Geometry-Conditioned Graph Neural Networks for Spray Prediction

Accurately predicting multiphase flows in complex geometries is critical for the design and optimisation of various systems. For example, sprays for drug delivery, agrochemical spraying or industrial processing is affected by small change in the upstream nozzle design, altering breakup dynamics and droplet size distributions. Resolving these effects requires solving complex equations on fine meshes, making iterative design, optimisation and control computationally prohibitive. We develop a geometry-conditioned Graph Neural Network (GNN) framework as a surrogate model to overcome standard MeshGraphNet limitations [1]: poor geometric sensitivity and local message passing constraints. We apply this to 2D nozzle atomisation cases simulated with the Basilisk solver using adaptive octree refinement. Nozzle geometries are parameterised via NURBS curves: p₁∈[0.05,0.2] and p₂∈[−0.2,−0.05], and width w∈[0.5,1.5] over axial length x∈[0,0.7]. Simulation track liquid injection using Volume of Fluids (VOF) model, resulting in velocity, pressure, volume fraction data every 0.1 seconds used for training GNN model. We implement three geometry-aware conditioning strategies: (1) Latent shape embeddings encode nozzle boundary coordinates into compact vectors using MLPs, which are concatenated with node features to broadcast geometric context across the graph. (2) Surface-to-volume conditioning processes boundary nodes separately with attention-based aggregation, pooling them into a global supernode representation that is injected into the flow domain [2]. (3) Graph Attention Networks replace standard aggregation with attention mechanisms, dynamically weighting neighbouring nodes and focusing on regions where geometry strongly influences flow. Our framework achieves low mean squared error on 10 unseen nozzle geometries and provides a 100× speedup over CFD. This combination of speed and geometric sensitivity advances surrogate modelling for geometry-dependent fluid dynamic systems.

[1] T. Pfaff et al. ICLR, 2021.

[2] J. Helwig et al. arXiv, Dec. 2024.