The dynamics of fluid flows vary significantly across operating conditions, and capturing these parameter‑dependent changes remains a central challenge in reduced‑order modelling. Parametric Dynamic Mode Decomposition (pDMD), as implemented in PyDMD, provides a data‑driven framework for this task, yet its accuracy and stability degrade in non‑linear or noisy regimes. This work develops and validates an improved pDMD algorithm. The method is first assessed on the laminar cylinder‑flow example, which also served as the reference case for evaluating the pDMD implementation in PyDMD, and is subsequently extended to transonic airfoil stall conditions with varying angle of attack. Results show that the proposed method, based on the mode‑realigned pointwise interpolation (MRPWI) framework, resolves the structural deficiencies of PyDMD's approach, producing smooth spectral variation across parameters, accurate mode interpolation, and stable long‑term reconstructions even at unseen operating points. In addition, the method demonstrates robustness to noise, maintaining consistent spectral alignment and reconstruction quality across increasing noise levels. For the airfoil case, the method successfully captures the
dominant buffet mode, its harmonics, and the associated shock‑oscillation dynamics despite the limited number of training parameters. These findings demonstrate that enforcing spectral consistency and interpolating aligned DMD quantities provides a reliable foundation for parametric reduced‑order modelling of non‑linear flows, offering a promising basis for future extensions to multi‑parameter applications.
Publication Date: 2026-05-28