Graph neural network modeling of free-surface flows in non-Newtonian power-law fluids

In this study, we propose a graph neural network (GNN)-based numerical model for efficiently predicting the flow behavior of non-Newtonian fluids with free surface dynamics. Conventional numerical approaches, such as the finite element method, often suffer from computational inefficiency and convergence issues when simulating non-Newtonian fluids whose viscosity varies dynamically with the local shear rate. To overcome these limitations, particle-based methods such as smoothed particle hydrodynamics (SPH) have been developed, offering greater robustness for complex free-surface flows. However, SPH remains constrained by hardware-dependent scalability, as even parallelization techniques using graphics processing units (GPUs) are limited by system-specific constraints and computational cost. To address these challenges, we extend the SPH framework by introducing a graph neural network (GNN)-based model, which achieves efficient, data-driven prediction of non-Newtonian fluid dynamics. In this work, we focus on power-law fluids, one of the simplest models of non-Newtonian behavior. Our GNN model is trained on SPH simulation data, learning the effects of particle accelerations in the presence of SPH particle interactions based on the fluid's power-law model parameters. We demonstrate that the GNN significantly accelerates computations while maintaining reliable accuracy in benchmark tests, including dam-break and droplet impact simulations. Quantitative evaluations demonstrate that the GNN reduces computation time by approximately 30% compared to conventional SPH simulations, while maintaining comparable accuracy across benchmark problems such as dam-break and droplet impact cases. The results highlight the potential of GNN-based frameworks for simulating non-Newtonian free-surface flows, paving the way for future data-driven non-Newtonian fluid modeling.