Spatially compressed spectral proper orthogonal decomposition.

Area of Science:

• Fluid Dynamics
• Computational Mechanics
• Data Science

Background:

• Recovering coherent flow structures from sparse data is challenging.
• Traditional spectral proper orthogonal decomposition (SPOD) methods face high computational costs and memory limitations.
• Incomplete data sampling hinders accurate flow diagnostics.

Purpose of the Study:

• To propose a spatially compressed SPOD (scSPOD) method for reconstructing global flow modes from nonuniform datasets.
• To overcome the limitations of traditional SPOD in terms of computational cost and data requirements.
• To enable accurate flow diagnostics from sparse or incomplete flow field data.

Main Methods:

• Integration of spectral translation assumption, clustering, compressed sensing, and optimization.
• Direct recovery of SPOD modes from spatial subsets while preserving spectral features.
• Validation using direct numerical simulation of flow past a cylinder and large eddy simulation of tip leakage flow.

Main Results:

• scSPOD accurately identifies spatial flow mode structures across the domain.
• High quantitative reconstruction accuracy for low-rank, first-order modes.
• Demonstrated significant data reduction (e.g., <10% data for high accuracy) with a spectral concentration metric threshold (θ≥0.75).

Conclusions:

• The scSPOD method is feasible and effective for reconstructing flow modes from sparse data.
• scSPOD offers a low-cost, high-fidelity solution for flow diagnostics in complex fluid systems.
• The method shows significant potential for applications where data acquisition is limited or computationally expensive.