Efficient Reduced Order Modeling of Large Data Sets Obtained from CFD Simulations

Abstract

The ever-increasing computational power has shifted direct numerical simulations towards higher Reynolds numbers and large eddy simulations towards industrially-relevant flow scales. However, this increase in both temporal and spatial resolution has severely increased the computational cost of model order reduction techniques. Reducing the full data set to a smaller subset in order to perform reduced-order modeling (ROM) may be an interesting method to keep the computational effort reasonable. Moreover, non-tomographic particle image velocimetry measurements obtain a 2D data set of a 3D flow field and an interesting research question would be to quantify the difference between this 2D ROM compared to the 3D ROM of the full flow field. To provide an answer to both issues, the aim of this study was to test a new method for obtaining POD basis functions from a small subset of data initially and using them afterwards in the ROM of either the complete data set or the reduced data set. Hence, no new method of ROM is presented, but we demonstrate a procedure to significantly reduce the computational effort required for the ROM of very large data sets and a quantification of the error introduced by reducing the size of those data sets. The method applies eigenvalue decomposition on a small subset of data extracted from a full 3D simulation and the obtained temporal coefficients are projected back on the 3D velocity fields to obtain the 3D spatial modes. To test the method, an annular jet was chosen as a flow topology due to its simple geometry and the rich dynamical content of its flow field. First, a smaller data set is extracted from the 2D cross-sectional planes and ROM is performed on that data set. Secondly, the full 3D spatial structures are reconstructed by projecting the temporal coefficients back on the 3D velocity fields and the 2D spatial structures by projecting the temporal coefficients back on the 2D velocity fields. It is shown that two perpendicular lateral planes are sufficient to capture the relevant large-scale structures. As such, the total processing time can be reduced by a factor of 136 and up to 22 times less RAM is needed to complete the ROM processing.