Graph-Based Learning of Free Surface Dynamics in Generalized Newtonian Fluids using Smoothed Particle Hydrodynamics

In this study, we propose a graph neural network (GNN) model for efficiently predicting the flow behavior of non-Newtonian fluids with free surface dynamics. The numerical analysis of non-Newtonian fluids presents significant challenges, as traditional algorithms designed for Newtonian fluids with constant viscosity often struggle to converge when applied to non-Newtonian cases, where rheological properties vary dynamically with flow conditions. Among these, power-law fluids exhibit viscosity that decreases exponentially as the shear rate increases, making numerical simulations particularly difficult. The complexity further escalates in free surface flow scenarios, where computational challenges intensify. In such cases, particle-based methods like smoothed particle hydrodynamics (SPH) provide advantages over traditional grid-based techniques, such as the finite element method (FEM). Building on this approach, we introduce a novel GNN-based numerical model to enhance the computational efficiency of non-Newtonian power-law fluid flow simulations. Our model is trained on SPH simulation data, learning the effects of particle accelerations in the presence of SPH interactions based on the fluid's power-law parameters. The GNN significantly accelerates computations while maintaining reliable accuracy in benchmark tests, including dam-break and droplet impact simulations. The results underscore the potential of GNN-based simulation frameworks for efficiently modeling non-Newtonian fluid behavior, paving the way for future advancements in data-driven fluid simulations.