Evaluation of reduced-order models for pulsatile flow over a two-dimensional backward-facing step

Reduced-order modeling (ROM) enables efficient analysis of unsteady separated flows, but most formulations are assessed under steady or purely periodic forcing and do not reflect physiologically realistic pulsatility. Here, two-dimensional backward-facing step simulations are performed under sinusoidal inflow and a physiologically inspired pulsatile waveform with intermittent bursts, including a sinusoidal control case matched to the pulsatile inflow in both frequency and amplitude. Proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) are applied to velocity and out-of-plane vorticity fields, and reconstruction accuracy and compactness are quantified, including DMD-I and DMD-E mode-ranking variants. In all cases, coherent vortices form downstream of the step due to separated shear-layer roll-up consistent with Kelvin–Helmholtz shear-layer dynamics. The forcing frequency and its harmonics are present in the modal spectra for all cases; however, cycle-to-cycle instantaneous fields are not identical, indicating organized dynamics without strict phase locking. Under pulsatile inflow, vortex interactions intensify through co-rotation, deformation, and merging, and an additional low-frequency component near 0.29 Hz appears across higher modes, consistent with slow modulation associated with waveform intermittency. POD provides the most robust balance of compression and accuracy, whereas DMD performs well for sinusoidal inflow but exhibits practical error plateaus around 10% under pulsatile forcing despite improved ranking strategies. Overall, waveform shape and intermittency increase effective flow dimensionality and challenge global linear ROMs, highlighting the need for localized or time-windowed reduction strategies to enable mechanistic insight in pulsatile biomedical flows and cardiovascular applications.