Efficient Projection-Based Reduced-Order Modeling for Computational Fluid Dynamics via Multifidelity Basis Construction

Abstract

Projection-based reduced-order models (PROMs) accelerate computational fluid dynamics simulations, but generating high-fidelity (HF) training snapshots remains expensive. We present a multifidelity methodology that reduces offline basis-construction costs by combining a small HF database with low-fidelity (LF) solutions. The method accommodates discrepancies in physical models and spatial discretizations. Parameter-matched HF and aligned LF snapshots define a correction basis. At new parameters, LF predictions are corrected by minimizing the HF residual over an affine trial space, with selective Reynolds-averaged Navier-Stokes (RANS) smoothing. Accepted snapshots enrich the training database and update the correction basis. The resulting basis is compatible with conventional projection methods, including least-squares Petrov-Galerkin projection. For steady flow over a NACA0012 airfoil, using fine-grid RANS and coarse-grid Euler models, four HF snapshots and 36 LF-derived snapshots reduce snapshot-generation cost by a factor of 7.8. At basis dimension 40, mean lift, drag, and lift-to-drag ratio errors are 1.1%, 3.6%, and 3.9%, and the mean relative skin-friction error is approximately 5%, compared with 0.18%, 2.9%, 2.8%, and 4% for an HF-only PROM. Errors are evaluated against fully converged HF solutions on a test set emphasizing shock-containing flows. Increasing the initial HF snapshot count raises cost without monotonically improving accuracy. Among the tested multifidelity configurations, ten initial HF snapshots give the lowest aerodynamic errors at dimension 40; increasing the count to twelve worsens all three. The results demonstrate reduced snapshot-generation costs while retaining compatibility with established PROM formulations.