Turbulence

Pure mathematics

Reynolds number

Field (mathematics)

Economics

Computer science

Physics

Mathematics

Flow (mathematics)

Cylinder

Conservation law

Wake

Mathematical analysis

Artificial intelligence

Geometry

Momentum (technical analysis)

Deep learning

Finance

Artificial neural network

Mechanics

Convolutional neural network

Adversarial system

Journal of Fluid Mechanics

Unsteady flow fields over a circular cylinder are used for training and then prediction using four different deep learning networks: generative adversarial networks with and without consideration of conservation laws; and convolutional neural networks with and without consideration of conservation laws. Flow fields at future occasions are predicted based on information on flow fields at previous occasions. Predictions of deep learning networks are made for flow fields at Reynolds numbers that were not used during training. Physical loss functions are proposed to explicitly provide information on conservation of mass and momentum to deep learning networks. An adversarial training is applied to extract features of flow dynamics in an unsupervised manner. Effects of the proposed physical loss functions and adversarial training on predicted results are analysed. Captured and missed flow physics from predictions are also analysed. Predicted flow fields using deep learning networks are in good agreement with flow fields computed by numerical simulations.

Data-driven prediction of unsteady flow over a circular cylinder using deep learning