Simulation of unsteady flow around bluff bodies using knowledge-enhanced convolutional neural network

The unsteady flow with massive separation poses challenges to accurately and efficiently simulate wind effects on civil structures, especially in the search for optimal aerodynamic shapes during the preliminary design stage. To this end, an encoding-transformation-decoding convolutional neural network (CNN) architecture is developed in this study to take the pixelated geometry of a bluff body as the input and instantly output the corresponding unsteady aerodynamic flow (represented by a sequence of consecutive flow snapshots). First, a unique (shared) encoding part is used to extract the low-resolution features from the structural shapes and associated initial flow conditions. Then, the transformation part consecutively maps the encoded features (originated from encoder) to a prediction of next flow snapshot in high-level feature space while the separate decoding part unravels the abstract features (from corresponding transformer) to pixelated velocity and pressure fields. Prior domain knowledge is leveraged at various stages of machine learning pipeline to enhance the learning efficiency and accuracy of the proposed convolutional encoder-transformer-decoder. Specifically, the qualitative knowledge that the flow fields vary on a very small length scale within the boundary layer is used to empirically design a nonuniform grid for CNN image inputs and outputs. In addition, the equation-free quantitative knowledge learned from previous flow snapshot (i.e., high-level features from the transformer and filters in the decoder) is employed in the learning of current flow snapshot as the CNN initial conditions based on transfer learning technique. Furthermore, the equation-based quantitative knowledge of both mass and momentum conservation laws is utilized to augment the CNN loss function. Numerical examples suggest good performance of the proposed knowledge-enhanced CNN for unsteady flow simulation of bridge decks. Effects of these three types of knowledge on the performance of the convolutional encoder-transformer-decoder are also examined to highlight their high efficacy to facilitate the training efficiency and simulation accuracy.