A novel method of low-dimensional representation for temporal behavior of flow fields using deep autoencoder

A method capable of comparing and analyzing the spatio-temporal structures of unsteady flow fields has not yet been established. Temporal analyses of unsteady flow fields are often done after the data of the fields are reduced to low-dimensional quantities such as forces acting on objects. Such an approach is disadvantageous as information about the flow field is lost. There are several data-driven low-dimensional representation methods that preserve the information of spatial structure; however, their use is limited due to their linearity. In this paper, we propose a method for analyzing the time series data of unsteady flow fields. We firstly propose a data-driven nonlinear low-dimensional representation method for unsteady flow fields that preserves its spatial structure; this method uses a convolutional autoencoder, which is a deep learning technique. In our proposed method, the spatio-temporal structure can be represented as a trajectory in a low-dimensional space using the visualization technique originally proposed for dynamic networks. We applied the proposed method to unsteady flows around a two-dimensional airfoil and demonstrated that it could briefly represents the changes in the spatial structure of the unsteady flow field over time. This method was demonstrated to also be able to visualize changes in the quasi-periodic state of the flow when the angle of attack of the airfoil was changed. Furthermore, we demonstrated that this method is able to compare flow fields that are constructed using different conditions such as different Reynolds numbers and angles of attack.