Hybrid Reduced-Order Models for Turbulent Flows Using Recurrent Neural Architectures

Proper-orthogonal decomposition (POD) based reduced-order models (ROM) of structurally dominant fluid flow can support a wide range of engineering applications. Yet, although they perform well for unsteady laminar flows, their straightforward extension to turbulent flows fails to capture the effects of small scale eddies and often leads to divergent solutions. Several approaches to mimic nonlinear closure terms modeling techniques within ROM frameworks have been employed to include the effect of higher modes that are often neglected. Recent success of neural network based models show promising results in modeling the effects of turbulence. In this study, we augment POD-ROM with a recurrent neural network (RNN) to develop ROM for turbulent flows. We simulate a three dimensional flow past a circular cylinder at Reynolds number of 1000. We first compute the POD modes and project the Navier-Stokes equations onto the limited number of modes in a Galerkin approach to develop a conventional ROM and LES-inspired ROM for comparison. We then develop a hybrid model by integrating the output of Galerkin projection ROM and long short-term memory (LSTM) RNN and term it as a physics-guided machine learning (PGML) model. The novelty of this study is to introduce a hybrid model that integrates LES inspired ROM and RNN to achieve more accurate and reliable predictions of turbulent flows. The results demonstrate that PGML for higher temporal coefficients outperforms the conventional and LES-inspired ROM.