Traditional Computational Fluid Dynamics (CFD) methods demand significant computational resources. Graph Network-based Simulators (GNS) have emerged as powerful surrogates, modeling complex physical systems by learning spatial-temporal interactions. In this paper, we evaluate a GNS model on nine exact analytical solutions of the Navier-Stokes equations, comprising four 2D and five 3D flows. By training the network to predict fluid particle evolution using localized message passing, we bypass Eulerian grid constraints and simulate fluid topologies in a Lagrangian framework. Our results demonstrate that the GNS approach achieves highly accurate rollouts (MSE $< 0.01$) while successfully capturing complex structures like viscous vortex decay. The model achieves its lowest rollout Mean Total MSE of $3.7852 \times 10^{-3}$ on the Lamb-Oseen 2D model, highlighting the generalizability and precision of deep graph architectures for exact fluid mechanics phenomena.
Afsahi,A . (2026). Predictive Modeling of Fluid Dynamics using Graph Neural Networks: A Benchmark Evaluation on Exact Navier-Stokes Solutions. Journal of Algorithms and Computation, 58(1), 1-12. doi: 10.22059/jac.2026.412728.1256
MLA
Afsahi,A . "Predictive Modeling of Fluid Dynamics using Graph Neural Networks: A Benchmark Evaluation on Exact Navier-Stokes Solutions", Journal of Algorithms and Computation, 58, 1, 2026, 1-12. doi: 10.22059/jac.2026.412728.1256
HARVARD
Afsahi A. (2026). 'Predictive Modeling of Fluid Dynamics using Graph Neural Networks: A Benchmark Evaluation on Exact Navier-Stokes Solutions', Journal of Algorithms and Computation, 58(1), pp. 1-12. doi: 10.22059/jac.2026.412728.1256
CHICAGO
A Afsahi, "Predictive Modeling of Fluid Dynamics using Graph Neural Networks: A Benchmark Evaluation on Exact Navier-Stokes Solutions," Journal of Algorithms and Computation, 58 1 (2026): 1-12, doi: 10.22059/jac.2026.412728.1256
VANCOUVER
Afsahi A. Predictive Modeling of Fluid Dynamics using Graph Neural Networks: A Benchmark Evaluation on Exact Navier-Stokes Solutions. J. Algo. Comp.. 2026;58(1):1-12. doi: 10.22059/jac.2026.412728.1256
