University Of Tehran Press Journal of Algorithms and Computation 2476-2776 Articles in Press 2026 04 15 Predictive Modeling of Fluid Dynamics using Graph Neural Networks: A Benchmark Evaluation on Exact Navier-Stokes Solutions 106551 10.22059/jac.2026.412728.1256 EN Asef Afsahi School of Engineering Science, College of Engineering, University of Tehran, Tehran, Iran Journal Article 2026 03 11 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.