Modeling-based hyper-reduction of multidimensional computational fluid dynamics data: Application to ship airwake data

This investigation focuses on hyper-reduction of computational fluid dynamics (CFD) data that depends on a series of coordinates (space, time) and/or parameters (e.g., flow speed, flow direction) into a series of basis vectors and generalized coordinates occupying much less storage. The data, first mapped on a multidimensional rectangular grid, can be "shuffled" into two-dimensional arrays on which proper orthogonal decomposition (POD) is applied. This shuffling can be done in various ways but also repeated, leading to a succession of POD-based data reductions, termed "progressive proper orthogonal decomposition" (p-POD). The possibility of downsampling is also explored using autoregressive (AR) modeling. These techniques are demonstrated on ship airwake data from two ships that depend on the three spatial coordinates, time, the wind-over-deck angle, and wind speed. The p-POD approach leads to a data reduction by a factor of 265 while maintaining99% of the energy. The AR-based approach allows a data reduction by a factor of 12.5 on its own and 297 with the p-POD. The stated reduction factors are computed with respect to the data on the Cartesian extraction grid. If the mapping on this grid is also included, the data reduction achieved from the CFD mesh maybe even much larger.