| Summary: | Computational fluid dynamics (CFD) simulation is an irreplaceable modelling step in many engineering designs, but it is often computationally expensive to execute numerically. Data-driven methods such as using neural networks to simulate the solving of partial differential equations such as Navier-Stokes solving have increasingly emerged. However, current methods still face challenges, often overlooking certain potential architectural or engineering advantages that can improve the model’s applicability in industrial settings.
For one, data scarcity limits the practicality of such methods in industrial settings. While the use of prior physical knowledge to alleviate data dependence has been proposed, the transition from case-specific feed-forward networks to more general convolutional networks has called for data-saving methods that are more applicable to the new architectures. Secondly, current graph neural network (GNN)-based methods inherit the weakness of traditional numerical simulators by having very limited information about internal objects and the surrounding environment in their input nodes. Also, they ignore cell characteristics of the mesh such as cell volume, face surface area, and face centroid, which are not included in their message-passing operations. Finally, prior studies generally exclude complex geometries, despite them being crucial for many modern engineering design processes.
To address these challenges, this thesis presents a combined work in three parts. The first addresses the growing needs of convolutional architectures by extending the methods of previous studies to convolutional network types, more practical for CFD tasks. It adapts schemes formerly used on multilayer perceptrons (MLPs), specifically physics-guided losses, in a convolutional neural network (CNN) setting to reduce data demands. It also presents the use of data augmentation to serve this purpose. Additionally, it will introduce two improved geometric representations for graph convolutional network (GCN) settings, and generalise the method of finite differences to use samples on an irregular mesh.
The second proposes improved global geometric representations while utilising finite volume mesh properties to enhance convolutions and enable them to more closely model traditional methods without adopting their weaknesses. It takes greater advantage of mesh features by further developing the two geometric representations from part I into the Shortest Vector (SV) and Directional Integrated Distance (DID), which provide global geometry perspective to each input node, and remove the need to collect this information through message-passing. It also introduces the use of Finite Volume Features (FVF) in graph convolutions as node and edge attributes, enabling its message-passing operations to adjust to different nodes. Additionally, it extends the use of residual training to improve flow field prediction for a GNN scenario with immersed object, when low resolution data is available.
Lastly, the third part aims to enhance flow predictions around complex geometries, which may often be deconstructed into multiple, simple bodies, by leveraging existing data on these single geometry flow fields. Using a case study of tandem-airfoils, it will introduce a method extending the DID representation for multiple objects, a residual pre-training scheme based on the freestream condition as a physical prior, and a residual training scheme utilising smooth combinations of single airfoil flow fields, also capitalising on the freestream condition. Additionally, to optimise memory usage during training in large domains and improve prediction performance, it demonstrates decomposing simulation domains into smaller sub-domains, each processed by a different network.
This work demonstrates that the combined use of data augmentation and physical losses can improve prediction accuracy of a CNN by 51% while reducing training data to 25%. Also, experimental results on two datasets with five different state-of-the-art GNN methods for CFD indicate that the SV, DID, FVF and low resolution-based residual training can effectively reduce the predictive error of current GNN-based methods by as much as 41%. Finally, extensive experiments on four newly provided tandem-airfoil datasets, comprising of over 2000 fluid simulations, demonstrate that our proposed method and techniques to leverage single-airfoil data can effectively enhance tandem-airfoil prediction accuracy by up to 96%.
In conclusion, this thesis advances the combined field of AI and physics by extending the data saving work of previous studies to more practical network types for CFD tasks, proposing the use of mesh properties to enhance input features and graph convolutions, and finally by developing schemes to leverage available simple-geometry data to facilitate the solving of complex cases. It conducted extensive experiments across various flow scenarios, data schemes, and architectures to show that the methods successfully reduce data dependence and predictive error of the models. These advancements have broad applications in industries reliant on fluid dynamics simulations, offering enhanced accuracy and efficiency
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