible Navier–Stokes flows in convection-dominated regimes remains challenging due to stability and accuracy limitations of standard Galerkin approaches. In this work, we propose a Streamline-Upwind Petrov–Galerkin reduced-order model (SUPG-ROM) combined with a difference-quotient time discretization. The proposed method extends SUPG stabilization to the reduced setting and provides a robust and efficient framework for reduced-order simulation at moderate to high Reynolds numbers. A proper orthogonal decomposition (POD) basis is employed to construct the reduced space, while the difference-quotient formulation allows for an efficient treatment of the nonlinear convective term. Stability properties and a priori error estimates of the proposed method are investigated. Numerical experiments demonstrate that the SUPG-ROM significantly improves robustness and accuracy compared to standard Galerkin ROMs, while retaining the computational efficiency characteristic of reduced-order models. The results highlight the potential of stabilized reduced-order methods for reliable simulation of convection-dominated incompressible flows.
