Higher-order dynamic mode decomposition on-the-fly: A low-order algorithm for complex fluid flows

• Published in: Journal of computational physics Vol. 475; p. 111849
• Main Authors: Amor, Christian, Schlatter, Philipp, Vinuesa, Ricardo, Le Clainche, Soledad
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 15.02.2023
• Subjects: Data-driven methods; Higher-order dynamic mode decomposition; Machine learning; Synthetic jets; Three-dimensional cylinder; Turbulent flows; Synthetic jets; Turbulent flows; Machine learning; Data-driven methods; Higher-order dynamic mode decomposition; Three-dimensional cylinder
• ISSN: 0021-9991; 1090-2716; 1090-2716
• DOI: 10.1016/j.jcp.2022.111849

This article presents a new method to identify the main patterns describing the flow motion in complex flows. The algorithm is an extension of the higher-order dynamic mode decomposition (HODMD), which compresses the snapshots from the analysed database and progressively updates new compressed snapshots on-the-fly, so it is denoted as HODMD on-the-fly (HODMD-of). This algorithm can be applied in parallel to the numerical simulations (or experiments), and it exhibits two main advantages over offline algorithms: (i) it automatically selects on-the-fly the number of necessary snapshots from the database to identify the relevant dynamics; and (ii) it can be used from the beginning of a numerical simulation (or experiment), since it uses a sliding-window to automatically select, also on-the-fly, the suitable interval to perform the data analysis, i.e. it automatically identifies and discards the transient dynamics. The HODMD-of algorithm is suitable to build reduced order models, which have a much lower computational cost than the original simulation. The performance of the method has been tested in three different cases: the axi-symmetric synthetic jet, the three-dimensional wake of a circular cylinder and the turbulent wake behind a wall-mounted square cylinder. The obtained speed-up factors are around 7 with respect to HODMD; this value depends on the simulation and the configuration of the hyperparameters. HODMD-of also provides a significant reduction of the memory requirements, between 40−80% amongst the two- and three-dimensional cases studied in this paper. •Novel algorithm based on HODMD that combines rank reduction strategies with the on-the-fly methodology.•The algorithm automatically selects the optimal time interval to extract the main flow patterns.•Significant reduction of the memory requirements and speed-up related with standard HODMD.•Suitable to build reduced order models.