Incremental singular value decomposition based model order reduction of scale resolving fluid dynamic simulations

Abstract

Scale-resolving flow simulations often feature several million [thousand] spatial [temporal] discrete degrees of freedom. When storing or re-using these data, e.g., to subsequently train some sort of data-based surrogate or compute consistent adjoint flow solutions, a brute-force storage approach is practically impossible. Therefore, – mandatory incremental – Reduced Order Modeling (ROM) approaches are an attractive alternative since only a specific time horizon is effectively stored, usually aligned with the amount of fast available, e.g., Random Access Memory (RAM). This bunched flow solution is then used to enhance the already computed ROM so that the allocated memory can be released and the procedure repeats.

This paper utilizes an incremental truncated Singular Value Decomposition (itSVD) procedure to compress flow data resulting from scale-resolving flow simulations. To this end, two scenarios are considered, referring to an academic Large Eddy Simulation (LES) around a circular cylinder at ${\mathrm{Re}}_D=1.4\cdot 10^5$ as well as an industrial case that employs a hybrid filtered/averaged Detached Eddy Simulation (DES) on the flow around the superstructure of a full-scale feeder ship at ${\mathrm{Re}}_L=5.0\cdot 10^8$.

The paper’s central focus is on an aspect of severe practical relevance: how much information of the computed scale-resolving solution should be used by the ROM, i.e., how much redundancy occurs in the resolved turbulent fluctuations that favors ROM. In the course of the tSVD employed, this goes hand in hand with the question of ”how many singular values of the flow-solution-snapshot-matrix should be neglected (or considered)” – without (a) re-running the simulation several times in a try-and-error procedure and (b) still obtain compressed results below the model and discretization error. An adaptive strategy is utilized, which features two comparatively simple adjusting screws, for which appropriate decision support is provided. Next to a general feasibility study, reported results show the capability to obtain a fully adaptive data reduction of $O\left(95\right)$ percent via a computational overhead of $O\left(10\right)$ percent with a mean accuracy of reconstructed local and global flow data of $O(10^{-3}-10^{-1})$ percent.