Low-dimensional approach for reconstruction of airfoil data via compressive sensing

Compressive sensing is used to compress and reconstruct a turbulent-flow particle image velocimetry database over a NACA 4412 airfoil. The spatial velocity data at a given time are sufficiently sparse in the discrete cosine transform basis, and the feasibility of compressive sensing for velocity data reconstruction is demonstrated. Application of the proper orthogonal decomposition/principal component analysis on the dataset works better than the compressive-sensing-based reconstruction approach with discrete cosine transform as the basis in terms of the reconstruction error, although the performance gap between the two schemes is not significant. Using the proper orthogonal decomposition/principal component analysis as the sparsifying basis, compressive-sensing-based velocity reconstruction is implemented, which outperformed discrete cosine transform. Compressive sensing preprocessing (filtering) with discrete cosine transform as the basis is applied to a reduced number of particle image velocimetry snapshots (to mimic conditions with limited time support) before application of proper orthogonal decomposition/principal component analysis. Using only 20 particle image velocimetry snapshots with a 10% compressive sensing compression, it is found that the proper orthogonal decomposition/principal component analysis modes 1 and 2 of the streamwise velocity component are very close to those extracted from full time support data (1000 particle image velocimetry snapshots in this case). Results demonstrate the feasibility and utility of a compressive-sensing-based approach for reconstruction of compressed or limited time support particle image velocimetry flow data.