SPOD Mode Interpolation with Frequency Alignment on the Grassmannian Manifold

The accuracy and robustness of reduced-order models (ROMs) often suffer from parameter variations, such as Mach number or angle of attack for fluid mechanics problems. Specifically, the reduced order basis obtained via spectral proper orthogonal decomposition (SPOD) suffers from reduced robustness due to frequency drifting of the dominant modes. Although the Grassmannian manifold interpolation method has proven successful for POD-based ROMs, the SPOD-based ROMs introduce an additional spectral component that challenges this interpolation method. This paper presents an interpolation method for the dominant SPOD modes on the Grassmannian manifold based on frequency alignment, reducing the SPOD mode interpolation problem back to the standard subspace interpolation problem. This method preserves mode orthogonality and ensures frequency consistency during interpolation via resampling the time series data. This technique is demonstrated with a vortex shedding problem behind a NACA 0012 airfoil and benchmarked against the direct interpolation method, showing improved interpolation results for the SPOD basis when the angle of attack is varied.