Date of Award
2022
Publication Type
Thesis
Degree Name
M.A.Sc.
Keywords
Graph neural networks, Machine learning, Computational Fluid Dynamics problems
Supervisor
R.Barron
Supervisor
R.Balachandar
Rights
info:eu-repo/semantics/openAccess
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Abstract
Graph neural networks provide a framework for learning on unstructured data, such as meshes used for solving Computational Fluid Dynamics problems. However, current applications do not take advantage of known physical laws in the training process. This thesis addresses that gap by introducing graph convolution layers to calculate the divergence and gradient operator. The convolutions are valid on any 2D or 3D graph storing spatial data, and can be added to existing graph architectures. Using these convolutions, the residuals of the conservation of mass and momentum equations are computed and minimized through a physics-aware loss function. Two classical fluid dynamics problems are studied: the 2D flow past a NACA 0012 airfoil, and the 3D flow in the wake of an Ahmed body. In each study, a baseline and physics-aware Graph U-Net model is trained to predict the pressure and velocity fields at varying operating conditions. Despite achieving similar mean squared error, the physics-aware model has an order of magnitude smaller error in the residuals of the conservation equations. Further, the physics-aware model predicts flow fields with smaller error in the gradient, making them appear smoother. The same methodology can be applied to any general graph learning problem which requires minimizing a quantity composed from divergence or gradient operations.
Recommended Citation
Raad, Emanuel, "Surrogate Modeling of Fluid Flows with Physics-Aware Graph Neural Networks" (2022). Electronic Theses and Dissertations. 9032.
https://scholar.uwindsor.ca/etd/9032