Artificial neural network-based reduced-order modeling for turbulent wake of a finite wall-mounted square cylinder

TL;DR

This paper develops an LSTM and BLSTM neural network-based reduced-order model using POD for turbulent wake flow around a wall-mounted square cylinder, enabling efficient flow prediction without solving Navier-Stokes equations.

Contribution

It introduces a transfer learning approach to improve neural network predictions and demonstrates BLSTM's superiority over LSTM for this application.

Findings

BLSTM outperforms LSTM in prediction accuracy.

Transfer learning significantly enhances model training.

Prediction error increases with longer time windows.

Abstract

This study presents an artificial neural network and proper orthogonal decomposition (POD)-based reduced-order model (ROM) of turbulent flow around a finite wall-mounted square cylinder. The proposed model is suitable for turbulent wake control applications because it can predict the dynamics of the main features of the flow field without computing Navier-Stokes equations. Long short-term memory neural network (LSTM NN) and bidirectional long short-term memory neural network (BLSTM NN) are used to predict the temporal evolution of the POD time coefficients at different planes along the height of the obstacle. The improved delayed detached-eddy simulation (IDDES) is performed to generate the training datasets. Transfer learning (TL) approach is utilized in the training process by using the weights of the LSTM/BLSTM NN that are used to predict the POD time coefficients of the planes at lower elevations to initialize the weights of the networks at higher elevations along the height of the obstacle. The use of TL results in a remarkable improvement in the capability of the LSTM/BLSTM NN prediction compared with the one when the network is initialized with random weights. BLSTM NN shows better results compared with LSTM NN in terms of training and prediction error, indicating that the BLSTM-POD model is more suitable to be used as a ROM for predicting the turbulent wake. Furthermore, the temporal behavior of the time coefficients is carefully examined using the phase space plots and Poincar$\acute{e}$ sections. The results of using different lengths of the prediction time window showed that the prediction error of the POD time coefficients increases as the prediction time window increases and the error increasing rate decreases with the ranking of the POD time coefficients.