DTE AICCOMAS 2025

Extracting Large-scale Coherent Structures from Turbulent Flow by Combining Dynamic Mode Decomposition and β-Variational Autoencoders

  • Halder, Rakesh (Barcelona Supercomputing Center)
  • Eiximeno, Benet (Barcelona Supercomputing Center)
  • Lehmkuhl, Oriol (Barcelona Supercomputing Center)

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The use of dimensionality reduction techniques in computational fluid dynamics (CFD) has become widespread to decompose flows into a small number of interpretable modes. This allows for building reduced-order models (ROMs) [1], which are low-dimensional surrogate models used to offer accurate approximations of the full-order CFD model at a drastically lower cost. Two popular dimensionality reduction methods used to build ROMs for CFD are the proper orthogonal decomposition (POD) [2] and dynamic mode decomposition (DMD) [3]. While both are linear subspace methods, DMD is particularly useful for the analysis of transient and highly turbulent flows, as it decomposes the flow into spatio-temporal modes with prescribed frequencies and growth/decay rates. This allows for the extraction of large-scale coherent structures from large eddy simulation (LES) or direct numerical simulation (DNS) datasets while filtering small-scale chaotic turbulent fluctuations, which are problematic for building ROMs due to their highly transient and unpredictable behavior, making tasks such as time-series prediction unfeasible. However, as DMD is a linear method, it often requires a prohibitively large number of modes to build accurate ROMs. More recently, convolutional autoencoders [4], a type of artificial neural network, have been used in ROMs to provide a nonlinear mapping between an adequately low-dimensional latent space and the full-order model, although this approach suffers from a lack of interpretability. To address this issue, β-variational autoencoders (β-VAEs) have been implemented [5] to extract interpretable nonlinear modes from CFD data while using a small number of modes. In this work, we propose using DMD as a data pre-processing tool to filter out small-scale turbulent fluctuations from LES datasets before using β-VAEs to extract a small number of interpretable nonlinear modes that can be used to reconstruct the large-scale coherent behavior of turbulent flows and build accurate ROMs. By filtering out chaotic turbulent fluctuations, the evolution of the latent variables are well-structured for time-series prediction while retaining the large-scale properties of the flow. The proposed method is tested on a combination of LES datasets of flow over a Windsor body at different yaw angles simulated using SOD2D [6], A GPU-enabled spectral finite elements CFD code.