Machine learning algorithms for fluid mechanics

Abstract

Neural networks have become increasingly popular in the field of fluid dynamics due to their ability to model complex, high-dimensional flow phenomena. Their flexibility in approximating continuous functions without any preconceived notion of functional form makes them a suitable tool for studying fluid dynamics. The main uses of neural networks in fluid dynamics include turbulence modelling, flow control, prediction of flow fields, and accelerating high-fidelity simulations. This thesis focuses on the latter two applications of neural networks.

First, the application of a convolutional neural network (CNN) to accelerate the solution of the Poisson equation step in the pressure projection method for incompressible fluid flows is investigated. The CNN learns to approximate the Poisson equation solution at a lower computational cost than traditional iterative solvers, enabling faster simulations of fluid flows. Results show that the CNN approach is accurate and efficient, achieving significant speedup in the Taylor-Green Vortex problem.

Next, predicting flow fields past arbitrarily-shaped bluff bodies from point sensor and plane velocity measurements using neural networks is focused on. A novel conformal-mapping-aided method is devised to embed geometry invariance for the outputs of the neural networks, which is shown to be critical for achieving good performance for flow datasets incorporating a diverse range of geometries. Results show that the proposed methods can accurately predict the flow field, demonstrating excellent agreement with simulation data. Moreover, the flow field predictions can be used to accurately predict lift and drag coefficients, making these methods useful for optimizing the shape of bluff bodies for specific applications.