📝 Abstract:
Accurate calculation of physical quantities such as surface pressure, wall shear stress, and temperature is crucial in aerodynamic design processes. Data-Driven Deep Learning methods have emerged as powerful surrogate models that accelerate design cycles. Meshes employed in Computational Fluid Dynamics (CFD) simulations possess an inherently geometric and relational structure, where nodes carry spatial coordinates and edges encode physical adjacency on the discretized domain. Geometric Deep Learning (GDL) framework encompasses architectures that operate on such non-Euclidean domains, making it suitable for mesh-based CFD surrogate modeling. In this thesis, the performance of GDL-based methods in predicting flow-induced physical quantities on various aerodynamic surfaces is investigated. To evaluate the generalization capability of the models, comprehensive 2D and 3D datasets with diverse flow conditions were generated. The MeshGraphNet architecture which has proven successful in learning mesh-based simulations is taken as a baseline and the effects of structural and geometric improvements applied to enhance the model's expressive power were examined. To explore relational paradigms beyond standard graph neural networks (GNN), the performance of the Transolver model, which adapts the Transformer architecture to physical simulations through geometry-aware attention, was evaluated. Finally, a hybrid model architecture was developed to combine the GNN's ability to learn local interactions with the Transformer's capacity to comprehend the global context. The models were comparatively analyzed in terms of node-based error metrics, aerodynamic coefficient correlations, and training throughput. The results showed that GDL-based methods learn aerodynamic surface distributions with high accuracy, and the proposed hybrid architecture and model enhancements significantly reduced prediction error, particularly on 3D datasets containing high node counts.