A hybrid method combining ISPH with graph neural network for simulating free-surface flows

The incompressible Smoothed Particle Hydrodynamics (ISPH) is a popular Lagrangian Particle method. In the conventional ISPH method for simulating free-surface flows, the pressure-projection phase, which solves the pressure Poisson's equation (PPE), is the most time-consuming. In this paper, we propose a novel hybrid method by combining the graph neural network (GNN) with the ISPH for modelling the free-surface flows. In the new hybrid method, the graph neural network (GNN) is employed to replace solving the PPE for pressure in the conventional ISPH. To the best of knowledge of the authors, this is the first attempt to combine the GNN with ISPH model in a Lagrangian formulation. The performance of the hybrid method will be evaluated by comparing its results with experimental data, analytical solution or numerical results from other methods for three benchmark test cases: dam breaking, sloshing wave and solitary wave propagation. In addition, the potential of generalization of the hybrid method will be studied by applying it with the GNN model trained on data for relatively simple cases to simulate more complex cases. It will be demonstrated that the hybrid method does not only give satisfactory results, but also shows good potential of generalization. In addition, the new method will be demonstrated to require the computation time which can be 80 times less than the conventional ISPH for estimating pressure for cases with a large number of particles that is usually needed in the practical free-surface flows simulation using ISPH.